Antimatter

These are various rocket engines trying to harness the awesome might of antimatter. While the fuel is about as potent as you can get, trying to actually use the stuff has many problems.

Generally your spacecraft has metric tons of propellant, and a few micrograms antimatter fuel. The exceptions are the antimatter beam-core and positron ablative engines.

Nanograms of antimatter fuel are injected into some matter. The energy release is used to heat the propellant, which flies out the exhaust nozzle to create thrust.

Antimatter rockets have analogous exhaust velocity limits to nuclear thermal rockets. The higher the engine heat, the higher the exhaust velocity, which is a good thing. Unfortunately once the heat level reaches the liquefaction point, the engine melts. Which is a bad thing. This limits the maximum exhaust velocity.

ANTIMATTER ROCKET EQUATION

(ed note: according to Adam Cowl, this equation applies when drives are power limited, based on the endurance of the engine rather than the energy of the fuel. I am not sure which engines beside antimatter qualify. Adam Cowl says the maximum mass ratio would be ~4.42, while the article below imples it will be ~4.9)

To those rocket engineers inured to the inevitable rise in vehicle mass ratio with increasing mission difficulty, antimatter rockets provide relief. The mass ratio of an antimatter rocket for any mission is always less than 4.9:1 [Shepherd, 1952], and cost-optimized mass ratios are as low as 2:1 [Forward, 1985]. In an antimatter rocket, the source of the propulsion energy is separate from the reaction fluid. Thus, the rocket's total initial mass consists of the vehicle's empty mass, the reaction fluid's mass, and the energy source's mass, half of which is the mass of the antimatter. According to the standard rocket equation, the mass ratio is now (assuming mr » me)

where

Δv = change in vehicle velocity (m/s)
ve = rocket exhaust velocity (m/s)
mi = initial mass of the vehicle (kg)
mf = final mass of the vehicle (kg)
mv = empty mass of the vehicle (kg)
mr = mass of the reaction fluid (kg)
me = mass of the energy source (kg)

The kinetic energy (K.E.) in the expellant at exhaust velocity (ve) comes from converting the fuel's rest-mass energy into thrust with an energy efficiency (ηe):

where

K.E. = kinetic energy (kg·m2/s2)
c = speed of light (3 × 108 m/s)

Solving Eq. (11.14) for the reaction mass (mr), substituting into Eq. (11.13), and solving for the energy source's mass (me) produces

We can find the minimum antimatter required to do a mission with a given Δv. We set the derivative of Eq. (11.15) with respect to the exhaust velocity ve equal to zero, and solving (numerically) for the exhaust velocity:

Substituting Eq. (11.16) into Eq. (11.13), we find that, because the optimal exhaust velocity is proportional to the mission Δv, the vehicle mass ratio is a constant:

The reaction mass (mr) is 3.9 times the vehicle mass (mv), while the antimatter fuel mass is negligible. Amazingly enough, this constant mass ratio is independent of the efficiency (ηe) with which the antimatter energy is converted into kinetic energy of the exhaust. (If the antimatter engine has low efficiency, we will need more antimatter to heat the reaction mass to the best exhaust velocity. The amount of reaction mass needed remains constant.) If we can develop antimatter engines that can handle jets with the very high exhaust velocities Eq. (11.16) implies, this constant mass ratio holds for all conceivable missions in the solar system. It starts to deviate significantly only for interstellar missions in which the mission Δv approaches the speed of light [Cassenti, 1984].

(ed note: Translation: to compensate for poor efficiency of antimatter energy converted into kinetic energy you do not need more reaction mass, you just need a few more milligrams of antimatter. Assuming the engine can resist being vaporized by the higher temperatures that come with the higher exhaust velocities.)

We can obtain the amount of antimatter needed for a specific mission by substituting Eq. (11.16) into Eq. (11.15) to get the mass of the energy source (me). The antimatter needed is just half of this mass. We find it to be a function of the square of the mission velocity (Δv) (essentially the mission energy), the empty vehicle's mass (mv), and the conversion efficiency (ηe):

(ed note: so the above equation is the important one, to figure how much antimatter fuel your spacecraft requires. Offhand I'd say the difference between antimatter solid core, beam core, and plasma core is the conversion efficiency (ηe) and the upper limit on antimatter per second fuel consumption set by the heat resistance of the engine)

The amount of antimatter calculated from Eq. (11.18) is typically measured in milligrams. Thus, no matter what the mission, the vehicle uses 3.9 tons of reaction mass for every ton of vehicle and an insignificant amount (by mass, not cost) of antimatter. Depending on the relative cost of antimatter and reaction mass after they have been boosted into space, missions trying to lower costs may use more antimatter than that given by Eq. (11.18) to heat the reaction mass to a higher exhaust velocity. If so, they would need less reaction mass to reach the same mission velocity. Such cost-optimized vehicles could have mass ratios closer to 2 than 4.9 [Forward, 1985].

The low mass ratio of antimatter rockets enables missions which are impossible using any other propulsion technique. For example, a reusable antimatter-powered vehicle using a single-stage-to-orbit has been designed [Pecchioli, 1988] with a dry mass of 11.3 tons, payload of 2.2 tons, and 22.5 tons of propellant, for a lift-off mass of 36 tons (mass ratio 2.7:1). This vehicle can put 2.2 tons of payload into GEO and bring back a similar 2.2 tons while using 10 milligrams of antimatter. Moving 5 tons of payload from low-Earth orbit to low Martian orbit with an 18-ton vehicle (mass ratio 3.6:1) requires only 4 milligrams of antimatter.

Antimatter rockets are a form of nuclear rocket. Although they do not emit many neutrons, they do emit large numbers of gamma rays and so require precautions concerning proper shielding and stand-off distance.

[Forward, 1985] Forward, Robert L., Brice N. Cassenti, and David Miller. 1985. Cost Comparison of Chemical and Antihydrogen Propulsion Systems for High AV Missions. AIAA Paper 85-1455, AIAA/SAE/ASME/ASEE 21st Joint Propulsion Conference, 8-10 July 1985, Monterey, California.

[Pecchioli, 1988] Pecchioli, M. and G. Vulpetti. 1988. A Multi-Megawatt Antimatter Engine Design Concept for Earth-Space and Interplanetary Unmanned Flights. Paper 88-264 presented at the 39th Congress of the International Astronautical Federation, Bangalore, India 8-15 October 1988.

[Shepherd, 1952] Shepherd, L. R. 1952. Interstellar Flight. Journal of the British Interplanetary Society. 11:149-167.

Antimatter Energy

Most of this is from Antiproton Annihilation Propulsion by Robert Forward.

From a practical standpoint, the proton-antiproton annihilation reaction produces two things: high-energy pions with an average kinetic energy of 250 MeV, and high-energy gamma rays with an average energy of 200 MeV.

Electron-positron annihilation just produces propulsion-worthless gamma rays, so nobody uses it for rockets. Except for the stranger antimatter engine designs.

To use the energy for propulsion, you have to either somehow direct the gamma rays and pions to shoot out the exhaust nozzle to produce thrust, or you have to used them to heat up a propellant and direct the hot propellant out the exhaust nozzle. To keep the crew and the computers alive you have to shield them from both gamma rays and pions. As far as the crew is concerned both reaction products come under the heading of "deadly radiation."


Charged Pions

Since pions are particles (unlike gamma rays) enough shielding will stop them all. Given an absorbing propellant or radiation shield of a specific density you can figure the thickness that will stop all the pions. This is the pion's "range" through that material.

In table 7-2 the columns under the yellow bar show how many centimeters (the "range") of the given stopping material is required to absorb 100 MeV of pion energy. The two sets of orange bars is because while the range is relatively constant for all high energies, the range becomes dramatically less at the point where the pion energy drops below 100 MeV (the "last 100 MeV").

For example: if the stopping material is water, absorbing 100 Mev from a 300 MeV hihg-energy pion requires 50 centimeters. But you only need 27 centimeters of water to absorb 100 MeV from a 75 MeV pion.

Since hydrogen, helium, and nitrogen have regrettably low densities the reaction chamber will have to operate at high pressure to get the density up to useful levels. "Useful" is defined as when the interaction range is shorter than the pion's mean life range. The Space Shuttle engines operated at a pressure of 213 atmospheres, 300 is a bit excessive. So of the gases nitrogen might be preferrable, even though you can get better specific impulse out of propellants with lower molecular weight.

Using detailed calculations they didn't explain, the report said hydrogen at 300 atm was about 65% efficient at converting the pion energy into heated propellant, while nitrogen at 100 atm was more like 95%.

Using more calculations that were not explained figure 7-4 was produced. The curve is the relative intensity of a charged pion at a given kinetic energy in MeV. The 125 MeV pions are the most intense (there are more of them), the average energy is 250 MeV.

Mean Life is the lifespan (not half-life) of a pion at that energy in nanoseconds. The range of a pion at that energy can be measured on the RANGE scales below, traveling through vacuum, hydrogen (H2) propellant at 300 atm, nitrogen (N2) propellant at 100 atm, and tungsten radiation shielding.


Gamma Rays

Sadly gamma rays cannot be used to propel the rocket (well, actually there are a couple of strange designs that do use gammas), all they do is kill anything living and destroy electronic equipment. So you have to shield the crew and electronics with radiation shielding. This is one of the big drawbacks to antimatter rockets. Gamma-rays would be useful if you were using antimatter as some sort of weapon instead of propulsion. But I digress.

A small number of "prompt" gamma-rays are produced directly from the annihilation reaction. The prompt gammas have a whopping 938 MeV, but they only contribute about 0.5% of the total. Almost ignorable.

A much larger amount of "delayed" gamma-rays are produced by the neutral pions decaying 90 attoseconds after the antimatter reaction. The spectrum peaks at about 70 MeV and trails off for many hundreds of MeV, with an average of 200 MeV.

Radiation Shielding

Most of this is from Antiproton Annihilation Propulsion by Robert Forward.

As mentioned above, the antimatter reaction is basically spitting out charged pions and gamma rays. The pions can be absorbed by the propellant and their energy utilized. The gamma rays on the other hand are just an inconvenient blast of deadly radiation traveling in all directions. The only redeeming feature is gamma rays are not neutrons, so at least they don't infect the ship structure with neutron embrittlement and turn the ship radioactive with neutron activation.

Since gamma rays are rays, not particles, they have that pesky exponential attenuation with shielding. It is like Zemo's paradox of Achilles and the tortoise, making the radiation shielding thicker reduces the amount of gamma rays penetrating but no matter how thick it becomes the gamma leakage never quite goes to zero. Particle shielding on the other hand have a thickness where nothing penetrates.

Gamma rays with energies higher than 100 MeV have a "attenuation coefficient" of about 0.1 cm2/g. Since tungsten has a density of 19.3 g/cm3 a tungsten radiation shield would have an attuation factor of 1.93 cm-1. Table 7-3 gives the attunation for various thickness of tungsten radiation shields.

This tells us that a 2 centimeter thick shield would absorb 97.9% of the gamma rays. 2.1×10-2 = 0.021 = 2.1%. 100% - 2.1% = 97.9%.

The main things that have to be shielded are the crew, the electronics, the cryogenic tankage, and the magnetic coils if this particular antimatter engine utilzes coils.


The radiation flux will be pretty bad. As an example, a ten metric ton rocket accelerating at 1 m/s2 will need a thrust level of 10,000 Newtons. If it has a specific impulse of 2000 s it will have an exhaust velocity of 20,000 m/s. This means the thrust power is Fp = (F * Ve ) / 2 = 100,000,000 watts = 100 megawatts.

Well, actually the report says 200 megawatts so obviously I made a mistake somewhere.

Anyway the thrust power basically is the fraction of the antimatter annihilation energy that becomes charged pions. Since 0.5% of the annihilation energy becomes prompt gamma rays, and the rest becomes 1.5 neutral pions (who become delayed gamma rays) and 3 charged pions then:

Eγ = (Eπ± * 1.506) - Eπ±

where:

Eπ± = charged pion energy = thrust power
Eγ = gamma ray energy

So if the example rocket has 200 megawatts of thrust power, the gamma ray flux will be:

Eγ = (Eπ± * 1.506) - Eπ±

Eγ = (200 * 1.506) - 200

Eγ = 101.2 megawatts of lethal gamma rays


To shield the inanimate superconducting coils, table 7-3 tells us 10 centimeters of shield will give us an attenuation of 4.2×10-9, reducing the 101.2 megawatts down to 0.4 watts. The coil coolant systems should be able to handle that. The superconducting coils do not care about the biological dose since the coils are already dead.

But you do not get something for nothing. The 10 centimeters of coil shield prevent the radiation from hitting the coils but it does not make the radiation magically disappear. The coil shield will need a large heat radiator system capable of rejecting 101.2 megawatts of heat.


You will need more to shadow shield the living crew and sensitive electronics.

The report cites the American Institute of Physics handbook which mentions a 1 Curie source of gamma rays with an average energy of 100 MeV at a distance of 1 meter will expose you to 29 röntgen/hr (0.29 sievert per hour).

Our antimatter gamma rays have an average energy of twice that, 200 MeV not 100 MeV. So it becomes 58 röntgen/hr (0.58 sv/hour).

Let's assume the crew habitat module is 10 meters away from the engine instead of 1 meter. Radiation falls of according to the inverse square law. Inverse square of 10 times the distance is 1/102 or 1/100. So it becomes 58 / 100 = 0.58 röntgen/hr (0.0058 sv/hr).

That is the dose for a 1 Curie source. Our engine is much more radioactive than that.

Extrapolating further, a single 200 MeV gamma ray photon has 3.2×10-11 joules. This means a 101.2 megawatt source of 200 Mev gamma rays will produce 3×1018 gamma rays per second. This is equal to 8.5×107 Curies. Which is quite larger than 1 Curie.

1 Curie of 200 MeV gamma rays at a distance of 10 meters is 0.58 röntgen/hr. So 8.5×107 Curies will increase the dosage 8.5×107 times, to 4.9×107 röntgen/hr (490,000 sv/hr or 136 sv/second). This is very very bad since a mere 80 sieverts is enough to instantly put a person into a coma with certain death following in less than 24 hours. The poor crew will get that dose in about half a second. A shadow shield is indicated.

Looking at table 7-3 again, we see that 14 centimeters of tungsten has an attunation factor of 1.8×10-12. This will reduce the dose to 0.0000882 röntgen/hr (8.82×10-7 sv/hr) which the report describes as a reasonable dose for a space mission.

In the conceptual schematic, the reaction chamber is about 1 meter in diameter. The pressure walls have an equivalent thickness of 2 centimeters of tungsten, absorbing most of the gamma rays and coverting them into heat. The pressure walls are cooled by hydrogen flowing through channels in the wall. The hot hydrogen is sprayed as a film over the exhaust nozzle to protect it from the ultrahot hydrogen plasma blasting out from the antimatter reaction.

As per the calculations above, the superconducting coils are shielded with 10 centimeters of tungsten, with the thermal shields aimed at the antimatter annihilation point. 1 meter reaction chamber diameter plus 10 centimeters of shield makes the shield rings have a diameter of about 1.1 meter.

Also as per the calculations above, the personnel will be protected by a shadow shield 14 centimeters thick and 0.6 meters in diameter located 0.6 meters from the annihilation point. This will provide a 10 meter diameter shadow at a distance of 10 meters from the engine, for the habitat module and other ship parts to shelter in.

The reaction chamber is 2,200 kilograms, each thermal shield ring is 750 kilograms, and the shadow shield is 800 kilograms.

Solid Core

p-Nerva engine (NRX)
Thrust4.4×105 N
Thrust Power2.7 GW
Engine Mass11,000 kg
T/W4.1
T/W >1.0yes
Specific Impulse1,100 sec to
1,300 sec
Exhaust Velocity10,790 m/s to
12,750 m/s
Fuelantiprotons (p)
Fuel Mass Flow13 μg/sec
(1.3×10-8 kg/s)
PropellantLH2
Propellant
Mass Flow
40.7 kg/s
p-LH2 Mix1×10-6 kg p per
7,000 kg LH2
Borowski p engine
Thrust4.4×105 N
Thrust Power2.7 GW
Engine Mass7,000 kg
(less p containment)
Specific Impulse1,100 sec
Exhaust Velocity10,790 m/s
Fuelantiprotons (p)
Fuel Mass Flow15 μg/sec
(1.5×10-8 kg/s)
PropellantLH2
Propellant
Mass Flow
41 kg/s

Basically a NERVA design where a tungsten antimatter target replaces the reactor.

A stream of antiprotons ( p ) antimatter fuel strike the tungsten target. The antiprotons annihilate protons inside the tungsten, producing gamma rays and pions. These are captured by the tungsten target, heating it. The tungsten target then heats the hydrogen propellant. Then the propellant rushes out the exhaust nozzle, creating rocket thrust.

Tungsten was chosen because it has an admirable effectiveness of stopping both the gamma rays and pions, a range of about 9 centimeters and a slowing down time of 0.5 nanoseconds. The tungsten is formed into a honeycomb, to allow the passage of propellant to be heated.

The tungsten also acts as the biological shadow shield.

Produces high thrust but the specific impulse is limited due to material constraints (translation: above a certain power level the blasted tungsten melts). Tungsten has a melting point of 2,683 K.

Predictably even though this engine has a thrust-to-weight ratio higher than one, the citizens are going to protest if you get the bright idea of using this rocket to boost payloads into orbit. Because an accident is going to be quite spectactular. You thought a nuclear explosion was bad, get a load of this!

According to Some Examples of Propulsion Applications Using Antimatter by Bruno Augenstein a tungsten block heated by antiprotons can heat hydrogen propellant up to a specific impulse of 1,000 to 1,300 seconds, depending up on the pressure the hydrogen operates at. This will require about one milligram (1×10-6 kg) of antiprotons per six or seven metric tons of hydrogen propellant, fed at a rate of 13 micrograms (1.3×10-8 kg) of antiprotons per second. One milligram of antiprotons has about the energy of an Aviation Thermobaric Bomb of Increased Power, or 43 tons of TNT.


According to Comparison of Fusion/Antiproton Propulsion Systems for Interplanetary Travel by Stanley K. Borowski (NASA Technical Memorandum 107030 AIAA–87–1814) a nuclear thermal engine needs all sorts of weird requirements to ensure nuclear criticality. Otherwise the reactor doesn't work. Antimatter, on the other hand, don't need no stinkin' criticality requirements. So the antimatter engine is much simpler.

All you need to do is make sure the tungsten target core is large enough to soak up most of the antimatter reaction products (so as to not waste antimatter energy and to protect the crew from radiation) and large enough to provide adequate hydrogen flow for cooling. Sadly there would be some neutron radiation due to positrons interacting with heavier nuclei. They figure the operating temperatures could be high enough to make the exhaust velocity around 9,810 m/s (Isp ~1,000 s). The tungsten core would be slightly smaller than a NTR reactor core, being a tungsten cylinder of about 80 cm diameter × 80 cm length. It would have a mass of 5,000 kg, assuming a 36% void fraction for the hydrogen coolant flow channels.

If you sized this engine for a crewed Mars mission, it would have a thrust of 4.4×105N, power level of 2.7 gigawatts, engine mass about 7,000 kg, and a specific impulse of about 1,100 sec (exhaust velocity of 10,790 m/s). Assuming a 100% deposition of antimatter energy in the tungsten and a 88.5% conversion efficiency into jet power, the engine would need a mass flow of 15 micrograms (1.5×10-8 kg) of antiprotons per second and a mass flow of 41 kg/sec of hydrogen propellant. For comparison a nuclear thermal rocket would need a burnup of about 33 milligrams (3.3×10-5) of U235 per second

Understand that the engine is going to require large masses of electric and magnetic field devices to safely store, extract, and inject the antiprotons into the tungsten without blowing the ship to tarnation. This is true of all antimatter powered rockets, but antimatter proponents tend to sweep this under the rug and seldom mention it in the weight estimates.

Gas Core

Gas-Core 5k sec
FuelAntiprotons (p)
Fuel Flow Rate2.25×10-8 kg/sec
PropellantLH2
Propellant Flow Rate0.9 kg/sec
Antimatter TargetTungsten
Annihilation Power4.05 GW
Thrust Power1.08 GW
Specific Impulse5,000 sec
Exhaust Velocity49,050 m/s
Thrust44,000 N
Cavity Radius1.2 m
Radiator Mass87,000 kg
Chamber Mass25,000 kg
Magnetic Coil Mass70,000 kg
Total Engine Mass182,000 kg
T/W Ratio2.5×10-2
Specific Power5.9 kW/kg
Gas-Core 1.25k sec
FuelAntiprotons (p)
Fuel Flow Rate1.125×10-8 kg/sec
PropellantLH2
Propellant Flow Rate14.3 kg/sec
Antimatter TargetTungsten
Annihilation Power2.025 GW
Thrust Power0.27 GW
Specific Impulse1,250 sec
Exhaust Velocity12,260 m/s
Thrust44,000 N
Cavity Radius1.2 m
Chamber Mass25,000 kg
Magnetic Coil Mass70,000 kg
Total Engine Mass95,000 kg
T/W Ratio4.7×10-2
Specific Power2.8 kW/kg

Antimatter rockets have analogous exhaust velocity limits to nuclear thermal rockets. Once the heat level reaches the liquefaction point (2,683 K), the tungsten core melts. This limits the solid core antimatter rocket's maximum exhaust velocity.

Rocket engineers quickly figured that if the antimatter rocket shared the same limitation as nuclear thermal rockets, perhaps they could use the same solutions. The nuclear thermal solution was the Gas Core NTR. May I present to you the Gas Core Antimatter Rocket. This is from Comparison of Fusion/Antiproton Propulsion Systems for Interplanetary Travel by Stanley K. Borowski.

The basic idea is to take the Gas Core NTR design, and replace the ball of fissioning uranium-235 gas with a ball of hot tungsten gas bombarded with a stream of antiprotons.

The tungsten gas will be a target for the antiprotons, being heated by the antimatter energy released, then heating up the hydrogen propellant by radiant heat. And because the tungsten is already vaporized, it can be safely heated to much higher that the 2,683 K which solid core antimatter engines are limited to.

Again, the task is easier because the GCNTR has to ensure the U235 gas is critical so as to undergo fission. Antimatter doesn't have to worry about that. For instance, the GCNTR requires a chamber pressure of 1,000 atmospheres to ensure the U235 achieves a critical mass. Antimatter version can get by on orders of magnitude less pressure. However, the antimatter version will require a tweek or two. Since the tungsten is vapor, an external magnetic field will be needed to trap the charged pions and follow-on decay products (the tungsten plasma can only capture 2/3 of the annihilation energy). The two candidate geometries for the magnetic field are Baseball Coil and Yin-yang. They will need a ferociously strong magnetic field, about 15 Tesla assuming the dimensions of the antimatter engine are about the same as the GCNTR.

Making some other assumptions based on the GCNTR, the report calculates that the antimatter power to be about 4.05 gigawatts, and require an antimatter flow rate of 22.5 μg/sec (2.25×10-8 kg/sec). This is with an assumed Isp of 5,000 sec, exhaust velocity of 49,050 m/s, propellant flow rate of 0.9 kg/sec, thrust of 44,000 newtons, and a propellant inlet temperature of 1,400 K.

If you do not do anything to capture the gamma-ray annihilation energy, it will hit the chamber walls and have to be removed as waste heat. 1.332 freaking gigawatts of the stuff (hydrogen regenerative cooling of the chamber walls remove an additional 0.018 GW). You'll need a heat radiator of about 193,000 kilograms (radiator specific mass of 19 kg/m2 and operating temperature of 1,225 K). 193 metric tons of heat radiator makes this propulsion system much less attractive. The heat radiator mass can be reduced to 87 metric tons if you raise the operating temperature to 1,500 K.

Alternatively you can alter some engine parameters to reduce the required antimatter fuel and antimatter power by half. Which also reduces the gamma ray waste heat by half. What you do is to increase the tungsten temperature to 3,250 K (the report is unclear as to what the value was before, something bigger than 2,683 K) and the propellant inlet temperature to the same. This drops the require antimatter power in half from 4.05 gigawatts to 2.025 GW and the antimatter flow rate from 22.5 μg/sec to 11.25 μg/sec. The waste gamma-ray annihilation energy drops from 1.332 GW to 0.675 GW. The propellant flow rate is drastically increased from 0.9 kg/sec to a whopping 14.3 kg/sec. This allows the propellant to absorb the 0.675 GW of gamma-ray energy, thus removing the need for the 87 metric tons of heat radiator.

The drawback is the increase in propellant flow rate catastrophically drops the specific impulse from 5,000 sec to a miserable 1,250 sec. Zounds! That is brutal. At that point you might as well use a fission gas-core NTR, it has a better specific impulse and the fuel is much cheaper.


Liquid Core Antimatter
Specific Impulse2,000 sec
Exhaust Velocity19,620 m/s
Thrust to Weight Ratio2.0
Specific Power190 kW/kg

Since the gas-core antimatter engine is either plagued by 87 metric tons of penalty weight or a catastrophic drop in specific impulse, engineers were wondering if the Liquid-core nuclear thermal rocket could be adapted to antimatter with better results.

In the fission version, a layer of liquid U235 is held to the spinning chamber walls by centrifugal force. Hydrogen propellant is injected through the chamber walls (cooling the walls), is heated by bubbling through the red-hot liquid uranium, emerges into the center of the chamber, and rushes with high velocity out the exhaust nozzle, creating thrust. Specific impulse between 1,300 to 1,500 seconds.

In the antimatter version, a 10 centimeter layer of red-hot liquid tungsten replaces the liquid uranium. It is sprayed with antiproton fuel to create annihilation energy. Since tungsten has a higher boiling point than uranium, at a chamber pressure of 10 atmospheres and an exhaust-to-chamber pressure ratio of 10-3, the antimatter liquid core could have a specific impulse up to 2,000 sec and an exhaust velocity of 19,620 m/s. Thrust-to-weight ratio about 2.0, specific power of 190 kW/kg. Which is better than the gas-core antimatter engine.


Forward Antimatter Gas Core
Exhaust Velocity24,500 m/s
Specific Impulse2,497 s
FuelAntimatter:
antihydrogen
ReactorLiquid Core
RemassWater
Remass AccelThermal Accel:
Reaction Heat
Thrust DirectorMagnetic Nozzle

Robert Forward has an altenate gas core antimatter rocket. Microscopic amounts of antimatter are injected into large amounts of water or hydrogen propellant. The intense reaction flashes the propellant into plasma, which exits through the exhaust nozzle. Magnetic fields constrain the charged pions from the reaction so they heat the propellant, but uncharged pions escape and do not contribute any heating. Less efficient than AM-Solid core, but can achieve a higher specific impulse. For complicated reasons, a spacecraft optimized to use an antimatter propulsion system need never to have a mass ratio greater than 4.9, and may be as low as 2. No matter what the required delta V, the spacecraft requires a maximum of 3.9 tons of reaction mass per ton of dry mass, and a variable amount of antimatter measured in micrograms to grams.

Well, actually this is not true if the delta V required approaches the speed of light, but it works for normal interplanetary delta Vs. And the engine has to be able to handle the waste heat.

Plasma Core

AM: Plasma
Water
Exhaust
Velocity
980,000 m/s
Specific
Impulse
99,898 s
Thrust61,000 N
Thrust
Power
29.9 GW
Mass
Flow
0.06 kg/s
T/W0.01
RemassWater
Specific
Power
17 kg/MW
AM: Plasma
Hydrogen
Exhaust
Velocity
7,840,000 m/s
Specific
Impulse
799,185 s
Thrust49,000 N
Thrust
Power
0.2 TW
Mass
Flow
0.01 kg/s
T/W0.01
RemassLiquid Hydrogen
Specific
Power
3 kg/MW
AM: Plasma
Both
Total
Engine Mass
500,000 kg
FuelAntimatter:
antihydrogen
ReactorPlasma Core
Remass
Accel
Thermal Accel:
Reaction Heat
Thrust
Director
Magnetic Nozzle

Similar to antimatter gas core, but more antimatter is used, raising the propellant temperature to levels that convert it into plasma. A magnetic bottle is required to contain the plasma.


LaPointe
antiproton
magnetically
confined
plasma
Moderate Density
Hydrogen
Density
1016 atoms/cm3
Antiproton
Density
1010 antiprotons/cm3 to
1012 antiprotons/cm3
Normalized
Thrust
7.6×10-7 N⋅s/cm3 to
9.8×10-6 N⋅s/cm3
Exhaust
Velocity
45,000 m/s to
590,000 m/s
Specific
Impulse
4,610 s to
60,000 s
High Density
Hydrogen
Density
1018 atoms/cm3
Antiproton
Density
1012 antiprotons/cm3
Normalized
Thrust
8.1×10-5 N⋅s/cm3
Exhaust
Velocity
49,000 m/s
Specific
Impulse
4,950 s

LaPointe Antiproton Magnetically Confined Plasma Engine

In NASA report AIAA-89-2334 (1989) Michael LaPointe analyzes a pulsed antimatter rocket engine that confines neutral hydrogen gas propellant and antiprotons inside a magnetic bottle. Refer to the report if you want the actual equations

The hydrogen propellant is injected radially across magnetic field lines and the antiprotons are injected axially along magnetic field lines. The antimatter explodes, heating the propellant into plasma, for as long as the magnetic bottle can contain the explosion. After that, the magnetic mirror at one end is relaxed, forming a magnetic nozzle allowing the hot propellant plasma to exit. The cycle repeats for each pulse. Remember that the hydrogen nucleus is a single proton, convenient to be annihilated by a fuel antiproton.

The magnetic bottle contains the antiprotons, charged particles from the antimatter reaction, and the ionized hydrogen propellant. Otherwise all of these would wreck the engine. The magnetic bottle is created by a solenoid coil, with the open ends capped by magnetic mirrors.

LaPointe studied a range of densities for the hydrogen propellant.

At moderate to high densities the engine is a plasma core antimatter rocket. Compared to beam-core, the plasma core has a lower exhaust velocity but a higher thrust. The engine can shift gears to any desired exhaust velocity/thrust combination within its range by merely adjusting the amount of antiprotons and hydrogen gas injected with each pulse. And of course it can shift gears to any desired combination even outside its range by adding cold hydrogen propellant to the plasma (which is the standard method).

The reaction is confined to a magnetic bottle instead of a chamber constructed out of metal or other matter, because the energy of antimatter easily vaporizes matter.


At moderate hydrogen densities there is a problem with the hydrogen sucking up every single bit of the thermal energy, lots of the charged particle reaction products escapes the hydrogen propellant without heating up hydrogen atoms. This is a waste of expensive antimatter.

At high hydrogen densities there is a problem with bremsstrahlung radiation. Charged particles from the antimatter reaction create bremsstrahlung x-rays as they heat up the hydrogen. You want as much as possible of the expensive antimatter energy turned into heated hydrogen, but at the same time you don't want more x-rays than your engine (or crew) can cope with.


In the table, it does not list the thrust of the engine, instead it lists the "normalized" thrust. For instance the high density engine has a normalized thrust of 8.1×10-5 N⋅s/cm3. Don't panic, let me explain. You see, the actual thrust depends upon the volume of the magnetic bottle and the engine pulse rate (the delay between engine pulses). This lets you scale the engine up or down, to make it just the right size.

T = (Tnormalized / ΔT) * Bvol

where

T = thrust (Newtons)
Tnormalized = normalized thrust (N⋅s/cm3)
ΔT = pulse rate (seconds)
Bvol = volume of magnetic bottle (cm3)
Example

Say your magnetic bottle had a radius of 1 meter (100 centimeters) and a height of 10 meters (1000 centimeters). Volume of a cylinder is V=πr2h, so the magnetic bottle has a volume of 3.14×107 cubic centimeters. A pulse rate of 10 milliseconds is 0.01 seconds. The high density engine has a normalized thrust of 8.1×10-5 N⋅s/cm3. What is the engine's thrust?

T = (Tnormalized / ΔT) * Bvol
T = (8.1×10-5 / 0.01) * 3.14×107
T = 0.0081 * 3.14×107
T = 254,340 Newtons

The propellant mass flow is:

mDotp = (mp * np * Bvol) / ΔT

where

mDotp = hydrogen propellant mass flow (kg)
mp = atomic mass of hydrogen (kg) = 1.672621777×10−27
np = hydrogen density (atoms/cm3)
Bvol = volume of magnetic bottle (cm3)
ΔT = pulse rate (seconds)

And obviously the antimatter mass flow is:

mDotp = (mp * np * Bvol) / ΔT

where

mDotp = antiproton fuel mass flow (kg)
mp = rest mass of antiproton (kg) = 1.672621777×10−27
np = antiproton density (antiproton/cm3)
Bvol = volume of magnetic bottle (cm3)
ΔT = pulse rate (seconds)

The optimum performance for LaPointe's engine was at a hydrogen propellant density of 1016 hydrogen atoms per cubic centimeters, and an antiproton density between 1010 and 1012 antiprotons per cubic centimeter. With an engine that can contain the reaction for 5 milliseconds (0.005 second), these densities produce a normalized thrust of 7.6x10-7 N⋅s/cm3 to 9.8x10-6 N⋅s/cm3 over a range of exhaust velocities (45,000 to 590,000 m/s). The propellant is only capturing about 2% of the antimatter heat, but at an acceptable level of bremsstrahlung x-rays.

The thrust can be increased by increasing the hydrogen propellant density to 1018cm-3, but then you start having problems with the hydrogen plasma radiatively cooling (losing its thrust energy). You'll have to expel the plasma no more than 200 or so μseconds (0.0002 second) after the antiprotons are injected. Assuming you can do that the engine will have a normalized thrust of 8.1×10-5 N⋅s/cm3 with an exhaust velocity of 49,000 m/s or so.


Key engineering issues:

  • Efficiently generating antiproton fuel on the ground (creating antimatter fuel is insanely expensive)
  • Antiproton containment (antimatter fuel tanks that won't blow up)
  • Designing strong enough magnetic field coils (magnetic field strong enough to contain hydrogen plasma created by exploding antimatter)
  • Switching system for efficient pulsed coil operation (allowing plasma to escape at precisely the right milisecond)
  • System to inject antiprotons into annihilation region (tranporting antimatter from the tank into the reaction chamber without any "accidents")
  • Radiation shielding (to protect the magnetic coils and the crew)

The superconducting magnetic coils will need not only radiation shielding from gamma rays created by the antimatter explosion, but also from the bremsstrahlung x-rays. The radiation shield will need to be heavy to stop the radiation, and extra shielding be needed to cope with to surface ablation and degradation. The majority of the engine mass will be due to radiation shielding, which will severely reduce the acceleration (drastically lowered thrust-to-weight ratio).

Antimatter Bottle

Antimatter Bottle
Antimatter Bottle
Exhaust Velocity78,480 m/s
Specific Impulse8,000 s
Thrust34,700 N
Thrust Power1.4 GW
Mass Flow0.44 kg/s
Total Engine Mass180,000 kg
T/W0.02
Frozen Flow eff.80%
Thermal eff.85%
Total eff.68%
FuelAntimatter:
antiprotons
ReactorAntimatter Catalyzed
RemassLead
Remass AccelThermal Accel:
Reaction Heat
Thrust DirectorMagnetic Nozzle
Specific Power132 kg/MW

Antimatter fuel can be stored as levitated antihydrogen ice. By illuminating it with UV to drive off the positrons, a bit is electromagnetically extracted and sent to a magnetic bottle.

There it is collided with 60 g of heavy metal propellant (9 × 1024 atoms of lead or depleted uranium). Each antiproton annihilates a proton or neutron in the nucleus of a heavy atom. The use of heavy metals helps to suppress neutral pion and gamma ray production by reabsorption within the fissioning nucleus. If regolith is used instead of a heavy metal, the gamma flux is trebled requiring far more cooling.

A pulse of 5 μg of fuel (3 × 1018 antiprotons) contains 900 MJ of energy, and at a repetition rate of 0.8 Hz, a power level of 700 MWth is attained.

Compared to fusion, antimatter rockets need higher magnetic field strengths: 16 Tesla in the bottle and 50 Tesla in the throat. After 7 ms, this field is relaxed to allow the plasma to escape at 6 keV and 350 atm.

These high temperatures and pressures cause higher bremsstrahlung X-ray losses than fusion reactors. Furthermore, the antiproton reaction products are short-lived charged pions and muons, that must be exhausted quickly to prevent an increasing amount of reaction power lost to neutrinos. About a third of the reaction energy is X-rays and neutrons stopped as heat in the shields (partly recoverable in a Brayton cycle), another third escapes as neutrinos. Only the final third is charged fragments directly converted to thrust or electricity in a MHD nozzle.

D.L. Morgan, “Concepts for the Design of an Antimatter Annihilation Rocket,” J. British Interplanetary Soc. 35, 1982. (For use in this game, to keep the radiator mass within reasonable bounds, I reduced the pulse rate from 60 Hz to 0.8 Hz.)

Robert L. Forward, “Antiproton Annihilation Propulsion”, University of Dayton, 1985.

From High Frontier by Philip Eklund

Beam Core

AM: Beam
Exhaust Velocity100,000,000 m/s
Specific Impulse10,193,680 s
Thrust10,000,000 N
Thrust Power500.0 TW
Mass Flow0.10 kg/s
Total Engine Mass10,000 kg
T/W102
FuelAntimatter:
antihydrogen
ReactorAntimatter Catalyzed
RemassReaction
Products
Remass AccelAnnihilation
Thrust DirectorMagnetic Nozzle
Specific Power2.00e-05 kg/MW

Microscopic amounts of antimatter are reacted with equal amounts of matter. Remember: unless you are using only electron-positron antimatter annihilation, mixing matter and antimatter does NOT turn them into pure energy. Instead you get some energy, some charged particles, and some uncharged particles.

The charged pions from the reaction are used directly as thrust, instead of being used to heat a propellant. A magnetic nozzle channels them. Without a technological break-through, this is a very low thrust propulsion system.

All antimatter rockets produce dangerous amounts of gamma rays. The gamma rays and the pions can transmute engine components into radioactive isotopes. The higher the mass of the element transmuted, the longer lived it is as a radioisotope.


Positron Ablative

Positron Ablative
Exhaust velocity49,000 m/s

This engine produces thrust when thin layers of material in the nozzle are vaporized by positrons in tiny capsules surrounded by lead. The capsules are shot into the nozzle compartment many times per second. Once in the nozzle compartment, the positrons are allowed to interact with the capsule, releasing gamma rays. The lead absorbs the gamma rays and radiates lower-energy X-rays, which vaporize the nozzle material. This complication is necessary because X-rays are more efficiently absorbed by the nozzle material than gamma rays would be.

Drawbacks include the fact that you need 1836 positrons to equal the energy of a single anti-proton, and only half the positrons will hit the pusher plate limiting the efficiency to 50%.

This system is very similar to Antiproton-catalyzed microfission

Fusion

Fusion propulsion uses the awesome might of nuclear fusion instead of nuclear fission or chemical power. They burn fusion fuels, and for reaction mass use either the fusion reaction products or cold propellant heated by the fusion energy.

Advantages include:

  • The exhaust velocity/specific impulse is attractively high

  • The fuel is so concentrated it is often measured in kilograms, instead of metric tons. Note this is not necessary true of the propellant.

Drawbacks include:

  • Mass flow/thrust is small and cannot be increased without lowering the exhaust velocity/specific impulse. And high exhaust velocity is one of the advantages of fusion propulsion in the first place.

  • The reaction is so hot that any physical reaction chamber would be instantly vaporized. So either magnetism or inertia is used instead, and those have limits.

  • The hot reaction will also vaporize the exhaust nozzle. So fusion propulsion tends to use exhaust nozzles composed of bladed laceworks and magnetism. These too have their limits.

  • Using open-cycle cooling to prevent the reaction chamber and nozzle from vaporizing also lowers the exhaust velocity/specific impulse.

  • Like fission propulsion, fusion produces lots of dangerous radiation.

There is a discussion of the problems with physical reaction chambers/exhaust nozzles here. There is a discussion of magnetic nozzles here.

Fusion Fuels

For more details about fusion fuels, go here.

Torchship Fusion

(ed note: Luke Campbell is giving advice to somebody trying to design a torchship. So when he says that magnetic confinement fusion won't work, he means won't work in a torchship. It will work just fine in a weak low-powered fusion drive.)

For one thing, forget muon catalyzed fusion. The temperature of the exhaust will not be high enough for torch ship like performance.

You might use a heavy ion beam driven inertial confinement fusion pulse drive, or a Z-pinch fusion pulse drive.

I don't think magnetic confinement fusion will work — you are dealing with a such high power levels I don't think you want to try confining this inside your spacecraft because it would melt.


D-T (deuterium-tritium) fusion is not very good for this purpose. You lose 80% of your energy to neutrons, which heat your spacecraft and don't provide propulsion. 80% of a terrawatt is an intensity of 800 gigawatts/(4 π r2) on your drive components at a distance of r from the fusion reaction zone. (see here for more about drive component spacing)

If we assume we need to keep the temperature of the drive machinery below 3000 K (to keep iron from melting, or diamond components from turning into graphite), you would need all non-expendable drive components to be located at least 120 meters away from the point where the fusion pulses go off.

(ed note: 120 meters = attunation 180,000. 800 gigawatts / 180,000 = 4.2 megawatts)


D-D (deuterium-deuterium) fusion gives you only 66% of the energy in neutrons. However, at the optimum temperature, you get radiation of bremsstrahlung x-rays equal to at least 30% of the fusion output power.

For a terawatt torch, this means you need to deal with 960 gigawatts of radiation. You need a 130 meter radius bell for your drive system to keep the temperature down.

(ed note: 130 meters = attunation 210,000. 960 gigawatts / 210,000 = 4.5 megawatts)


D-3He (deuterium-helium-3) fusion gives off maybe 5% of its energy as neutrons. A bigger worry is bremsstrahlung x-rays are also radiated accounting for at least 20% of the fusion output power. This lets you get away with a 66 meter radius bell for a terawatt torch.

(ed note: 66 meters = attunation 55,000. 250 gigawatts / 55,000 = 4.5 megawatts. I guess 4.5 megawatts is the level that will keep the drive machinery below 3000 k)

To minimize the amount of x-rays emitted, you need to run the reaction at 100 keV per particle, or 1.16 × 109 K. If it is hotter or colder, you get more x-rays radiated and more heat to deal with.

This puts your maximum exhaust velocity at 7,600,000 m/s, giving you a mass flow of propellant of 34.6 grams per second at 1 terawatt output, and a thrust of 263,000 Newtons per terawatt.

This could provide 1 G of acceleration to a spacecraft with a mass of at most 26,300 kg, or 26.3 metric tons. If we say we have a payload of 20 metric tons and the rest is propellant, you have 50 hours of acceleration at maximum thrust. Note that this is insufficient to run a 1 G brachistochrone. Burn at the beginning for a transfer orbit, then burn at the end to brake at your destination.


Note that thrust and rate of propellant flow scales linearly with drive power, while the required bell radius scales as the square root of the drive power. If you use active cooling, with fluid filled heat pipes pumping the heat away to radiators, you could reduce the size of the drive bell somewhat, maybe by a factor of two or three. Also note that the propellant mass flow is quite insufficient for open cycle cooling as you proposed in an earlier post in this thread.

Due to the nature of fusion torch drives, your small ships may be sitting on the end of a large volume drive assembly. The drive does not have to be solid — it could be a filigree of magnetic coils and beam directing machinery for the heavy ion beams, plus a fuel pellet gun. The ion beams zap the pellet from far away when it has drifted to the center of the drive assembly, and the magnetic fields direct the hot fusion plasma out the back for thrust.

Deuterium-Tritium

Exhaust Velocity22,000 m/s
Specific Impulse2,243 s
Thrust108,000 N
Thrust Power1.2 GW
Mass Flow5 kg/s
Total Engine Mass10,000 kg
T/W1
FuelDeuterium-Tritium
Fusion
Specific Power8 kg/MW

Fuel: deuterium and tritium. Propellant: lithium. 1 atom of Deuterium fuses with 1 atom of Tritium to produce 17.6 MeV of energy. One gigawatt of power requires burning a mere 0.00297 grams of D-T fuel per second.

Note that Tritium has an exceedingly short half-life of 12.32 years. Use it or lose it. Most designs using Tritium included a blanket of Lithium to breed more fresh Tritium fuel.

Hydrogen-Boron

H-B Fusion
Exhaust Velocity980,000 m/s
Specific Impulse99,898 s
Thrust61,000 N
Thrust Power29.9 GW
Mass Flow0.06 kg/s
Total Engine Mass300,000 kg
T/W0.02
FuelHydrogen-Boron
Fusion
Specific Power10 kg/MW

Fuel is Hydrogen and Boron-11. Propellant is hydrogen. Bombard Boron-11 atoms with Protons (i.e., ionized Hydrogen) and you get a whopping 16 Mev of energy, three Alpha particles, and no deadly neutron radiation.

Well, sort of. Current research indicatates that there may be some neutrons. Paul Dietz says there are two nasty side reactions. One makes a Carbon-12 atom and a gamma ray, the other makes a Nitrogen-14 atom and a neutron. The first side reaction is quite a bit less likely than the desired reaction, but gamma rays are harmful and quite penetrating. The second side reaction occurs with secondary alpha particles before they are thermalized.

The Hydrogen - Boron reaction is sometimes termed "thermonuclear fission" as opposed to the more common "thermonuclear fusion".

A pity about the low thrust. The fusion drives in Larry Niven's "Known Space" novels probably have performance similar to H-B Fusion, but with millions of newtons of thrust.

It sounded too good to be true, so I asked "What's the catch?"

The catch is, you have to arrange for the protons to impact with 300 keV of energy, and even then the reaction cross section is fairly small. Shoot a 300 keV proton beam through a cloud of boron plasma, and most of the protons will just shoot right through. 300 keV proton beam against solid boron, and most will be stopped by successive collisions without reacting. Either way, you won't likely get enough energy from the few which fuse to pay for accelerating all the ones which didn't.

Now, a dense p-B plasma at a temperature of 300 keV is another matter. With everything bouncing around at about the right energy, sooner or later everything will fuse. But containing such a dense, hot plasma for any reasonable length of time, is well beyond the current state of the art. We're still working on 25 keV plasmas for D-T fusion.

If you could make it work with reasonable efficiency, you'd get on the order of ten gigawatt-hours of usable power per kilogram of fuel.

Professor N. Rostoker, et. al think they have the solution, utilizing colliding beams. Graduate Student Alex H.Y. Cheung is looking into turning this concept into a propulsion system.

Helium3-Deuterium

He3-D Fusion
Exhaust Velocity7,840,000 m/s
Specific Impulse799,185 s
Thrust49,000 N
Thrust Power0.2 TW
Mass Flow0.01 kg/s
Total Engine Mass1,200,000 kg
T/W4.00e-03
FuelHelium3-Deuterium
Fusion
Specific Power6 kg/MW

Fuel is helium3 and deuterium. Propellant is hydrogen. 1 atom of Deuterium fuses with 1 atom of Helium-3 to produce 18.35 MeV of energy. One gigawatt of power requires burning a mere 0.00285 grams of 3He-D fuel per second.

Confinement

Fusion Containment

There are five general methods for confining plasmas long enough and hot enough for achieving a positive Q (more energy out of a reaction than you need to ignite it, "break even"):


  • Closed-field magnetic confinement
  • Open-field magnetic confinement
  • Inertial confinement (see D-D inertial fusion)
  • Electrostatic inertial confinement (see 6Li-H fusor)
  • Cold fusion (see H-B cat fusion)
  • Of these reactions, the fusion of deuterium and tritium (D-T), has the lowest ignition temperature (40 million degrees K, or 5.2 keV). However, 80% of its energy output is in highly energetic neutral particles (neutrons) that cannot be contained by magnetic fields or directed for thrust.

    In contrast, the 3He-D fusion reaction (ignition temperature = 30 keV) generates 77% of its energy in charged particles, resulting in substantial reduction of shielding and radiator mass. However, troublesome neutrons comprise a small part of its energy (4% at ion temperatures = 50 keV, due to a D-D side reaction), and moreover the energy density is 10 times less then D-T. Another disadvantage is that 3He is so rare that 240,000 tonnes of regolith scavenging would be needed to obtain a kilogram of it. (Alternatively, helium 3 can be scooped from the atmospheres of Jupiter or Saturn.)

    Deuterium, in contrast, is abundant and cheap. The fusion of deuterium to itself (D-D) occurs at too high a temperature (45 keV) and has too many neutrons (60%) to be of interest. However, the neutron energy output can be reduced to 40% by catalyzing this reaction to affect a 100% burn-up of its tritium and 3He by-products with D.

    The fusion of 10% hydrogen to 90% boron (using 11B, the most common isotope of boron, obtained by processing seawater or borax) has an even higher ignition temperature (200 keV) than 3He-D, and the energy density is smaller. Its advantage is that is suffers no side reactions and emits no neutrons, and hence the reactor components do not become radioactive.

    The 6Li-H reaction is similarly clean. However, both the H-B and 6Li-H reactions run hot, and thus ion-electron collisions in the plasma cause high bremsstrahllung x-ray losses to the reactor first wall.

    From High Frontier by Philip Eklund

    The samples below are from Nuclear Propulsion—A Vital Technology for the Exploration of Mars and the Planets Beyond (1987).

    There are two types of mission. One way missions go from planet A to planet B (AB or A→B) or from planet B to planet A (BA or B→A). Round trip (RT or A→A) missions go from A to B and back to A.

    The bottom line is that inertial confinement fusion is far superior to magnetic confinement fusion.

    Sample Closed-field
    Magnetic Confinement
    (Tokamak)
    Fusion Rocket
    FuelD-3He (spin polarized)
    Specific Impulse20,000 s
    Mass Flow0.308 kg/s
    Engine Alpha5.75 kW/kg
    Engine Mass1,033,000 kg
    Payload Mass200,000 kg
    Sample
    Inertial
    Confinement
    Fusion Rocket
    FuelCat-DD
    Specific Impulse270,000 s
    Mass Flow0.015 kg/s
    Engine Alpha110 kW/kg
    Engine Mass486,000 kg
    Payload Mass200,000 kg
    Sample Tokamak Fusion Rocket
    One-way continuous-burn constant-Isp trajectory
    Mission


    Distance

    DAB (A.U.)
    Mass
    Ratio
    RM
    Initial
    Mass
    Mi (mT)
    Propellant
    Mass
    Mp (mT)
    Payload
    Mass
    ML/Mi (%)
    Travel
    Time
    τAB (days)
    Initial
    Acceleration
    ai (10-3 g0)
    Mars0.5241.7322,1359029.433.0~2.9
    Ceres1.7672.4973,0791,8466.569.42.0
    Jupiter4.2033.5904,4273,1944.5120.0~1.4
    Sample Tokamak Fusion Rocket
    Round-trip trajectory
    Mission



    Mass
    Ratio

    RM
    Propellant
    Mass
    MpA→B
    (mT)
    Propellant
    Mass
    MpB→A
    (mT)
    Propellant
    Mass
    MpA→A
    (mT)
    Initial
    Mass
    Mi
    (mT)
    Travel
    Time
    τAB
    (days)
    Travel
    Time
    τBA
    (days)
    Travel
    Time
    τRT
    (days)
    Mars2.6641,1499022,0513,28443.233.977.1
    Ceres4.6672,6751,8464,5215,754100.569.4169.9
    Jupiter7.7835,1693,1948,3639,596194.3120.0314.3
    Sample Inertial Confinement Fusion Rocket
    Round-trip continuous-burn constant-Isp trajectory
    Mission



    Distance

    DAB (A.U.)
    Mass
    Ratio

    RM
    Initial
    Mass
    Mi
    (mT)
    Propellant
    Mass
    MpA→A
    (mT)
    Payload
    Mass
    ML/Mi (%)
    Travel
    Time
    τAB
    (days)
    Travel
    Time
    τRT
    (days)
    Mars0.5241.104757.371.326.427.755.0
    Ceres1.7671.196820.5134.524.453.1103.7
    Jupiter4.2031.309898212.022.384.6163.6
    Saturn8.5391.453997311.020.1125.5239.8
    Uranus18.1821.6891,159473.017.3194.1364.7
    Neptune29.0581.9011,304618.015.3257.3476.9
    Pluto38.5182.0631,415729.014.1306.6562.7

    The above tables were calculated with the following equations:

    Wf = Mf * g0

    MB = Mf + MpB→A

    1 / α = Mi / MB

    1 / β = MB / Mf

    Pf = Mp / Mi

    RM = 1 / (α * β) (two way)

    RM = 1 / β (one way)

    τAB = (Isp / (F / Wf)) * (1 / β) * ((1 / α) -1) (equation 10)

    τBA = (Isp / (F / Wf)) * (1 / β - 1) (equation 11)

    τRT = τAB + τBA (equation 12a)

    τRT = (Isp / (F / Wf)) * (1 / (α * β) - 1) (equation 12b)

    DAB(m) = ((g0 * Isp2) / (F / Wf))) * (1 / β) * ((1 / sqrt(α)) - 1)2 (equation 13a)

    DBA(m) = ((g0 * Isp2) / (F / Wf))) * ((1 / sqrt(β)) - 1)2 (equation 14)

    DAB(m) = DBA(m) (equation 13b)

    where:

    αp = engine alpha (W/kg)
    DAB = distance between A and B (meters)
    DBA = distance between B and A (meters)
    Isp = engine specific impulse (seconds)
    IMEO = initial mass in Earth orbit (kg)
    MB = dry mass plus just propellant to travel from B to A (kg)
    ML = mass of payload (kg)
    MW = mass of engine (kg)
    Mf = dry mass (kg)
    Mi = initial mass in Earth orbit (kg)
    MpA→A = mass of propellant used traveling round-trip from A to B to A (kg)
    MpA→B = mass of propellant used traveling one-way from A to B (kg)
    MpB→A = mass of propellant used traveling one-way from B to A (kg)
    p = propellant mass flow (kg/s)
    Pf = propellant mass fraction
    RM = spacecraft mass ratio
    τAB = time to travel one way from A to B (seconds)
    τBA = time to travel one way from B to A (seconds)
    τRT = time to travel round trop from A to B to A (seconds)
    Wf = dry weight (Newtons)

    Inertial Confinement

    Inertial Confinement Fusion is in the Pulse section.

    Electrostatic Inertial

    H-Li6 Fusor Reactor
    H-Li6 Fusor
    Exhaust Velocity19,620 m/s
    Specific Impulse2,000 s
    Thrust67,100 N
    Thrust Power0.7 GW
    Mass Flow3 kg/s
    Total Engine Mass54,000 kg
    T/W0.13
    Frozen Flow eff.92%
    Thermal eff.90%
    Total eff.83%
    FuelHydrogen-Lithium6
    Fusion
    ReactorElectrostatic
    Confinement
    RemassReaction
    Products
    Remass AccelElectrostatic
    Acceleration
    Thrust DirectorMagnetic Nozzle
    Specific Power82 kg/MW

    A Farnsworth-Bussard fusor is little more than two charged concentric spheres dangling in a vacuum chamber, producing fusion through inertial electrostatic confinement. Electrons are emitted from an outer shell (the cathode), and directed towards a central anode called the grid. The grid is a hollow sphere of wire mesh, with the elements magnetically-shielded so that the electrons do not strike them. Instead, they zip right on through, oscillating back and forth about the center, creating a deep electrostatic well to trap the ions of lithium 6 and hydrogen that form the fusion fuel. With a one meter diameter grid and a fuel consumption rate of 7 mg/sec, the fusion power produced is 360 MWth.

    Half of this energy is bremsstrahlung X-rays, which must be captured in a lithium heat engine. The other half are isotopes of helium (3He and 4He), each at about 8 MeV. (Overall efficiency is 36%). Since both products are doubly charged, a 4 MeV electric field will decelerate them and produce two electrons from each, producing an 18 amp current at extremely high voltage.

    An electron gun using this 4 million volt energy would emit electrons at relativistic speeds. This beam dissipates quickly in space, unless neutralized by positrons or converted into a free electron laser beam.

    “Inertia-Electrostatic-Fusion Propulsion Spectrum: Air-Breathing to Interstellar Flight,” R W. Bussard and L. W. Jameson, Journal of Propulsion and Power, v. 11, no. 2, pp. 365-372.

    (Philo Farnsworth, the farm boy who invented the television, spent his last years in a lonely quest to attain break-even fusion in his ultra-cheap fusor devices. His ideas are enjoying a renaissance, thanks to Dr. Bussard, and working fusion reactors are making an appearance in high school science fairs. On the theory that the fusor is power-limited, I have scaled down Bussard’s 10 GW design to 360 MW.)

    From High Frontier by Philip Eklund

    Magnetic Confinement

    MC-Fusion
    Thrust Power200 GW
    Exhaust velocity8,000,000 m/s
    Thrust50,000 n
    Engine mass0.6 tonne
    T/W >1.0yes

    A magnetic bottle contains the fusion reaction. Very difficult to do. Researchers in this field say that containing fusion plasma in a magnetic bottle is like trying to support a large slab of gelatin with a web of rubber bands. Making a magnetic bottle which has a magnetic rocket exhaust nozzle is roughly 100 times more difficult.

    Since the engine is using a powerful but tightly controlled magnetic field, it might be almost impossible to have a cluster of several magnetic confinement fusion engines. The magnetic fields will interfere with each other.

    There are two main forms of magnetic bottles: linear (in a straight line) and toroidal (donut shaped, a linear bent into a circle with the ends joined together).

    Linear Fusion
    Gasdynamic Mirror
    Exhaust Velocity1,960,000 m/s
    Specific Impulse199,796 s
    Thrust47,000 N
    Thrust Power46.1 GW
    Mass Flow0.02 kg/s
    FuelDeuterium-Tritium
    Fusion
    ReactorMagnetic Confinement
    Linear
    RemassLiquid Hydrogen
    Remass AccelThermal Accel:
    Reaction Heat
    Thrust DirectorMagnetic Nozzle

    Also known as "Open-field magnetic confinement".

    Examples include the Gasdynamic Mirror, Hedrick Fusion Spacecraft, and the Santarius Fusion Rocket.

    3He-D Mirror Cell
    3He-D Mirror Cell
    Exhaust Velocity313,920 m/s
    Specific Impulse32,000 s
    Thrust10,600 N
    Thrust Power1.7 GW
    Mass Flow0.03 kg/s
    Total Engine Mass106,667 kg
    T/W0.01
    Frozen Flow eff.92%
    Thermal eff.90%
    Total eff.83%
    FuelHelium3-Deuterium
    Fusion
    ReactorMagnetic Confinement
    Linear
    RemassReaction
    Products
    Remass AccelThermal Accel:
    Reaction Heat
    Thrust DirectorMagnetic Nozzle
    Specific Power64 kg/MW

    Helium 3 is an isotope of helium, and deuterium (abbreviated D) is an isotope of hydrogen. The 3He-D fusion cycle is superior to the D-T cycle since almost all the fusion energy, rather than just 20%, is deposited in the plasma as fast charged particles.

    Magnetic containers with a linear rather than toroidal geometry, such as steady-state mirrors, have superior ratios of plasma pressure to magnet pressure (β >30%) and higher power densities necessary for reaching the high (50 keV) 3He-D operating temperatures.

    The mirror design shown is a tube of 11 Tesla superconducting magnetic coils, with choke coils for reflection at the ends. The magnets weigh 12 tonnes, plus another 24 tonnes for 60 cm of magnet radiation shielding and refrigeration. A mirror has low radiation losses (20% bremsstrahlung, 3% neutrons) compared to its end losses (77% fast charged particles). These losses limit the Q to about unity and prevent ignition. (This is not a problem for propulsion, since reaching break-even is not required to achieve thrust. The plasma is held in stable energy equilibrium by the constant injection of auxiliary microwave heating.)

    The Q can be improved by a tandem arrangement: stacking identical mirror cells end to end so that one’s loss is another’s gain. The exhaust exiting one end can be converted to power by direct conversion (MHD), and the other end’s exhaust can be expanded in a magnetic flux tube for thrust.

    Mirrors improved by vortex technology, called field-reversed mirrors, introduce an azimuthal electron current which creates a poloidal magnetic field component strong enough to reverse the polarity of the magnetic induction along the cylindrical axis. This creates a hot compact toroid that both plugs end losses and raises the temperature of the scrape-off plasma layer fourfold (to 2.5 keV), corresponding to a specific impulse of 32 ksec.

    Mirrors, like all magnetic fusion devices, can readily augment their thrust by open-cycle cooling.

    “Considerations for Steady-State FRC-Based Fusion Space Propulsion,” M.J. Schaffer, General Atomics Project 4437, Dec 2000.

    From High Frontier by Philip Eklund
    Toroidal Fusion

    Also known as "Closed-field magnetic confinement".

    Discovery II
    Discovery II
    PropulsionHelium3-Deuterium
    MC Fusion
    Exhaust Velocity347,000 m/s
    Specific Impulse35,372 s
    Thrust18,000 N
    Thrust Power3.1 GW
    Mass Flow0.05 kg/s
    FuelHelium3-Deuterium
    Fusion
    ReactorMagnetic Confinement
    Toroidal
    RemassLiquid Hydrogen
    Remass AccelThermal Accel:
    Reaction Heat
    Thrust DirectorMagnetic Nozzle
    Wet Mass1,690,000 kg
    Dry Mass883,000 kg
    Mass Ratio1.91 m/s
    ΔV225,258 m/s
    Specific Power3.5 kW/kg (3,540 W/kg)
    Initial Acceleration1.68 milli-g
    Payload172,000 kg
    Length240 m
    Diameter60 m wide
    D-T Fusion Tokamak
    D-T Fusion Tokamak
    Exhaust Velocity66,800 m/s
    Specific Impulse6,809 s
    Thrust66,800 N
    Thrust Power2.2 GW
    Mass Flow1 kg/s
    Total Engine Mass197,000 kg
    T/W0.04
    Frozen Flow eff.77%
    Thermal eff.85%
    Total eff.65%
    FuelDeuterium-Tritium
    Fusion
    ReactorMagnetic Confinement
    Toroidal
    RemassReaction
    Products
    Remass AccelThermal Accel:
    Reaction Heat
    Thrust DirectorMagnetic Nozzle
    Specific Power88 kg/MW

    Of all the fusion reactions, the easiest to attain is a mixture of the isotopes of hydrogen called deuterium and tritium (D-T). This reaction is “dirty”, only 20% of the reaction power is charged particles (alphas) that can be magnetically extracted with a diverter for power or thrust. The remaining energy (neutron, bremsstrahlung, and cyclotron radiation) must be captured in a surrounding jacket of cold dense Li plasma. The heated lithium is either exhausted as open-cycle coolant, or recirculated through a heat engine (to generate the power needed for the microwave plasma heater).

    The 2 GWth magnetically-confined reactor shown uses eight poloidal superconducting 30 Tesla coils, twisted into a Tokamak configuration. These weigh 22 tonnes with stiffeners and neutron shielding.

    The pulsed D-T plasma, containing tens of megamps, is super-heated by 50 MW of microwaves or colliding beams to 20 keV. The Q (gain factor) is 40. Closed field line devices such as this can ignite and burn, in which case the Q goes to infinity and microwave heating is no longer needed. However, since ignition is inherently unstable (once ignited, the plasma rapidly heats away from the ignition point), the reactor is kept at slightly below ignition.

    Fuel is replenished at 24 mg/sec by gas puffing to maintain a plasma ion density of 5 × 1020/m3 at 26 atm. At a power density of 250 MWth /m3, the lithium-cooled first wall has a neutron loading of 1 MW/m2 and a radiation loading of 5 MW/m2.

    More advanced vortex designs, which do away with the first wall, separate the hot fusion fuel from the cool lithium plasma by swirling the mixture. The thermal efficiency is 50% in open-cycle mode.

    Williams, Borowski, Dudzinski, and Juhasz, “A Spherical Torus Nuclear Fusion Reactor Space Propulsion Vehicle Concept for Fast Interplanetary Travel,” Lewis Research Center, 1998.

    (The Tokamak used in High Frontier is a smaller lower tech version of the Lewis design, which uses aneutronic 3He-D fuel.)

    From High Frontier by Philip Eklund

    Fusion Engines

    To make the fusion reactor into a fusion rocket, the fusion energy has to be used to accelerate reaction mass. The method will determine the exhaust velocity/specific impulse, which is the critical variable in the delta V equation.

    There are three types of energy that come from fusion reactions:

    • Plasma thermal energy: When the fusion fuel undergoes fusion, the fuel atoms are ionized into useful hot plasma ions containing most of the fusion energy in a convenient easy-to-use form. We like plasma thermal energy.

    • Neutron energy: Many fusion reactions or side reactions also produce deadly and worthless neutron radiation. It is lethal to human beings. It can cause neutron embrittlement and neutron activation in the engine parts. Neutron energy is considered to be wasted energy.

    • Bremsstrahlung radiation energy: This occurs when the hot plasma ions from the fusion reaction collide with the electrons (which are there because "ionization of fusion fuel atoms" means "ripping off their electrons and tossing them into the plasma soup"). Bremsstrahlung steals the hot ion's useful plasma thermal energy and converts it into worthless and dangerous x-rays plus cold ions. This is also considered to be wasted energy.

    Pure fusion rockets use the fusion products themselves as reaction mass. Fusion afterburners and fusion dual-mode engines use the fusion energy (plasma thermal energy, neutron energy, and bremsstrahlung radiation energy) to heat additional reaction mass. So afterburners and dual-mode reduce the exhaust velocity in order to increase thrust.

    • Pure fusion rockets use just the plasma thermal energy, and just the fusion products as reaction mass. The neutron and bremsstrahlung radiation energy is considered to be waste.
      This mode has the highest exhaust velocity/specific impulse and the lowest thrust/propellant mass flow of the three fusion engine types.

    • Fusion afterburners use just the plasma thermal energy, but adds extra cold reaction mass to be heated by plasma energy. Again neutron and bremsstrahlung are wasted.

    • Dual-mode use the neutron and bremsstrahlung radiation energy to heat a blanket of cold reaction mass which thrusts out of separate conventional exhaust nozzles. In addition a Dual-mode can switch into Pure Fusion mode.
      This mode has the highest thrust/propellant mass flow and the lowest exhaust velocity/specific impulse.

    Dr. Stuhlinger notes that high-thrust mode allows fast human transport (but low payloads) while high-specific-impulse mode allows cargo vessels with large payload ratios (but long transit times). He compares these to sports cars and trucks, respectively.

    In the Santarius Fusion Rocket using D-3He fusion:

    Santarius Fusion Rocket
    D-3He Fusion
    ModeSpecific ImpulseThrust
    Pure Fusion1×106 sec88 N
    Afterburner5×105 sec to
    1×104 sec
    125 N to
    5,000 N
    Dual-Mode7×102 sec to
    7×101 sec
    12,500 N to
    125,000 N

    Pure Fusion Engines

    Pure fusion rockets use just the plasma thermal energy, and just the fusion products as reaction mass.

    The advantage is incredibly high exhaust velocity (though sometimes it can be too high).

    The disadvantage it the absurdly small thrust.

    To calculate the exhaust velocity of a Pure Fusion Rocket:

    Ve = sqrt( (2 * E) / m )

    where

    • Ve = exhaust velocity (m/s)
    • E = energy (j)
    • m = mass of fuel (kg)

    Remember Einstein's famous e = mc2? For our thermal calculations, we will use the percentage of the fuel mass that is transformed into energy for E. This will make m into 1, and turn the equation into:

    Ve = sqrt(2 * Ep)

    where

    • Ep = fraction of fuel that is transformed into energy
    • Ve = exhaust velocity (percentage of the speed of light)

    Multiply Ve 299,792,458 to convert it into meters per second.

    Example

    D-T fusion has a starting mass of 5.029053 and a mass defect of 0.018882. Divide 0.018882 by 5.029053 to get Ep of 0.00375.

    Plugging that into our equation Ve = sqrt(2 * 0.00375) = 0.0866 = 8.7% c. In meters per second 0.0866 * 299,792,458 = 25,962,027 m/s.

    Afterburner Fusion Engines

    Fusion afterburners use just the plasma thermal energy, but adds extra cold reaction mass to the fusion products.

    This is based on information from physicist Luke Campbell.

    For a given mission with a given delta V requirement, it is possible to calculate the optimum exhaust velocity. In many cases a fusion engine has thrust too low to be practical, but the exhaust velocity is way above optimal. It is possible to increase the thrust at the expense of the exhaust velocity (and vice versa) by shifting gears. An afterburner for a fusion engine is a way to shift gears.

    A pure fusion engine just uses the hot spent fusion products as the reaction mass. An afterburner fusion engine has a second plasma chamber (the afterburner) constantly filled with some cold propellant (generally hydrogen or water, but you can use anything that the spend fusion plasma can vaporize). The hot spent fusion products are vented into the afterburner, heating up the cold propellant. The average temperature goes down (decreasing the exhaust velocity) while the propellant mass flow goes up (increasing the thrust). The propellant mass flow increases naturally because instead of just sending the fusion products out the exhaust nozzle, you are sending out the fusion products plus the cold propellant. The contents of the afterburner are sent out the exhaust nozzle and Newton's Third Law creates thrust.

    In the equations below, a nozzle with an efficiency of 100% would have a efficiency factor of 2.0. But in practice the efficiency maxes out at about 85%, which has an efficiency factor of 1.7

    eq.1     Ptherm = F2 / (1.7 * (F / Ve))

    eq.2     mDot = F2 / (1.7 * Ptherm)

    eq.3     Ptherm = F2 / (1.7 * mDot)

    eq.4     F = sqrt[ 1.7 * Ptherm * mDot ]

    eq.5     Ve = F / mDot

    eq.6     mDot = F / Ve

    where:

    F = thrust (newtons)
    Ptherm = Thermal power (watts)
    mDot = propellant mass flow (kg/s) spent fusion product propellant + cold reaction mass
    Ve = Exhaust Velocity (m/s)
    1.7 = efficiency factor
    sqrt[ x ] = square root of x

    The thermal power is obtained from the fusion fuel table, using the % Thermal value. For instance, if you were using D + T fuel, 21% of the power from the burning fuel is what you use for Ptherm. That is, if the engine is burning 0.001 kilograms of D+T per second, it is outputting 339.72×1012 * 1×10-3 = 339.72×109 watts of energy, so Ptherm equals 339.72×109 * 0.21 = 7.1341×1010 watts.

    The amount of mDot contributed by spent fusion products can also be obtained from the fusion fuel table by using the TJ/kg column. For instance, with D+T fusion, if the rocket needs Ptherm of 2 terawatts, the total energy needed is 2 / 0.21 = 9.52 terawatts. The spent fusion products mDot is 9.52 / 339.72 = 0.028 kg/s. Usually the spent fusion product mass will be miniscule compared to the cold propellant mass. That is the reason the thrust was so miserably low to start with.

    The equation you use depends upon which value you are trying to figure out.

    1. When you have decided on the thrust and exhaust velocity, and want to know how much Thermal Power you need.
    2. When you have decided on the thrust and thermal power, and want to know how much propellant mass flow you need.
    3. When you have decided on the thrust and propellant mass flow, and want to know how much Thermal Power you need.
    4. When you have decided on the thermal power and the propellant mass flow, and want to know how much thrust you will get.
    5. When you have decided on the thrust and propellant mass flow, and want to know how much exhaust velocity you will get.
    6. When you have decided on the thrust and exhaust velocity, and want to know how much propellant mass flow you will need.

    Dual-Mode Fusion Engines

    Dual-mode use the neutron and bremsstrahlung radiation energy (which is otherwise wasted) to heat cold reaction mass, in parallel to the fusion products exhaust. In addition a Dual-mode can switch into Pure Fusion mode.

    This is based on information from physicist Luke Campbell.

    The neutron and bremsstrahlung energy produced by the fusion reaction is basically wasted energy when it comes to rocket propulsion. A dual-mode engine can switch from pure fusion mode into harvesting mode. This means additional cold propellant mass is moved around the fusion reaction chamber to be heated by the neutrons and bremsstrahlung radiation. This augments the thrust, at the expense of increasing the propellant usage rate.

    If the additional exhaust nozzles have an efficiency of 70%, and the additional propellant has an exhaust velocity of 10,000 m/s, the harvesting mode engine will create thrust of 1 newton per 7,000 watts of neutron + bremsstrahlung power, and consume 0.0001 kilograms of propellant per newton of thrust per second.

    There are some designs that try to harvest the wasted neutron and bremsstrahlung energy by attempting to turn it into electricity instead of thrust. But sometimes it is not worth it. To avoid excessive radiators the power generator typically have a maximum efficiency of 25% or less. So a maximum of 25% of the combined neutron+bremsstrahlung energy can be turned into electricity. This requires a turbine and electrical generator, which cuts into the payload mass.

    Nuclear Magnetic Spin Alignment

    This is an unobtanium way of turning a deuterium-tritium fusion reaction into a torch drive. You can find details here.

    ( STARFIRE Fusion Afterburner )

    This is a fictional fusion propulsion which is ingenious but probably impractical.

    Since the 1960s one of the leading schemes for controlling fusion, known as inertial confinement, had involved the implosion of tiny spheres of frozen hydrogen, spheres so small that hundreds could fit on the head of a pin—and every sphere a miniature H-bomb. The nation’s weapons laboratories, Los Alamos in New Mexico, Livermore in Califomia, Sandia in both states, had a monopoly on the classified knowledge essential to inertial confinement projects; who else regularly set off nuclear bombs and measured their behavior? Who else could generate mathematical models of nuclear explosions on the world's fastest computers?

    These diminutive superbombs were to be triggered by an array of powerful lasers or particle accelerators—ray guns, that is—arranged in a circle, pointing inward. Firing simultaneously, the beams would hit each frozen pellet as it fell into their midst. As the flash-heated surface expanded it would crush the sphere's interior until the hydrogen nuclei were fused into new elemental combinations—ideally releasing some three orders of magnitude more energy than that used to trigger the blast. Provided that it did not instantly melt the machine or blow it to pieces, this thousandfold increase in energy could be used to produce electrical power. Or to do other things. Fusion research had long been entangled with the military's yen for Buck Rogers-style death rays.

    That was okay with Linwood Deveraux. As reticent and gentle and genuinely polite as his soft Louisiana accent and his long-nosed, sad face suggested he was, Linwood nevertheless loved things that went zap and boom.

    His job, as one member of a brainy team at Livermore that called itself Q Branch, was to build an inertial confinement chamber that would convert thermonuclear explosions into directed beams of energy—ray guns thousands of times more powerful than those used as the spark plugs to ignite their hydrogen-pellet fuel.

    At the precise hour when the late afternoon photons came screaming through the westward window, bouncing off the neighbor’s asparagus fern in a blaze of light, tickling the shy lithops, punching him in the eye, Linwood got his modest idea.

    Several tricks were needed to design any fusion reactor, but they all required an intimate knowledge of the behavior of atoms and subatomic particles in the presence of strong electric and magnetic fields. That sort of knowledge, in turn, rested partly on a powerful intuition of geometry, and there is no useful theorem in geometry that cannot be at least qualitatively suggested with a paper and pencil. He sketched the lab’s current test machine,with its ring of lasers firing inward toward the tiny hydrogen pellet target and the strong magnetic “nozzle” that contained and directed the resulting explosion (Linwood Sketch 1).

    What is the heart of a thermonuclear explosion? Provided it starts and ends clean—uncontaminated by heavy elements like plutonium or uranium, which are intrinsic to the brute force of real H-bombs—a thermonuclear explosion is a clear hot soup, a plasma of protons, electrons, ionized helium, free neutrons, un-ionized hydrogen atoms and leftover neutrinos and such. All the electrically charged particles will stay in the soup, if it is confined and shaped by electric and magnetic fields.

    Most of the energy of the explosion, more than three quarters, is in the form of speeding neutrons. Neutrons aren’t significantly affected by electric or magnetic fields, but they can be slowed in a materially dense "blanket”—liquid lithium or some such substance—their energy thus converted to heat.

    What happens to the heat depends on what the reactor is designed to do. A power reactor uses it to make steam, and eventually electricity, but in ray guns most of the heat is a waste and a nuisance. Over the decades ray gun designers had played with various ways of using the energy of a thermonuclear explosion, for example, by letting it squeeze magnetic fields to produce huge electrostatic charges, or by opening one end of the magnetic bottle to let the products spew out, or by focusing some of the energy into x-ray beams, and so on—but no matter what the scheme, most of the thermonuclear reactor’s energy was wasted as heat.

    On his sketch pad, Linwood roughed in the liquid blanket and the circulating coolant systems required to dispose of the waste heat (Linwood Sketch 2). There he paused.

    To Linwood, with his passion for efficiency, wasting so much heat had always seemed criminal. Surely something clever could be done with those copious neutrons!

    In power reactors, neutrons were intrinsic to the fusion fuel cycle; they were captured to breed radioactive tritium, the rarer (because of its short half-life) of the two isotopes of hydrogen that composed the fusion fuel, the other being the more common deuterium. Tritium breeding was a secondary process, however, a civilian process. A ray gun orbiting in space would be supplied with all the tritium it was ever likely to need.

    Linwood wondered about other neutron-capture scenarios. In the heart of the sun, neutron capture contributed to the formation of heavier elements…but to take advantage of stellar fusion processes was a dream of the far future, awaiting the day when truly monstrous magnetic fields could be generated, capable of rivaling gravity at the heart of a star.

    Linwood thought about all this a long time and drew nothing. Applying the old creative principle that when the going gets tough the smart go somewhere else, he balled up his rough sketch and threw it away.

    He stared morosely at the lithops, now faintly glowing in the setting sun's last light.

    At the lab his discarded sketch would have been sucked into a high-temperature furnace and instantly reduced to fine ash, but at home Linwood had an open wastebasket beside his table, the contents of which he conscientiously burned…whenever he remembered to. The security disadvantages of this practice were offset by certain practicalities, one of which Linwood now demonstrated to himself—

    —by changing his mind. He fished the crumpled wad of paper out of the basket and flattened it on his table. Now what if, instead…

    The lithium-neutron reaction that yields tritium is quite efficient: a neutron entering a blanket of liquid lithium travels ten or twenty centimeters and scatters from a few lithium atoms, heating up the neighborhood before strongly interacting with one of them to create a helium nucleus and a tritium nucleus. A typical power reactor circulates the liquid metal lithium through heat exchangers, meanwhile tapping a small side flow from which the tritium is chemically extracted.

    Instead of thinking of the lithium blanket as a coolant, optional for his purposes, Linwood tried thinking of it as an extra fuel tank. He imagined introducing lithium into an annular ring around the reaction chamber at a steady rate, letting it circulate long enough to be bombarded by sufficient neutrons to produce a good proportion of tritium. He imagined mixing this tritium-enriched fluid with a separate supply of deuterium. He imagined injecting the lithium-tritium-deuterium mix into a magnetically confined and compressed outflow of hot plasma from the primary reactor—in such a manner that it burst into a secondary fusion reaction, additionally heating an outgoing beam (Linwood Sketch 3).

    Hot stuff. Not all that efficient in the long run—only a small fraction of the injected fuel would fuse, even under ideal circumstances, and a great deal of waste heat would still have to be disposed of by radiators—but Linwood was satisfied that at least he had salvaged some neutrons.

    It was dark outside when Linwood happily finished his sketching. Not that he made an improvement on the Q Branch beam projector; he knew that what he'd drawn had little or nothing to do with death rays. That was fine with him. He turned out the light and went upstairs, made himself a wiener sandwich, and lay down in bed, after popping a chip into the viddie—that classic British thriller from the 1950s, X the Unknown, starring Dean Jagger; it had a great monster, a puddle of smart, ravenous, radioactive mud.

    The next day, when Linwood displayed a suitably gussied—up draft of his idea to his coworkers in Q Branch, the youngest of them, a kid on summer loan from MIT, had an attack of giggles. What Linwood had drawn had nothing to do with ray guns, said the pimpled kid—who spoke as an authority on ray guns, having read in his short life a great deal of space opera and very little else—and it wasn't even all that original. What ol' Linwood had here was an afterburner for a fusion rocketship.


    From STARFIRE by Paul Preuss (1988)

    ( AV:T Fusion )

    AV:T Fusion
    Cruise mode
    Exhaust Velocity832,928 m/s
    Specific Impulse84,906 s
    Thrust245,250 N
    Thrust Power0.1 TW
    Mass Flow0.29 kg/s
    FuelHelium3-Deuterium
    Fusion
    Combat mode
    Exhaust Velocity104,116 m/s
    Specific Impulse10,613 s
    Thrust48,828,125 N
    Thrust Power2.5 TW
    Mass Flow469 kg/s
    FuelHelium3-Deuterium
    Fusion

    Fictional magnetic bottle fusion drive from the Attack Vector: Tactical wargame. It uses an as yet undiscovered principle to direct the heat from the fusion reaction out the exhaust instead of vaporizing the reaction chamber. Like the VASIMR it has "gears", a combat mode and a cruise mode. The latter increases specific impulse (exhaust velocity) at the expense of thrust.

    In the illustration, the spikes are solid-state graphite heat radiators, the cage the spikes emerge from is the magnetic bottle, the sphere is the crew quarters and the yellow rectangles are the retractable power reactor heat radiators. The ship in the lower left corner is signaling its surrender by deploying its radiators.

    ( THS Fusion Pulse )

    Fusion Pulse low gear
    Exhaust Velocity150,000 m/s
    Specific Impulse15,291 s
    Thrust80,000 N
    Mass Flow0.53 kg/s
    T/W2
    Fusion Pulse high gear
    Exhaust Velocity300,000 m/s
    Specific Impulse30,581 s
    Thrust40,000 N
    Mass Flow0.13 kg/s
    T/W1
    Both
    Thrust Power6.0 GW
    Total Engine Mass4,000 kg
    FuelHelium3-Deuterium
    Fusion
    Specific Power1 kg/MW

    Fictional inertial-confinement fusion drive from the game GURPS: Transhuman Space. Like the VASIMR it has "gears", one increases specific impulse (exhaust velocity) at the expense of thrust.

    ( Epstein Drive )

    Epstein Drive
    Thrust Power5.5 TW
    Exhaust Velocity11,000,000 m/s
    Specific Impulse1,100,000 s
    Thrust1,000,000 N
    Mass Flow0.09 kg/s

    Fictional Magnetic Confinement Fusion drive from The Expanse series. The sparse details I managed to find were from the short story Drive.

    The inventor mounted the newly-invented drive in a small interplanetary yacht whose living space was smaller that Epstein's first Mars apartment. When the fuel/propellant tanks were 90% full, the drive could produce 68 m/s2 acceleration (6.9 g). Which was quite a few times higher than Epstein was expecting. He was instantly pinned by the acceleration and could not turn the drive off. The drive burned until the tanks were dry, which took 37 hours and had delta-V'd the yacht up to 5% c (roughly 15,000,000 m/s). By this time Epstein was long dead and the yacht can still be seen by a powerful enough telescope on its way to nowhere.

    The drive was some species of fusion drive using Epstein's innovative "magnetic coil exhaust". The yacht started with propellant tanks 90% full. After 10 minutes they had dropped to 89.6% full. After 2 more minutes 89.5%. After 2.5 more minutes 89.4%. After 37 hours 0% full.

    Thus ends the canon knowledge.


    My Analysis

    Now comes conjecture on my part. Please note this is totally non-canon and unofficial, I'm just playing with numbers here.

    I made lots of assumptions. I assumed the yacht had a mass ratio of 4, since Jerry Pournelle was of the opinion that was about the maximum for an economical spacecraft. I also assumed the yacht had a mass of 15 metric tons, because that was the wet mass of the Apollo Command and Service module.

    What does those assumptions give us?

    If the delta V is 5% c and the mass ratio is 4, the exhaust velocity has to be about 11,000,000 m/s, or 3.7% c. ( Ve = ΔV / ln[R] )

    Looking over the theoretical maximum exhaust of various fusion reactions we find we are in luck. Pretty much all of them can manage more than that exhaust velocity, with the exception of Deuterium-Helium3.

    Given an acceleration of 68 m/s2 and estimated wet mass of 15,000 kg, the thrust has to be 1,000,000 Newtons. ( F = Mc * A ). For one engine.

    If we use the estimated thrust of 1,000,000 Newtons and estimated exhaust velocity of 11,000,000 m/s, the propellant mass flow is an economical 0.09 kg/s. ( mDot = F / Ve )

    Of course the thrust power is a whopping 5.5 terawatts, but what did you expect from a torchship? ( Fp = (F * Ve ) / 2 )

    Feel free to make your own assumptions and see what results you get.


    Scott Manley's Analysis

    The legendary Scott Manley does his own analysis of Epstein's experimental ship in this video. He figures that: Yes a fusion drive will give the needed performance but No the heat from the drive will vaporize the entire ship in a fraction of a second.


    Monstah's Analysis

    Independently of assuming a specific ship's mass and propellant fraction, he takes the hard canon facts of Epstein's experimental ship having an acceleration of 6.9 gees and a delta V of 5% c, and calculates a result of an exhaust velocity of 13,000,000 meters per second and a mass ratio of 3.0 to 3.3.

    Start with mass ratio equation

    R = M / Me = (Mpt + Me) / Me

    where Me and Mpt are dry and propellant masses.

    Now, substitute an expression for propellant mass

    Mpt = mDot * t

    where mDot is the mass flow and t the time till total consumption (t=37 hours is given in the problem).

    Mass flow mDot can be calculated from thrust and exhaust velocity

    mDot = F / Ve

    Thrust (and fuel flow) can be assumed constant; calculated at the initial time, it's

    F = m * A

    for A = 68 m/s2 (6.9 gees) and m the initial mass (same used for mass fraction, M)

    We now have

    R = (Me + Mpt) / Me = (Me + (mDot * t)) / Me = (Me + (m * A / Ve) * t) / Me

    The equation above simplifies to

    1 / (1-(t*A / Ve)) = R = expV / Ve)

    where ΔV is 5% c given

    We now have an equation with a single variable, Ve! However, it's an ugly ass equation where Ve appears both as a denominator in an exponent and a denominator in a nested fraction. Ew.

    Wolfram Alpha to the rescue! \o/

    Telling it to solve for Ve, we get

    Ve = A * ΔV * t / (A * t * productlog(-ΔV / (A*t) * exp(-ΔV / (A*t))) + ΔV)

    where productlog() is the "ProductLog function". Don't ask.

    If you just plug in the values where they appear you'll get a timeout, so I'll precalculate A*ΔV * t, A*t and ΔV / (A*t), convert everything to meters and seconds and ignore the units, and throw in WolframAlpha again.

    The answer is Ve ~ 13,000 km/s (13,000,000 m/s or 4.3% c).

    Very close to your 11,000 km/s (but, importantly, independently of any assumptions of ship mass and fuel fraction). You assumed R = 4, the result here is closer to 3. But then, our initial time had the ship at 90% propellant tank capacity, so the ship's actual design is for something around Mass Ratio 3.3

    From MONSTAH

    Erin Schmidt's Analysis

    Erin Schmidt did a quick analysis of the Epstein-drive ship Rocinate (not Epstein's experimental ship), hinging on some very loose assumptions. He figures the thrust power is 11 terawatts. Egads.

    SWAG
    Mass Ratio R = 3.0
    Dry Mass Me = 500,000 kg

    NOVEL STATES Rocinante can accelerate at 0.25 g for 3 to 4 weeks (2.45 m/s2 for 2.419×106 seconds)
    Delta-V
    2.45 * 2.419×106 = 5,933,000 m/s = 6000 m/s delta-V

    Specific Impulse
    Isp = (ΔV / ln(R)) / g0
    Isp = (5,933,000 / ln(3.0)) / 9.81
    Isp = 551,000 seconds

    Exhaust Velocity
    Ve = ΔV / ln(R)
    Ve = 5,933,000 / 1.0986
    Ve = 5,400,000 m/s = 0.018c = 18% c

    Wet Mass
    M = R * Me
    M = 3.0 * 500,000
    M = 1,500,000 kg

    Thrust
    F = M * 0.25 * g0
    F = 1,500,000 * 0.25 * 9.81
    F = 3,680,000 Newtons = 3700 kN

    Thrust Power
    Fp = (F * Ve ) / 2
    Fp = (3,700,000 * 6,000,000 ) / 2
    Fp = 11,100,000,000,000 Watts = 11 TW

    Nuclear Thermal

    Basically a Nuclear Thermal Rockets (NTR) is a nuclear reactor where the propellant is the coolant. And instead of the coolant being directed into a cooling tower, it instead exits out the exhaust nozzle, creating thrust.

    They use the heat generated from a nuclear reaction to heat up propellant. The nuclear reaction is controlled by adjusting the amount of free neutrons inside the mass of fissioning material (like all nuclear reactors do, generally with reactor control drums).

    As a side effect, if you have a cluster of several such engines it is vitally important to have distance and neutron isolation shields between them. Otherwise the nuclear reaction in each engine will flare out of control due to the neutron flux from its neighbor engines.

    The fact that the propellant is also the coolant means that after a thrusting period is over, you still have to vent propellant through the reactor after you turn it off. Until the reactor goes cold.

    Exhaust Velocity Limits on Nuclear Thermal Rockets

    The exhaust velocity and specific impulse of NTR are proportional to the thermal levels inside the reactor. Which a fancy way to say "the hotter the reactor, the higher the exhaust velocity."

    Which brings us to the exhaust velocity limit. Solid core NTRs use a solid-core nuclear reactor. Such reactors are made of matter. And as with all matter, if you raise the temperature, at some point it will get hot enough so that the reactor melts. Which means the core ain't solid any more. This is a bad thing, technical term is Nuclear meltdown, non-technical term is The China Syndrome. The molten remains of the reactor shoots out the exhaust bell like a radioactive bat from hell, killing anybody nearby and leaving the spacecraft without an engine.

    To avoid this unhappy state of affairs, solid core NTRs are limited to a temperature of about 2,750 K (4,490° F), which translates into an exhaust velocity limit of about 8,093 m/s (with liquid hydrogen, double that if you've manage to figure out how to stablize monoatomic hydrogen). Some fancy high temperature designs can push that up to an exhaust velocity of about 11,800 m/s.

    Lateral thinking rocket engineers had the brainstorm of "what if the reactor starts out molten in the first place?" This lead to the design of liquid-core NTR, with a temperature of 5,250 K and an exhaust velocity of 16,000 m/s.

    Because rocket engineers can't resist turning it up to 11, they figured if liquid is good then gaseous should be even better. This is the open-cycle gas-core NTR, with an exhaust velocity of a whopping 34,000 m/s.

    The major draw-back of open-cycle GCNTR is that there is no feasible to prevent any of the radioactive fission products and unburnt uranium from escaping out the exhaust. Which more or less makes the exhaust plume a weapon of mass destruction, and significatly increases the radiation exposure on the poor ship's crew.

    Engineers tried to fix the radiation problem of the open-cycle GCNTR by making it closed-cycle; that is, preventing physical contact between the gaseous uranium and the propellant. This turned out to be an attempt to have your cake and eat it too. The entire point of gas core was to allow outrageous engine temperatures by not having any solid components inside the engine, but sadly baffles that prevent the uranium from mixing with the propellant are solid components. They managed an makeshift solution, but the price was the exhaust velocity was cut in half.

    Solid Core

    Solid Core NTR
    3200° K
    Exhaust velocity (H1)16,000? m/s
    Exhaust velocity (H2)8,093 m/s
    Exhaust velocity (CH4)6,318 m/s
    Exhaust velocity (NH3)5,101 m/s
    Exhaust velocity (H2O)4,042 m/s
    Exhaust velocity (CO2)3,306 m/s
    Exhaust velocity (CO or N2)2,649 m/s

    Nuclear thermal rocket / solid core fission. It's a real simple concept. Put a nuclear reactor on top of an exhaust nozzle. Instead of running water through the reactor and into a generator, run hydrogen through it and into the nozzle. By diverting the hydrogen to a turbine generator 60 megawatts can be generated. The reactor elements have to be durable, since erosion will contaminate the exhaust with fissionable materials. The exhaust velocity limit is fixed by the melting point of the reactor.

    Solid core nuclear thermal rockets have a nominal core temperature of 2,750 K (4,490° F).

    Hydrogen gives the best exhaust velocity, but the other propellants are given in the table since a spacecraft may be forced to re-fuel on whatever working fluids are available locally (what Jerry Pournelle calls "Wilderness re-fuelling", Robert Zubrin calls "In-situ Resource Utilization", and I call "the enlisted men get to go out and shovel whatever they can find into the propellant tanks"). For thermal drives in general, and NTR-SOLID in particular, the exhaust velocity imparted to a particular propellant by a given temperature is proportional to 1 / sqrt( molar mass of propellant chemical ).

    The value for "hydrogen" in the table is for molecular hydrogen, i.e., H2. Atomic hydrogen would be even better, but unfortunately it tends to explode at the clank of a falling dust speck (Heinlein calls atomic hydrogen "Single-H"). Another reason to avoid hydrogen is the difficulty of storing the blasted stuff, and its annoyingly low density (Ammonia is about eight times as dense!). Exhaust velocities are listed for a realistically attainable core temperature of 3200 degrees K for the propellants Hydrogen (H2), Methane (CH4), Ammonia (NH3), Water (H2O), Carbon Dioxide (CO2), Carbon Monoxide (CO), and Nitrogen (N2).

    The exhaust velocities are larger than what one would expect given the molecular weight of the propellants because in the intense heat they break down into their components. Ammonia is nice because it breaks down into gases (Hydrogen and Nitrogen). Methane is nasty because it breaks down into Hydrogen and Carbon, the latter tends to clog the reactor with soot deposits. Water is most unhelpful since it doesn't break down much at all.

    Dr. John Schilling figures that as an order of magnitude guess, about one day of full power operation would result in enough fuel burnup to require reprocessing of the fissionable fuel elements. (meaning that while there is still plenty of fissionables in the fuel rod, enough by-products have accumulated that the clogged rod produces less and less energy) A reprocessing plant could recover 55-95% of the fuel. With reprocessing, in the long term each totally consumed kilogram of plutonium or highly enriched uranium (HEU) will yield ~1E10 newton-seconds of impulse at a specific impulse of ~1000 seconds.

    Dr. Schilling also warns that there is a minimum amount of fissionable material for a viable reactor. Figure a minimum of 50 kilograms of HEU.

    One problem with solid-core NTRs is that if the propellant is corrosive, that is, if it is oxidizing or reducing, heating it up to three thousand degrees is just going to make it more reactive. Without a protective coating, the propellant will start corroding away the interior of the reactor, which will make for some real excitement when it starts dissolving the radioactive fuel rods. What's worse, a protective coating against an oxidizing chemical is worthless against a reducing chemical, which will put a crimp in your wilderness refueling. And trying to protect against both is an engineering nightmare. Oxidizing propellants include oxygen, water, and carbon dioxide, while reducing propellants include hydrogen, ammonia, and methane. Carbon Monoxide is neither, as the carbon atom has a death-grip on the oxygen atom.

    Keep in mind that the oxidizing/reducing effect is only a problem with solid-core NTRs, not the other kinds. This is because only the solid-core NTRs have solid reactor elements exposed to the propellant (for heating).

    HOW VINTAGE ROCKET TECH COULD BE NASA'S TICKET TO MARS AND BEYOND

    Dangerous radiation. Overstuffed pantries. Cabin fever. NASA could sidestep many of the impediments to a Mars mission if they could just get there faster. But sluggish chemical rockets aren't cutting it — and to find what comes next, one group of engineers is rebooting research into an engine last fired in 1972.

    The energy liberated by burning chemical fuel brought astronauts to the moon, but that rocket science makes for a long trip to Mars. And although search for a fission-based shortcut dates back to the 1950s, such engines have never flown. In August, NASA boosted those efforts when the agency announced an $18.8-million-dollar contract with nuclear company BWXT to design fuel and a reactor suitable for nuclear thermal propulsion (NTP), a rocket technology that could jumpstart a new era of space exploration.

    "The strengths with NTP are the ability to do the very fast round trip [to Mars], the ability to abort even if you're 2 to 3 months into the missions, the overall architectural robustness, and also the growth potential to even more advanced systems," Michael Houts, principal investigator for the NTP project at NASA's Marshall Space Flight Center, told Space.com. [Superfast Space Propulsion Concepts (Images)]

    Superior gas mileage

    NTP rockets would pull all that off by offering about twice the bang for the buck that chemical rockets do (exhaust velocity of 8,000 m/s as opposed to 4,400 m/s). Rather than burning fuel with oxygen, a nuclear fission reactor would serve as a powerful furnace, heating liquid hydrogen and expelling the resulting gas for thrust. How much oomph a rocket gets from its fuel depends largely on how fast it can hurl particles out the back, which in turn hinges on their mass. And NTP's single or double hydrogen atoms would be up to a dozen times lighter than chemical rocket outputs. 

    That atomic bean counting could add up to significant time savings. "Nuclear thermal propulsion can enable you to get to Mars faster, on the order of twice as fast," said Vishal Patel, a researcher involved in subcontract work for BWXT at the Ultra Safe Nuclear Corp. in Los Alamos, New Mexico. "We're looking at nice 3- to 4-month transit times."

    New tricks with an old technology

    Unlike truly exotic propulsion proposals using antimatter or nuclear fusion, researchers have long considered nuclear fission rockets technologically feasible. Concrete development began with the Atomic Energy Commission's Project Rover in 1955 — three years before NASA's founding — and continued with the NERVA rocket prototype, which fired for nearly 2 hours straight during ground tests before budget cuts ended development in 1972. 

    By then, NASA had already canceled Apollo 18 through 20, as well as Saturn V rocket production. When Mars plans followed suit, the multibillion-dollar NERVA project lost its main purpose, Houts said. The technology saw a brief revival in the late '80s and early '90s with the Space Nuclear Thermal Propulsion (SNTP) program, which also ran out of funding before flight testing.  

    But now, with interest turning back toward Mars, past research is finding new life in current projects. 

    "The key thing is, [the NERVA rocket] was extremely well documented," said John Helmey, project manager for BWXT's NTP project. "We aren't starting from scratch. We're building upon really good work that was done back in that time frame," he told Space.com. Over the course of the contract, which extends through 2019, BWXT will develop conceptual designs focusing on fuel elements and the reactor core.

    Three main challenges distinguish modern efforts from the legacy research.

    Nuclear-testing rules have changed, said Jonathon Witter, BWXT NTP project chief engineer. The potential for trace levels of radioactivity in the engine exhaust means that engineers can no longer let clouds of hydrogen gas billow into the atmosphere. Instead, BWXT plans to test a trick developed at NASA's Stennis Space Center and combust the hydrogen gas with oxygen to make easy-to-catch water. Early, small-scale demonstrations will use non-nuclear hydrogen gas to test this exhaust-capturing method, but water from future nuclear tests could be decontaminated with off-the-shelf technology.

    Engineers are also redesigning the fuel elements with new materials surrounding the uranium fuel particles, according to Witter. Rocket efficiency depends on temperature too, and BWXT expects that a ceramic and tungsten composite will allow for better operation at higher temperatures.

    What's more, NERVA ran on 90 percent highly enriched uranium that would today qualify as weapons-grade. But because the fission process throws off more than enough heat, those levels are overkill, Patel said. BWXT's designs will harness material enriched to just below 20 percent (19.75%), putting it in the less-tightly regulated low enriched uranium (LEU) category. On top of allowing safer reactors, the modest levels of fissionable material could open the door to more public-private partnerships. (I'm sure that got Elon Musk's attention)

    "The LEU thing really enables the idea that non-governmental entities can get in on this," Patel said. "It's potentially game changing."

    But extensive design and many years of testing separate NTP's on-paper potential from single-season jaunts to the Red Planet, and nuclear space technology's history of false starts makes it a long shot for NASA's early Mars missions, currently scheduled for the 2030s. "It's one of several advanced propulsion options, Houts said. "There're a lot of good options that use chemical systems, and options that use electric propulsion."

    Scott Hall, a developer of one such electric propulsion prototype that recently broke records at the University of Michigan, says he'd love to see any of these technologies get into space, but doesn't think it'll happen soon. 

    "Optimistically, it will be 15 years," Hall said of his high-powered ion thruster, "and realistically it's probably more like 50… The process is just moving so slowly, and I imagine the nuclear guys are in a similar boat." 

    But whether it takes one decade or 10, Houts thinks nuclear technology could transform space exploration. He cites Martian power plants and the possibility of spacecraft that refuel from naturally occurring resources like water or methane as examples of far-off possibilities. 

    "What we're talking about is a first generation system. The systems beyond that could have extremely advanced capabilities," he said.

    Nasty Methane Carbon Build-up

         Rip started to announce his name, rank, and the fact that he was reporting as ordered. Commander O’Brine brushed his words aside and stated flatly, “You’re a Planeteer. I don’t like Planeteers.”
         Rip didn’t know what to say, so he kept still. But sharp anger was rising inside of him.
         O’Brine went on, “Instructions say I’m to hand you your orders en-route. They don’t say when. I’ll decide that. Until I do decide, I have a job for you and your men. Do you know anything about nuclear physics?”
         Rip’s eyes narrowed. He said cautiously, “A little, sir.”
         “I’ll assume you know nothing. Foster, the designation SCN means Space Cruiser, Nuclear. This ship is powered by a nuclear reactor. In other words, an atomic pile. You’ve heard of one?”
         Rip controlled his voice, but his red hair stood on end with anger. O’Brine was being deliberately insulting. This was stuff any Planeteer recruit knew. “I’ve heard, sir.”
         “Fine. It’s more than I had expected. Well, Foster, a nuclear reactor produces heat. Great heat. We use that heat to turn a chemical called methane into its component parts. Methane is known as marsh gas, Foster. I wouldn’t expect a Planeteer to know that. It is composed of carbon and hydrogen. When We pump it into the heat coils of the reactor, it breaks down and creates a gas that burns and drives us through space. But that isn’t all it does.”
         Rip had an idea What was coming, and he didn’t like it. Nor did he like Commander O’Brine. It was not until much later that he learned that O’Brine had been on his way to Terra to see his family for the first time in four years when the cruiser’s orders were changed. To the commander, whose assignments had been made necessary by the needs of the Special Order Squadrons, it was too much. So he took his disappointment out on the nearest Planeteer, who happened to be Rip.
         “The gases go through tubes,” O’Brine went on. “A little nuclear material also leaks into the tubes. The tubes get coated With carbon, Foster. They also get coated with nuclear fuel. We use thorium. Thorium is radioactive. I won’t give you a lecture on radioactivity, Foster. But thorium mostly gives off the kind of radiation known as alpha particles. Alpha is not dangerous unless breathed or eaten. It won’t go through clothes or skin. But when mixed with fine carbon, thorium alpha contamination makes a mess. It’s a dirty mess, Foster. So dirty that I don’t want my spacemen to fool with it.

    (ed note: now in a real solid-core NTR, nuclear fuel leaking from the reactor elements is a major malfunction)

         “I want you to take care of it instead,” O’Brine said. “You and your men. The deputy commander will assign you to a squadron. Settle in, then draw equipment from the supply room and get going. When I want to talk to you again, I’ll call for you. Now blast off, Lieutenant, and rake that radiation. Rake it clean.”
         Rip forced a bright and friendly smile. “Yes, sir,” he said sweetly. “We’ll rake it so clean you can see your face in it, sir.” He paused, then added politely, “If you don’t mind looking at your face, sir—to see how clean the tubes are, I mean.”
         Rip turned and got out of there.
         Koa was waiting in the passageway outside. Rip told him what had happened, mimicking O’Brine’s Irish accent.
         The sergeant-major shook his head sadly. “This is what I meant, Lieutenant. Cruisers don’t clean their tubes more’n once in ten accelerations. The commander is just thinking up dirty work for us to do, like I said.”
         “Never mind,” Rip told him. “Let’s find our squadron and get settled, then draw some protective clothing and equipment. We’ll clean his tubes for him. Our turn will come later.”
         He remembered the last thing Joe Barris had said, only a few hours before. “Joe was right,” he thought. “To ourselves we’re supermen, but to the spacemen we’re just simps.” Evidently O’Brine was the kind of space officer who ate Planeteers for breakfast.
         Rip thought of the way the commander had turned red with rage at that crack about his face, and resolved, “He may eat me for breakfast, but I’ll try to be a good, tough mouthful!”
         Commander O’Brine had not exaggerated. The residue of carbon and thorium on the blast tube walls was stubborn, dirty, and penetrating. It was caked on in a solid sheet, but when scraped, it broke up into fine powder.
         The Planeteers wore coveralls, gloves, and face masks with respirators, but that didn’t prevent the stuff from sifting through onto their bodies. Rip, who directed the work and kept track of the radiation with a gamma-beta ion chamber and an alpha proportional counter, knew they would have to undergo personal decontamination.

    (ed note: in a real rocket, the tubes would be in vacuum, so the crew would need space suits. The tubes would also be close to the reactor. The reactor is not very radioactive if it is shut down, except for neutron activation.)

         He took a reading on the ion chamber. Only a few milliroentgens of beta and gamma radiation. That was the dangerous kind, because both beta particles and gamma rays could penetrate clothing and skin. But the Planeteers wouldn’t get enough of a dose to do any harm at all. The alpha count was high, but so long as they didn’t breathe any of the dust it was not dangerous.
         The Scorpius had six tubes. Rip divided the Planeteers into two squads, one under his direction and one under Koa’s. Each tube took a couple of hours’ hard Work. Several times during the cleaning the men would leave the tube and go into the main mixing chamber while the tube was blasted with live steam to throw the stuff they had scraped off out into space.
         Each squad was on its last tube when a spaceman arrived. He saluted Rip. “Sir, the safety officer says to secure the tubes.”
         That could mean only one thing: deceleration. Rip rounded up his men. “We’re finished. The safety officer passed the word to secure the tubes, which means we’re going to decelerate.” He smiled grimly. “You all know they gave us this job just out of pure love for the Planeteers. So remember it when you go through the control room to the decontamination chamber.”
         The Planeteers nodded enthusiastically.
         Rip led the way from the mixing chamber through the heavy safety door into the engine control room. His entrance was met with poorly concealed grins by the spacemen.
         Halfway across the room Rip turned suddenly and into Sergeant major Koa. Koa fell to the deck arms flailing for balance—but flailing against his protective clothing. The other Planeteers rushed to pick him up, and somehow all their arms and hands beat against each other.
         The protective clothing was saturated with fine dust. It rose from them in a choking cloud, was picked up, and dispersed by the ventilating system. It was contaminated dust. The automatic radiation safety equipment filled the ship with an earsplitting buzz of warning. Spacemen clapped emergency respirators to their faces and spoke unkindly of Rip’s Planeteers in the saltiest space language they could think of.
         Rip and his men picked up Koa and continued the march to the decontamination room, grinning under their respirators at the consternation around them. There was no danger to the spacemen since they had clapped on respirators the moment the warning sounded. But even a little contamination meant the whole ship had to be gone over with instruments, and the ventilating system would have to be cleaned.
         The deputy commander met Rip at the door of the radiation room. Above the respirator, his face looked furious.
         “Lieutenant,” he bellowed, “haven’t you any more sense than to bring contaminated clothing into the engine control room?”
         Rip was sorry the deputy commander couldn’t see him grinning under his respirator. He said innocently, “No, sir. I haven’t any more sense than that.”
         The deputy grated, “I’ll have you up before the Discipline Board for this.”
         Rip was enjoying himself thoroughly. “I don’t think so, sir. The regulations are very clear. They say, ‘It is the responsibility of the safety officer to insure compliance with all safety regulations both by complete instructions to personnel and personal supervision.’ Your safety officer didn’t instruct us and he didn’t supervise us. You better run him up before the Board.”
         The deputy commander made harsh sounds into his respirator. Rip had him, and he knew it. “He thought even a stupid Planeteer had sense enough to obey radiation safety rules,” he yelled.
         “He was wrong,” Rip said gently. Then, just to make himself perfectly clear, he added, “Commander O’Brine was within his rights when he made us rake radiation. But he forgot one thing. Planeteers know the regulations, too. Excuse me, sir. I have to get my men decontaminated.”
         Inside the decontamination chamber, the Planeteers took off their masks and faced Rip with admiring grins. For a moment he grinned back, feeling pretty good. He had held his own with the spacemen, and he sensed that his men liked him.
         “All right,” he said briskly. “Strip down and get into the showers.”
         In a few moments they were all standing under the chemically treated water, washing off the contaminated dust. Rip paid special attention to his hair, because that was where the dust was most likely to stick. He had it well lathered when the Water suddenly cut off. At the same moment, the cruiser shuddered slightly as control blasts stopped its spinning and left them all weightless. Rip saw instantly what had happened. He called, “All right, men. Down on the floor.”
         The Planeteers instantly slid to the shower deck. In a few seconds the pressure of deceleration pushed at them.
         “I like spacemen,” Rip said wryly. “They wait until just the right moment before they cut the water and decelerate. Now we’re stuck in our birthday suits until we land—wherever that may be.”

    From Rip Foster Rides the Gray Planet by Blake Savage {Harold Leland Goodwin} (1952)

    NERVA

    Nuclear Engine for Rocket Vehicle Applications. The first type of NTR-SOLID propulsion systems. It used reactor fuel rods surrounded by a neutron reflector. Unfortunately its thrust to weight ratio is less than one, so no lift-offs with this rocket. The trouble was inadequate propellant mass flow, the result of trying to squeeze too much hydrogen through too few channels in the reactor.

    NERVA
    Thrust Power0.198-0.065 GW
    Exhaust velocitySee Table
    Thrust49,000 n
    Engine mass10 tonne
    T/W >1.0no
    NERVA (H2)
    Exhaust Velocity8,093 m/s
    Specific Impulse825 s
    Thrust49,000 N
    Thrust Power0.2 GW
    Mass Flow6 kg/s
    Total Engine Mass10,000 kg
    T/W0.50
    FuelFission:
    Uranium 235
    ReactorSolid Core
    RemassLiquid Hydrogen
    Remass AccelThermal Accel:
    Reaction Heat
    Thrust DirectorNozzle
    Specific Power50 kg/MW
    Resuable Nuclear Shuttle [+]
    Propulsion SystemNERVA
    Exhaust Velocity8,000 m/s
    Specific Impulse815 s
    Thrust344,000 N
    Thrust Power1.4 GW
    Mass Flow43 kg/s
    Wet Mass170,000 kg
    Dry Mass30,000 kg
    Mass Ratio5.67 m/s
    ΔV13,877 m/s
    Widmer Mars Mission [+]
    Propulsion SystemNERVA
    Exhaust Velocity8,000 m/s
    Specific Impulse815 s
    Thrust580,000 N
    Thrust Power2.3 GW
    Mass Flow72 kg/s
    Wet Mass400,000 kg
    Dry Mass150,000 kg
    Mass Ratio2.67 m/s
    ΔV7,847 m/s
    HELIOS 2nd Stage [+]
    Propulsion SystemNTR Solid
    Exhaust Velocity7,800 m/s
    Specific Impulse795 s
    Thrust981,000 N
    Thrust Power3.8 GW
    Mass Flow126 kg/s
    Wet Mass100,000 kg
    Dry Mass6,800 kg
    Mass Ratio14.71 m/s
    ΔV20,968 m/s
    Atomic V-2 [+]
    Propulsion SystemNTR Solid
    Exhaust Velocity8,980 m/s
    Specific Impulse915 s
    Thrust1,050,000 N
    Thrust Power4.7 GW
    Mass Flow117 kg/s
    Total Engine Mass4,200 kg
    T/W25
    Wet Mass42,000 kg
    Dry Mass17,000 kg
    Mass Ratio2.47 m/s
    ΔV8,122 m/s
    Specific Power1 kg/MW

    Pewee-class

    Pewee-class Engine
    Exhaust Velocity9,200 m/s
    Specific Impulse940 s
    Thrust111,200 N
    (25 klbf)
    Thrust Power512 MWt
    Mass Flow12.5 kg/s
    Total Engine Mass3,240 kg
    T/W3.5
    FuelFission:
    Uranium 235
    Fissle Loading0.25 g U per cm3
    Max Fuel Temp2940 K
    Fuel Element
    Length
    1.32 m
    U-235 Mass36.8 kg
    Chamber Pressure1000 psi
    ReactorSolid Core
    RemassLiquid Hydrogen
    Remass AccelThermal Accel:
    Reaction Heat
    Thrust DirectorNozzle
    Engine Length
    (inc. skirt ext)
    7.01 m
    Nozzle Skirt
    Extension
    2.16 m
    Nozzle Exit Dia1.87 m
    Specific Power6.3 kg/MW
    Longest Single
    Burn
    44.5 min
    Total Burn
    Duration
    79.2 min
    Num Burns4

    The 25 kilo-pounds-force (25 klbf) "Pewee" solid-core nuclear thermal rocket was the smallest engine size tested during U.S. Project Rover. While small, a cluster of three is adequate for a typical Mars mission. Single engines were adequate for unmanned scientific interplanetary missions or small nuclear tugs.

    A cluster of three Pewee-class engines were selected to be used with NASA's Design Reference Architecture (DRA 5.0) Mars Mission, but later designs replaced them with a cluster of three SNRE-class.

    One source suggested that each engine would require a 2,150 kg anti-radiation shadow shield to protect the crew (6.45 metric tons total for a cluster of three), assuming an 80 meter separation between the engines and the habitat module and all the liquid hydrogen propellant tanks used as additional shielding.

    SNRE-class

    The Small Nuclear Rocket Engine (SNRE) is from the report Affordable Development and Demonstration of a Small NTR Engine and Stage: How Small is Big Enough? by Stanley Borowsky et al (2015). The scientists wanted to promote the development of a right-sized solid core nuclear thermal rocket that was as small as possible, but no smaller.

    The 111,200 N (25 klbr) "Pewee-class" from the U.S. Project Rover was the smallest Rover engine. A cluster of three was specified for the NASA DRA 5.0 reference, but Borowsky et al determined that was still a bit larger than was strictly necessary.

    They looked at a 33,000 Newton (7.5 klbr) engine which was pretty much the smallest NTR possible due to limits on nuclear criticality. There is a minimum amount of fissionable fuel for a reactor, or it just cannot support a chain reaction. But it was a bit too small to do anything useful, even in a cluster of three. About all it was good for was an unmanned robotic science mission.

    A 73,000 Newton (16.5 klbr) engine on the other hand could perform quite a few proposed missions. It hit the goldilocks zone, it was just right. Some researchers took designs from NASA's Design Reference Architecture (DRA 5.0) Mars Mission and swapped out the trio of Pewee-class engines for a trio of SNREs.

    The engine uses a graphite composite core, because that allowed them to build on the expertise from the old NERVA program.

    One source suggested that each SNRE-class would require a 2,000 kg anti-radiation shadow shield to protect the crew (six metric tons for a trio of SNREs), assuming an 80 meter separation between the engines and the habitat module.

    The criticality-limited engine has a retractable section of the nozzle, the SNRE-class engine has a nozzle skirt that folds on a hinge (see diagrams below). These are strictly for launch purposes. The spacecraft is boosted in modular parts by several flights of launch vehicle, and assembled in orbit. By retracting/folding the engine nozzle the engine's overall length is reduced enough so that the engine, the liquid hydrogen fuel tank and a small mission payload can be crammed into the launch vehicle's payload faring. Once the spacecraft is assembled, the nozzles are unretracted/unfolded and permanently latched into place.

    Criticality-limited Engine
    Exhaust Velocity8,770 m/s
    Specific Impulse894 s
    Thrust33,000 N
    (7.4 klbf)
    Thrust Power145 MWt
    Mass Flow3.8 kg/s
    Total Engine Mass1,770 kg
    T/W1.9
    FuelFission:
    Uranium 235
    Max Enrichment93% U-235 wt
    Num Fuel Elements260
    Num Tie-tube
    Elements
    251
    Fissle Loading0.6 g U per cm3
    Max Fuel Temp2736 K
    U-235 Mass27.5 kg
    ReactorSolid Core
    RemassLiquid Hydrogen
    Remass AccelThermal Accel:
    Reaction Heat
    Thrust DirectorNozzle
    Specific Power12.2 kg/MW
    Engine Length6.19 m
    Fuel Length
    Pressure Vessel
    Diameter
    0.877 m
    Nozzle Exit
    Diameter
    1.32 m
    Longest Single
    Burn
    22 min
    Total Burn
    Duration
    29.5 min
    Num Burns2
    SNRE-class Engine
    Exhaust Velocity8,829 m/s
    Specific Impulse900 s
    Thrust73,000 N
    (16.7 klbf)
    Thrust Power367 MWt
    Mass Flow8.4 kg/s
    Total Engine Mass2,400 kg
    T/W3.06
    FuelFission:
    Uranium 235
    Max Enrichment93% U-235 wt
    Num Fuel Elements564
    Num Tie-tube
    Elements
    241
    Fissle Loading0.6 g U per cm3
    Max Fuel Temp2,726 K
    U-235 Mass59.6 kg
    ReactorSolid Core
    RemassLiquid Hydrogen
    Remass AccelThermal Accel:
    Reaction Heat
    Thrust DirectorNozzle
    Specific Power6.5 kg/MW
    Engine Length4.46 m
    Fuel Length0.89 m
    Pressure Vessel
    Diameter
    0.98 m
    Nozzle Exit
    Diameter
    2.26 m
    Longest Single
    Burn
    21.4 min
    Total Burn
    Duration
    55 min
    Num Burns5

    NERVA Derivative

    NERVA Deriv
    Exhaust Velocity8,085 m/s
    Specific Impulse824 s
    Thrust334,061 N
    Thrust Power1.4 GW
    Mass Flow41 kg/s
    Total Engine Mass10,100 kg
    T/W3
    FuelFission:
    Uranium 235
    ReactorSolid Core
    RemassLiquid Hydrogen
    Remass AccelThermal Accel:
    Reaction Heat
    Thrust DirectorNozzle
    Specific Power7 kg/MW

    DUMBO

    General Dumbo
    Thrust Power14.0-4.6 GW
    Exhaust velocitySee Table
    Thrust3,500,000 n
    Engine mass5 tonne
    T/W >1.0yes
    Dumbo (H2)
    Exhaust Velocity8,093 m/s
    Specific Impulse825 s
    Thrust3,500,000 N
    Thrust Power14.2 GW
    Mass Flow432 kg/s
    Total Engine Mass5,000 kg
    T/W71
    FuelFission:
    Uranium 235
    ReactorSolid Core
    RemassLiquid Hydrogen
    Remass AccelThermal Accel:
    Reaction Heat
    Thrust DirectorNozzle
    Dumbo Model A
    Engine mass0.7 tonne
    Thrust400,000 n
    Propellant mass flow52 kg/sec
    Exhaust velocity7,700 m/sec
    Engine Height0.6 m
    Engine Radius0.3 m
    Engine Volume0.2 m3
    T/W58
    Dumbo Model B
    Engine mass2.8 tonne
    Thrust3,560,000 n
    Propellant mass flow460 kg/sec
    Exhaust velocity7,700 m/sec
    Engine Height0.6 m
    Engine Radius1.0 m
    Engine Volume1.8 m3
    T/W130
    Dumbo Model C
    Engine mass2.1 tonne
    Thrust400,000 n
    Propellant mass flow48 kg/sec
    Exhaust velocity8,300 m/sec
    Engine Height0.6 m
    Engine Radius0.4 m
    Engine Volume0.3 m3
    T/W20

    This was a competing design to NERVA. It was shelved political decision that, (in order to cut costs on the atomic rocket projects) required both projects to use an already designed NEVRA engine nozzle. Unfortunately, said nozzle was not compatible with the DUMBO active cooling needs. Dumbo does, however, have a far superior mass flow to the NERVA, and thus a far superior thrust. Dumbo actually had a thrust to weight ratio greater than one. NASA still shelved DUMBO because [a] NERVA used off the shelf components and [b] they knew there was no way in heck that they could get permission for nuclear lift-off rocket so who cares if T/W < 0? You can read more about Dumbo in this document.

    Note that the "engine mass" entry for the various models does not include extras like the mass of the exhaust nozzle, mass of control drums, or mass of radiation shadow shield.

    Pebble Bed

    Pebble Bed
    Exhaust Velocity9,530 m/s
    Specific Impulse971 s
    Thrust333,617 N
    Thrust Power1.6 GW
    Mass Flow35 kg/s
    Total Engine Mass1,700 kg
    T/W20
    FuelFission:
    Uranium 235
    ReactorSolid Core
    RemassLiquid Hydrogen
    Remass AccelThermal Accel:
    Reaction Heat
    Thrust DirectorNozzle
    Specific Power1 kg/MW

    Particle bed / nuclear thermal rocket AKA fluidized-bed, dust-bed, or rotating-bed reactor. In the particle-bed reactor, the nuclear fuel is in the form of a particulate bed through which the working fluid is pumped. This permits operation at a higher temperature than the solid-core reactor by reducing the fuel strength requirements . The core of the reactor is rotated (approximately 3000 rpm) about its longitudinal axis such that the fuel bed is centrifuged against the inner surface of a cylindrical wall through which hydrogen gas is injected. This rotating bed reactor has the advantage that the radioactive particle core can be dumped at the end of an operational cycle and recharged prior to a subsequent burn, thus eliminating the need for decay heat removal, minimizing shielding requirements, and simplifying maintenance and refurbishment operations.

    Cermet

    Cermet NERVA
    Exhaust Velocity9,120 m/s
    Specific Impulse930 s
    Thrust445,267 N
    Thrust Power2.0 GW
    Mass Flow49 kg/s
    Total Engine Mass9,000 kg
    T/W5
    FuelFission:
    Uranium 235
    ReactorSolid Core
    RemassLiquid Hydrogen
    Remass AccelThermal Accel:
    Reaction Heat
    Thrust DirectorNozzle
    Specific Power4 kg/MW
    Cermet NERVA
    Cermet NERVA
    Exhaust Velocity9,810 m/s
    Specific Impulse1,000 s
    Thrust134,400 N
    Thrust Power0.7 GW
    Mass Flow14 kg/s
    Total Engine Mass32,546 kg
    T/W0.42
    Frozen Flow eff.73%
    Thermal eff.96%
    Total eff.70%
    FuelFission:
    Uranium 235
    ReactorSolid Core
    RemassLiquid Hydrogen
    Remass AccelThermal Accel:
    Reaction Heat
    Thrust DirectorNozzle
    Specific Power49 kg/MW

    The NERVA (Nuclear Engine for Rocket Vehicle Application) system captures the neutronic energy of a nuclear reaction using a heat exchanger cooled by water or liquid hydrogen. The exchanger uses thin foil or advanced dumbo fuel elements with cermet (ceramic-metal) substrates, jacketed by a beryllium oxide neutron reflector.

    The chamber temperature is limited to 3100K for the extended operational life of the solid fuel elements, which can be fission, fusion, or antimatter. At this temperature, the disassociation of molecular H2 to H significantly boosts specific impulse at chamber pressures below 10 atm.

    A propellant tank pressurized to 2 atm expels the LH2 coolant into the exchanger without the need for turbopumps. This open-cycle coolant is expanded through a hydrogen-cooled nozzle of refractory metal to obtain thrust.

    The efficiencies are 96% thermal, 76% frozen-flow (mainly H2 dissociation, less recombination in the nozzle), and 96% nozzle. A 940 MWth heat exchanger yields a thrust of 134 kN, and a specific impulse of 1 ksec, at a power density of 340 MW/m3.

    Altseimer, et al., “Operating Characteristics and Requirements for the NERVA Flight Engine,” AIAA Paper 70-676, June 1970.

    From High Frontier by Philip Eklund

    Pulsed Solid-core NTR

    The pulsed nuclear thermal rocket is a type of solid-core nuclear thermal rocket concept developed at the Polytechnic University of Catalonia, Spain and presented at the 2016 AIAA/SAE/ASEE Propulsion Conference. It isn't a torchship but it is heading in that direction. Thanks to Isaac Kuo for bringing this to my attention.

    As previously mentioned, solid core nuclear thermal rockets have to stay under the temperature at which the nuclear reactor core melts. Having your engine go all China Syndrome on you and shooting out what's left of the exhaust nozzle in a deadly radioactive spray of molten reactor core elements is generally considered to be a Bad Thing. But Dr Francisco Arias found a clever way to get around this by pulsing the engine like a TRIGA reactor. The engine can be used bimodally, that is, mode 1 is as a standard solid-core NTR (Dr. Arias calls this "stationary mode"), and mode 2 is pulsed mode.

    Pulse mode can be used two ways:


    Direct Thrust Amplification: Garden variety solid core NTRs can increase their thrust by shifting gears. You turn up the propellant mass flow. But since the reactor's energy has to be divided up to service more propellant per second, each kilogram of propellant gets less energy, so the exhaust velocity and specific impulse goes down.

    But if you shift to pulse mode along with increased propellant mass flow, the reactor's effective energy output increases. So you can arrange matters in such a way that each kilogram of propellant still gets the same share of energy. Bottom line: the thrust increases but the specific impulse is not degraded.


    Specific Impulse Amplification: This is really clever. For this trick you keep the propellant mass flow the same as it was.

    In a fission nuclear reactor 95% of the reactor energy comes from fission-fragments, and only 5% come from prompt neutrons. In a conventional solid-core NTR the propellant is not exposed to enough neutrons to get any measurable energy from them. All the energy comes from fission fragments.

    But in pulse mode, that 5% energy from neutrons could be higher than the 95% fission-fragment energy in stationary mode. The difference is that fission fragment energy heats the reactor and reactor heat gives energy to the propellant. And if the reactor heats too much it melts. But neutron energy does not heat the reactor, it passes through and directly heats the propellant.

    The end result is that in pulse mode, you can actually make the propellant hotter than the reactor. Which means a much higher specific impulse than a conventional solid-core NTR which running hot enough to be right on the edge of melting.

    Thermodynamics will not allow heat energy to pass from something colder to something hotter, so it cannot make the propellant hotter than the reactor. But in this case we are heating the propellant with neutron kinetic energy, which has zippity-do-dah to do with thermodynamics.

    The drawback of course is that the 95% fission-fragment energy is increased as well as the neutron energy. The important point is by using pulsing you can use an auxiliary cooling system to cool the reactor off before the blasted thing melts, unlike a conventional NTR.

    Apparently Dr. Arias' paper claims the pulsed NTR can have a higher specific impulse than a fission fragment engine. I am no rocket scientist but I find that difficult to believe. Fission fragment can have a specific impulse on the order of 1,000,000 seconds.


    How Does It Work?

    TRIGA reactor have what is called a large, prompt negative fuel temperature coefficient of reactivity. Translation: as the nuclear fuel elements heat up they stop working. It automatically turns itself off if it gets too hot. Technical term is "quenching."

    Which means you can overload it in pulses. The TRIGA is designed for a steady power level of 100 watts but you can pulse the blasted thing up to 22,000 freaking megawatts. It automatically shuts off after one-twentieth of a second, quickly enough so the coolant system can handle the waste heat pulse.


    Amplification Factor

    The amount of amplification of thrust or specific impulse requires the value of N, or energy ratio between the pulsed mode and the stationary mode (pulsed mode energy divided by stationary mode energy). This can be calculated by the formidable equation

    ΔT is the temperature increase during a pulse (in Kelvin), t is the residence time of the propellant in the reactor (seconds), and [ ΔT/t ] is the quench rate (K/sec). ΔT will probably be about 103 K (assuming propellant velocity of hundreds of meters per second and chambers about one meter long), t will probably be from 10-3 sec to 10-2 sec. This means [ ΔT/t ] will be about 105 to 106 K/s.

    I'm not going to explain the other variables, you can read about them here.

    Be that as it may, Wikipedia states that if you use standard reactor fuels like MOX fuel or Uranium dioxide, fuel heat capacity ≅ 300J/(mol ⋅ K), fuel thermal conductivity ≅ 6W/(K ⋅ m2), fuel density of ≅ 104kg/(m3), cylindrical fuel radius of ≅ 10-2m and a fuel temperature drop from centerline to cladding edge of 600K then:

    N ≅ 6×10-3 * [ ΔT/t ]

    This boils down to N being between 600 and 6,000.


    Direct Thrust Amplification Details

    Thrust power is:

    Fp = (F * Ve ) / 2

    Thrust is:

    F = mDot * Ve

    Specific Impulse is:

    Isp = Ve / g0

    where:

    Fp = Thrust Power (w)
    F = Thrust (N)
    Ve = Exhaust Velocity (m/s)
    mDot = Propellant Mass Flow (kg/s)
    Isp = Specific Impulse (s)
    g0 = acceleration due to gravity (9.81 m/s2)

    With a conventional solid NTR, thrust power is a constant. So if you wanted to increase the thrust by, for instance 5 time, you have to increase the propellant mass flow by 52 = 25 times and decrease the exhaust velocity by 1/5 = 0.2 times. Which decreases the specific impulse 0.2 times.

    But a pulsed NTR can increase thrust power. So if you want to increase the thrust by 5 times, you increase the thrust power by 5 times, the propellant mass flow five times, and keep the exhaust velocity and specific impulse the same.

    The limit on the increase in thrust power is N.


    Specific Impulse Amplification Details

    If in pulse mode the amplification factor is N, then the amplified specific impulse is:

    IspPulse = IspS * sqrt[ (fn * N) + 1]

    where:

    IspPulse = Specific Impulse in Pulse Mode
    IspS = Specific Impulse in Stationary Mode
    fn = fraction of the prompt neutrons (0.05)
    N = energy amplification by pulsing the reactor
    sqrt[x] = square root of x

    So if N is between 600 and 6,000, the specific impulse will increase by a factor of 5.57 to 17.35. With a basic NERVA having a specific impulse of about 800 seconds, a pulsed version would have instead 4,460 to 13,880 seconds!

    Project Timberwind

    Project Timberwind was started in President Reagan infamous Strategic Defense Initiative ("Star Wars"). It was later transferred to the Air Force Space Nuclear Thermal Propulsion (SNTP) program. The project was cancelled by President William Clinton.

    NTR Comparison
    NERVATimberwind
    45
    Engine Mass6,803 kg1,500 kg
    Thrust (Vac)333.6 kN392.8 kN
    Specific Impulse850 s1,000 s
    Burn Time1,200 s449 s
    T/W530 !!!

    The idea was to make a nuclear-powered interceptor to destroy incoming Soviet ICBMs. The Timberwind NTR upper stage would have to make the NERVA engine look like a child's toy, with huge specific impulse and an outrageously high thrust-to-weight ratio. The project managers babbled about advances in high-temperature metals, computer modelling and nuclear engineering in general justifying suspiciously too-good-to-be-true performance. It was based on the pebble-bed concept.

    Timberwind
    45
    Timberwind
    75
    Timberwind
    250
    Diameter4.25 m2.03 m8.70 m
    Thrust (Vac)392.8 kN735.5 kN2,451.6 kN
    Specific Impulse1,000 s1,000 s1,000 s
    Engine Mass1,500 kg2,500 kg8,300 kg
    T/W303030
    Burn Time449 s357 s493 s

    Russian Twisted Ribbon

    These are from Russian Nuclear Rocket Engine Design for Mars Exploration by Vadim Zakirov and Vladimir Pavshook. The unique "twisted ribbon" fuel elements were developed in the Soviet Union, and continued development in Russia. The twisted ribbon surface-to-volume ratio is 2.6 times higher than that of the US NERVA fuel elements, which enhances the heat transfer between fuel and propellant.

    The prototype RD-0140 engine was a pure rocket engine, while the nuclear power and propulsion system (NPPS) is a Bi-Modal NTR acting as an electrical power generator in between thrust periods. A spacecraft designed for a Mars mission would have three or four NPPS engines.

    Twisted Ribbon Engines
    RD-0140NPPS
    Thrust (vac) (kN)35.2868
    PropellantH2 + HexaneH2
    Propellant Mass Flow (kg/s)~4~7.1
    Specific Impulse (vac) (s)~900~920
    Core outlet temparture (K)3,0002,800 to 2,900
    Chamber Pressure (105 Pa)7060
    U235 enrichment (%)9090
    Fuel Composition(U,Nb,Zn)CU-Zr-C-N
    Fuel Element FormTwisted ribbonTwisted ribbon
    Generated electrical power (kW)N/A50
    Working fluid for power loop
    (% by mass)
    N/A93% Xe + 7% He
    Max temp for power loop (K)N/A1,500
    Max press for power loop (105 Pa)N/A9
    Working fluid flow rate (kg/s)N/A1.2
    Thermal power - propulsion mode (MW)196340
    Thermal power - power mode (MW)N/A0.098
    Core length (mm)800700
    Core diameter (mm)500515
    Engine length (mm)3,700No Data
    Engine diameter (mm)1,200No Data
    Lifetime - propulsion mode (h)15
    Lifetime - power mode (yr)N/A2
    Mass (kg)2,000*1,800**

    N/A = not applicable. * = including radiation shield and adapter. ** = reactor mass.

    In the RD-0140 they added hexane to the liquid hydrogen propellant. Unfortunately pure hot hydrogen tended to erode the fuel elements and make the exhaust radioactive.

    NTR DESIGN OPTIONS
    Twisted Ribbon Engine
    Thrust power1,650 MW
    Exhaust velocity9,420 m/s
    Specific impulse960 s
    Thrust330,000 N
    Engine mass5,260 kg
    T/W6.4

    The CIS engine developed jointly by the US/CIS industry team of Aerojet, Energopool and B&W utilizes a heterogeneous reactor core design with hydrogen-cooled ZrH moderator and ternary carbide fuel materials. The ZrH moderator, in the form of close-packed rods, is located between reactor fuel assemblies and is very efficient in minimizing the inventory of fissile material in the reactor core.

    The CIS fuel assembly (shown in Figure 6) is an axial flow design and contains a series of stacked 45 mm diameter bundles of thin (~1 mm) "twisted ribbon" fuel elements approximately 2 mm in width by 100 mm in length.

    The "fueled length" and power output from each assembly is determined by specifying the engine thrust level and hydrogen exhaust temperature (or desired Isp).

    For the 75 klbf (330,000 N) CIS engine design point indicated in Figure 4, 102 fuel assemblies (each containing 10 fuel bundles) produce ~1650 MWt with a Isp of ~960 s.

    For a 15 klbf (67,000 N) engine, 34 fuel assemblies (with 6 fuel bundles each) are used to generate the required 340 MWt of reactor power at the same Isp.

    The fuel material in each "twisted ribbon" element is composed of a solid solution of uranium, zirconium and niobium ceramic carbides having a maximum operating temperature expected to be about 3200 K. The fuel composition along the fuel assembly length is tailored to provide increased power generation where the propellant temperature is low and reduced power output near the bottom of the fuel assembly where the propellant is nearing its exhaust temperature design limit. In the present CIS design a value of 2900 K has been selected to provide a robust temperature margin. During reactor tests, hydrogen exhaust temperatures of 3100 K for over one hour and 2000 K for 2000 hours were demonstrated in the CIS.

    At 2900 K, an engine lifetime of ~4.5 hours is predicted.

    The Aerojet, Energopool, B&W NTR design utilizes a dual turbopump, recuperated expander cycle. Hydrogen flowing from each pump is split with ~84% of the flow going to a combination recuperator/gamma radiation shield and the remaining 16% used to cool the nozzle. The recuperator/shield, located at the top of the engine, provides all of the necessary turbine drive power. The turbine exhaust cools the reactor pressure vessel and is then merged with the nozzle coolant to cool the moderator and reflector regions of the engine. The coolant then passes through borated ZrH and lithium hydride (LiH) neutron shields located within the pressure vessel between the reactor core and the recuperator/gamma shield, before returning to the recuperator where it heats the pump discharge flow. Exiting the recuperator the cooled hydrogen is then routed to the core fuel assemblies where it is heated to 2900 K.

    The 75 klbf (330,000 N) CIS engine design point has a chamber pressure of 2000 psia (14,000 kpa), a nozzle area ratio of 300 to 1, and a 110% bell length nozzle resulting in a Isp of ~960 s.

    (ed note: from the chart, the 75 klbf CIS engine has a thrust-to-weight ratio of 6.4. If my slide rule is not lying to me, that means the engine has a mass of 5,260 kilograms)

    The same pressure and nozzle conditions were maintained for the 15 (67,000), 25 (110,000) and 50 klbf (220,000 N) engine design points with the resulting weight scaling indicated in Figure 4.

    The approximate engine lengths for the 15 (67,000), 25 (110,000), 50 (220,000) and 75 klbf (330,000 N) CIS engines are 4.3 m, 5.2 m, 6.5 m, and 7.6 m, respectively.

    Low Pressure NTR

    Low Pressure NTR
    Engine Mass835 kg
    Full Thrust49,000 newtons
    Full T/W6.0
    Full Isp1,210 sec
    Single-H Thrust9,800 newtons
    Single-H T/W1.2
    Single-H Isp1,350 sec

    This is from Low Pressure Nuclear Thermal Rocket (LPNTR) concept (1991)

    This is a theoretical concept, but it has enough impressive advantages over conventional solid-core NTRs that it is well worth looking into. The engine has a specific impulse of up to 1,350 seconds (exhaust velocity 13,200 m/s) which is virtually the theoretical maximum for solid-core NTR. It also is very lightweight plus much more reliable. The latter is due to the absence of certain heavy and fault-prone components (those with moving parts) required for solid-core.


    Solid-core NTRs commonly use liquid hydrogen as propellant, since that is the propellant with the sweet spot of low molecular weight and convenience. The lower the molecular weight, the higher the specific impulse and exhaust velocity.

    There is one propellant with an even lower molecular weight, but it is anything but convenient. Monatomic hydrogen has half the molecular weight of molecular hydrogen so it has a much higher performance. A pity it explodes like a bomb if you give it a stern look. In his novels Robert Heinlein calls monatomic hydrogen "Single-H", and handwaves really hard that future engineers will figure out some way to stablize the dire stuff. Sorry Mr. Heinlein, we need a real-world solution here.

    Heating molecular hydrogen to above 3,000 Kelvin will dissociate it into single-H. Sadly at the high pressures commonly used in solid-core reactors, the temperature and the propellant mass flow would combine into a heat flux high enough to destroy the reactor. Remember the difference between heat and temperature: temperature is an interesting number but it is the heat joules that ruin the reactor.

    Dr. Ramsthaler said "Ah, but what if we designed the engine to use low pressure?" Then we can make single-H at a heat flux low enough for the reactor to survive, allowing our specific impulse will climb to amazing levels. A standard NERVA has an engine pressure of 31 bar (450 pounds force per square inch), the LPNTR only has a pressure of 1 bar (14.5 psia). This means the LPNTR has a heat flux that is 50-to-one less than the NERVA.

    The drawback is the low pressure will drastically reduce the propellant mass flow, which reduces the thrust (because thrust = propellant mass flow times exhaust velocity). This problem can be addressed with clever engineering. Dr. Ramsthaler thinks it is possible to push the engine up to a thrust-to-weight ratio of 1.2. The Monatomic-H MITEE tries the same low-pressure trick, but only at a thrust-to-weight ratio of 1.0.

    Everything comes at a cost. The engine can do a T/W ratio of 6.0 at full thrust, but this means the specific impulse is only 1,210 seconds. If you shift it into temperatures that allow dissociation to create Single-H, the T/W ratio is only 1.2 but the Single-H makes a specific impulse of 1,350 seconds. So the engine has two gears.

    In addition, a low pressure engine means it does not need turbopumps to create high pressure. Turbopumps are penalty-weight, turbopumbs need complicated plumbing to supply the energy needed to spin the little darling, and turbopumps contain several points of mechanical failure with all their moving parts. Good riddance to bad rubbish. The natural propellant tank pressure is enough for the LPNTR to operate.

    Also the low heat flux means the engine only needs an exhaust nozzle that is very short compared to a NERVA. 50-to-one less than the NERVA, remember?


    Dr. Ramsthaler's secret is a reactor with a radial outflow core: it maximizes propellant mass flow at low pressure but high temperature. Remember:

    • High temperature is needed to make Single-H and crank up the specific impulse to 11, er, ah, 1,350 seconds
    • Low pressure counteracts the high temperature so the heat level is not high enough to melt the reactor
    • Maximizing propellant mass flow counteracts the low pressure so the thrust-to-weight ratio is at least 6.0

    For standard NERVA and related solid-core NTRs, at low pressure the critical flow is where the propellant exits the core. The propellant enters the top of the cylindrical core, is heated inside the core, and exits the core at the bottom. Then it enters the exhaust nozzle.

    Dr. Ramsthaler's design uses a spherical core. The propellant enters the center of the core, is heated inside the core, and exits the core from its surface. Given the 120 flow outlet holes on the surface, the engine has almost 50% flow area at the exit of the core.

    The design can accommodate almost any kind of nuclear fuel elements: pebbles, plates, whatever.


    Safety and reliabily was Dr. Ramsthaler's primary goal. But his solution to control of the nuclear reactor raises eyebrows.

    Conventional NERVA engines use control drums to control the criticality in the nuclear reactor. Spin the drums so the neutron reflector face the nuclear fuel elements and the reactor fires up. Spin the drums so the neutron poison faces the fuel elements and the reactor shuts down like a blown-out match.

    As it turns out, the liquid hydrogen propellant is a pretty good neutron moderator all by itself. The spacecraft engineer has to be careful about feeding propellant into a dry hot reactor. Otherwise neutron transients will build into full-fledged runaway nuclear oscillations and your reactor will go all Chernobyl on you. The addition of the moderator changes the nuclear characteristics of the reactor.

    Anyway Dr. Ramsthaler looked at the way the propellant altered the reactor behaviour and wondered if careful propellant control could replace the control drums. Control drums are penalty-weight, control drums require electricity, and control drums contain several points of mechanical failure with all their moving parts. Using propellant to control the reactor would happily reduce the engine mass even more, and increase the engine reliabilty.

    The hydrogen propellant is injected into the center of the spherical core, remember? This turns out to be the perfect location for the hydrogen to moderate the neutrons flux, where the neutrons are thickest. The hydrogen turns worthless fast neutrons into reactor-grade thermal neutrons which maintain the fission chain reaction.

    The dry reactor just sits there, its nuclear characteristics are such that no chain reaction can happen. But as soon as the liquid hydrogen fills the center, the reactor goes critical and starts generating large amounts of thermal energy by the miracle of nuclear fission.

    But just in case the reaction gets out of hand, there is a rod of neutron poison that can be slammed into the center of the core to scram the engine.


    Dr. Ramsthaler figures with such low engine mass, the spacecraft could afford to have seven engines. This would allow thrust vectoring by throttling engines instead of the mechanical nightmare of gimbaled engines. All together now: engine gimbals are are penalty-weight, engine gimbals require hydraulics, and engine gimbals contain several points of mechanical failure with all their moving parts. Get rid of them.

    Rob Davidoff points out that the above gimbal-less scheme will do yaw and pitch thrust vectoring just fine. But it is incapable of performing roll vectoring. A spacecraft using such a scheme will have to rely upon its reaction control system (attitude jets) for rolls.

    In addition, a cluster of seven engines would allow the spacecraft to lose up to two engines and still limp through the mission ("two-engine-out" capability). Instead of total mission failure and all the crew dying.


    LPNTR advantage IMEO for Mars mission
    T/WMission
    EngineIspEngineEngine
    + shield
    Ref
    IMEO
    500 KM
    Earth Orbit
    IMEO
    Ref NERVA85042.68841400
    Adv NERVA92563.37131037
    LPNTR
    3200 K
    105062.2603814
    LPNTR
    3600 K
    121062.2485611
    LPNTR
    3600 K
    Dual mode
    1210
    (1350)
    6
    (1.25)
    2.2
    (0.44)
    440534

    The Ref mission is a Mars mission that ends with the spacecraft in a huge ecliptic orbit around Terra. This will require lots of energy when you want to reuse the spacecraft. The 500 KM Earth Orbit mission is the Mars mission, using extra propellant and delta V to end with the spacecraft in a nice circular orbit for easy spacecraft reuse.

    You can see how the Initial Mass in Earth Orbit (IMEO) nicely drops as the engine Isp increases. And how using a dual-mode engine with the Single-H mode drops the IMEO by 77 metric tons of propellant compared to the single-mode engine.

    LANTR

    LANTR
    LANTR NERVA mode
    Exhaust Velocity9,221 m/s
    Specific Impulse940 s
    Thrust67,000 N
    Thrust Power0.3 GW
    Mass Flow7 kg/s
    RemassLiquid Hydrogen
    LANTR LOX mode
    Exhaust Velocity6,347 m/s
    Specific Impulse647 s
    Thrust184,000 N
    Thrust Power0.6 GW
    Mass Flow29 kg/s
    RemassHydrogen + Oxygen
    LANTR Both
    FuelFission:
    Uranium 235
    ReactorSolid Core
    Remass AccelThermal Accel:
    Reaction Heat
    Thrust DirectorNozzle
    SpecialLow-High Gear
    Nuclear DC-X NERVA
    High Gear
    Exhaust Velocity9,810 m/s
    Specific Impulse1,000 s
    Thrust/Engine1,112,000 N
    Thrust5,560,000 N
    Thrust Power27.3 GW
    Mass Flow567 kg/s
    T/W3
    RemassHydrogen
    Specific Power7 kg/MW
    Low Gear
    Exhaust Velocity5,900 m/s
    Specific Impulse601 s
    Thrust/Engine3,336,000 N
    Thrust16,680,000 N
    Thrust Power49.2 GW
    Mass Flow2,827 kg/s
    T/W9
    RemassWater
    Remass AccelThermal Accel:
    Reaction Heat
    Thrust DirectorNozzle
    Specific Power4 kg/MW
    Both
    Number Thrustersx5
    Total Engine Mass199,600 kg
    FuelFission:
    Uranium 235
    SpecialLow-High Gear
    Wet Mass460,000 kg

    LOX-augmented Nuclear Thermal Rocket. One of the systems that can increase thrust by lowering Isp, in other words Shifting Gears. This concept involves the use of a "conventional" hydrogen (H2) NTR with oxygen (O2) injected into the nozzle. The injected O2 acts like an "afterburner" and operates in a "reverse scramjet" mode. This makes it possible to augment (and vary) the thrust (from what would otherwise be a relatively small NTR engine) at the expense of reduced Isp

    Bi-Modal NTR

    Bimodal NTR Solid (NASA)
    Propulsion SystemNTR Solid Bimodal
    Exhaust Velocity8,980 m/s
    Specific Impulse915 s
    Thrust/Engine66,667 N
    Number Thrustersx3
    Thrust200,000 N
    Thrust Power0.9 GW
    Mass Flow22 kg/s
    Total Engine Mass6,672 kg
    T/W3
    FuelFission:
    Uranium 235
    ReactorSolid Core
    RemassLiquid Hydrogen
    Remass AccelThermal Accel:
    Reaction Heat
    Thrust DirectorNozzle
    SpecialBimodal
    Wet Mass80,000 kg
    Dry Mass26,830 kg
    Mass Ratio2.98 m/s
    ΔV9,811 m/s
    Specific Power7 kg/MW

    A useful refinement is the Bimodal NTR.

    Say your spacecraft has an honest-to-Johnny NERVA nuclear-thermal propulsion system. Typically it operates for a few minutes at a time, then sits idle for the rest of the entire mission. Before each use, one has to warm up the reactor, and after use the reactor has to be cooled down. Each of these thermal cycles puts stress on the engine. And the cooling process consists of wasting propellant, flushing it through the reactor just to cool it off instead of producing thrust.

    Meanwhile, during the rest of the mission, your spacecraft needs electricity to run life support, radio, radar, computers, and other incidental things.

    So make that reactor do double duty (that's where the "Bimodal" comes in) and kill two birds with one stone. Refer to below diagram. Basically you take a NERVA and attach a power generation unit to the side. The NERVA section is the "cryogenic H2 propellant tank", the turbopump, and the thermal propulsion unit. The power generation section is the generator, the radiator, the heat exchanger, and the compressor.

    Warm up your reactor once, do a thrust burn, stop the propellant flow and use the heat exchanger and radiator to partially cool the reactor to power generation levels, and keep the reactor warm for the rest of the mission while generating electricity for the ship.

    This allows you to get away with only one full warm/cool thermal cycle in the entire mission instead of one per burn. No propellant is wasted as coolant since the radiator cools down the reactor. The reactor supplies needed electricity. And as an added bonus, the reactor is in a constant pre-heated state. This means that in case of emergency one can power up and do a burn in a fraction of the time required by a cold reactor.

    Pretty ingenious, eh?

    An even further refinement is the Hybrid BNTR/EP option. This is where the electrical power output has a connection to an Ion Drive. This is a crude form of Shifting Gears: trading thrust for specific impulse/exhaust velocity. So it can do low-gear NTR thrust mode, high-gear ion-drive thrust mode, and no-thrust electricity generation mode while coasting.


    And the Pratt & Whitney company went one step better. They took the Bimodal NTR concept and merged it with the LANTR concept to make a Trimodal NTR. Called the Triton, it uses a LANTR engine to allow Shifting Gears. So it can do low-gear NTR-Afterburner thrust mode, high-gear NTR thrust mode, and no-thrust electricity generation mode while coasting.

    Dual-mode Fission
    Dual-mode Fission
    Exhaust Velocity9,810 m/s
    Specific Impulse1,000 s
    Thrust124,700 N
    Thrust Power0.6 GW
    Mass Flow13 kg/s
    Total Engine Mass33,000 kg
    T/W0.39
    Thermal eff.94%
    Total eff.94%
    FuelFission:
    Uranium 235
    ReactorSolid Core
    RemassLiquid Hydrogen
    Remass AccelThermal Accel:
    Reaction Heat
    Thrust DirectorNozzle
    Specific Power54 kg/MW
    SpecialBimodal
    Thermal Electrical eff.19%
    Electrical Power60 MWe

    When struck by a thermal neutron, a fissile nuclide splits into two fragments plus energy. For example, the fission of the 235U atom produces 165 MeV of energy plus 12 MeV of neutral radiation (gammas and a couple of fast neutrons). The fast neutrons must be thermalized by a low Z moderator (a surrounding blanket of about 80 cm of D2O, Be, liquid or gas D2, or CD4), which returns enough thermal neutrons to the core to sustain the chain reaction. (Thermal neutrons diffuse through the reactor like a low pressure gas.) Alternatively, a molybdenum neutron reflector can be used. Much of a reactor’s mass is constant, regardless of power level. Therefore, nuclear power sources are more attractive at higher power levels.

    The 650 MWth system illustrated is dual mode, which can either generate electricity, or directly exhaust coolant for thrust. It uses a fast reactor with fuel tubes interspersed with cooling tubes. The coolant is lithium, which for electrical power is passed to a potassium boiler at 1650 K. The potassium vapor is passed to a static (AMTEC) or dynamic (turbine) heat engine for power generation (60 MWe), or heats hydrogen in a heat exchanger for thrust (125 kN at a specific impulse of 1 ks). The thermal efficiency is 19% if closed-cycle (for power generation) or 94% if open-cycle (for thrust).

    From High Frontier by Philip Eklund
    Dual-mode Pebble Bed
    Pebble-bed Fission Reactor
    Exhaust Velocity9,810 m/s
    Specific Impulse1,000 s
    Thrust172,700 N
    Thrust Power0.8 GW
    Mass Flow18 kg/s
    Total Engine Mass58,000 kg
    T/W0.30
    Thermal eff.94%
    Total eff.94%
    FuelFission:
    Uranium 233
    ReactorSolid Core
    RemassLiquid Hydrogen
    Remass AccelThermal Accel:
    Reaction Heat
    Thrust DirectorNozzle
    Specific Power68 kg/MW
    SpecialBimodal
    Electrical Power60 MWe

    This is a graphite-moderated, gas-cooled, nuclear reactor that uses spherical fuel elements called "pebbles". These tennis ball-sized pebbles are made of pyrolytic graphite (which acts as the moderator), interspersed with thousands of micro fuel particles of a fissile material (such as 235U).

    In the reactor illustrated, 360,000 pebbles are placed together to create a 120 MWth reactor. The spaces between the pebbles form the "piping" in the core for the coolant, either propellant or inert He/Xe gas.

    The design illustrated can is dual mode. It can operate either as a generator for 60 MWe of electricity, or act as a solid-core thruster using hydrogen propellant/coolant expelled at a specific impulse of 1 ksec. When used as a thruster, it offers a slight increase in specific impulse but significant acceleration benefits over traditional fission reactors. Moreover, the high temperatures (up to 1900 K) allow higher thermal efficiencies (up to 50%).

    From High Frontier by Philip Eklund

    MITEE

    MInature ReacTor EnginE. MITEE is actually a family of engines. These are small designs, suitable for launching on existing boosters. You can find more details here.

    Basic
    Basic MITEE
    Exhaust Velocity9,810 m/s
    Specific Impulse1,000 s
    Thrust14,000 N
    Thrust Power68.7 MW
    Mass Flow1 kg/s
    Total Engine Mass200 kg
    T/W7
    FuelFission:
    Uranium 235
    ReactorSolid Core
    RemassLiquid Hydrogen
    Remass AccelThermal Accel:
    Reaction Heat
    Thrust DirectorNozzle
    Specific Power3 kg/MW

    The baseline design is a fairly conventional NTR. Unlike earlier designs it keeps the fuel elements in individual pressure tubes instead of a single pressure vessel, making it lighter and allowing slightly higher temperatures and a bit better exhaust velocity.

    Monatomic H
    Monatomic-H MITEE
    Exhaust Velocity12,750 m/s
    Specific Impulse1,300 s
    Thrust2,350 N
    Thrust Power15.0 MW
    Mass Flow0.18 kg/s
    Total Engine Mass200 kg
    T/W1
    FuelFission:
    Uranium 235
    ReactorSolid Core
    RemassLiquid Hydrogen
    Remass AccelThermal Accel:
    Reaction Heat
    Thrust DirectorNozzle
    Specific Power13 kg/MW

    This advanced design works at a lower chamber pressure so that some of the H2 propellant disassociates into monatomic hydrogen, although the chamber temperature is only slightly greater. The drawback is that this reduces the mass flow through the reactor, limiting reactor power.

    Hybrid
    HybridMITEE
    Exhaust Velocity17,660 m/s
    Specific Impulse1,800 s
    Thrust1,700 N
    Thrust Power15.0 MW
    Mass Flow0.10 kg/s
    Total Engine Mass10,000 kg
    T/W0.02
    FuelFission:
    Uranium 235
    ReactorSolid Core
    RemassSingle-H
    Remass AccelThermal Accel:
    Reaction Heat
    Thrust DirectorNozzle
    Specific Power666 kg/MW

    The use of individual pressure tubes in the reactor allows some fuel channels to be run at high pressure while others are run at a lower pressure, facilitating a hybrid electro-thermal design. In this design cold H2 is heated in the high pressure section of the reactor, is expanded through a turbine connected to a generator, then reheated in the low pressure section of the reactor before flowing to the nozzle. The electricity generated by the turbine is used to break down more H2 into monatomic hydrogen, increasing the exhaust velocity. Since this is a once through system there is no need for radiators so the weight penalty would not be excessive.

    Liquid Core

    Liquid Core 1
    Exhaust Velocity16,000 m/s
    Specific Impulse1,631 s
    Thrust7,000,000 N
    Thrust Power56.0 GW
    Mass Flow438 kg/s
    Total Engine Mass70,000 kg
    T/W10
    FuelFission:
    Uranium 235
    ReactorLiquid Core
    RemassWater
    Remass AccelThermal Accel:
    Reaction Heat
    Thrust DirectorNozzle
    Specific Power1 kg/MW
    Liquid Core 2
    Exhaust velocity14,700 to 25,500 m/s

    Nuclear thermal rocket / liquid core fission. Similar to an NTR-GAS, but the fissionable core is merely molten, not gaseous. A dense high temperature fluid contains the fissionable material, and the hydrogen propellant is bubbled through to be heated. The propellant will be raised to a temperature somewhere between the melting and boiling point of the fluid. Candidates for the fluid include tungsten (boiling 6160K), osmium (boiling 5770K), rhenium (boiling 6170K), or tantalum (boiling 6370K).

    Liquid core nuclear thermal rockets have a nominal core temperature of 5,250 K (8,990°F).

    The reaction chamber is a cylinder which is spun to make the molten fluid adhere to the walls, the reaction mass in injected radially (cooling the walls of the chamber) to be heated and expelled out the exhaust nozzle.

    Starting up the engine for a thrust burn will be complicated and tricky, shutting it down even more so. Keeping the fissioning fluid contained in the chamber instead of escaping out the nozzle will also be a problem.

    LARS

    LARS
    Exhaust Velocity19,620 m/s
    Specific Impulse2,000 s
    Thrust20,000 N
    Thrust Power0.2 GW
    Mass Flow1 kg/s
    Total Engine Mass1,000 kg
    T/W2
    FuelFission:
    Uranium 235
    ReactorLiquid Core
    RemassLiquid Hydrogen
    Remass AccelThermal Accel:
    Reaction Heat
    Thrust DirectorNozzle
    Specific Power5 kg/MW
    Luna
    Propulsion SystemLARS
    Exhaust Velocity10,300 m/s
    Specific Impulse1,050 s
    Thrust11,000,000 N
    Thrust Power56.6 GW
    Mass Flow1,068 kg/s
    Total Engine Mass9,000 kg
    T/W125
    FuelFission:
    Uranium 235
    RemassWater
    Thrust DirectorNozzle
    Wet Mass226,000 kg
    Dry Mass45,000 kg
    Mass Ratio5.02 m/s
    ΔV16,623 m/s

    Nuclear thermal rocket / liquid annular reactor system. A type of NTR-LIQUID. You can find more details here

    The molten fissioning uranium is held in tubes which are spun to provide centifugal gravity. This keeps the uranium from escaping out the exhaust, mostly. Seeded hydrogen propellant is injected down the spin axis where it is heated by the nuclear reaction then escapse out the exhaust nozzle.

    These engines have a specific impulse ranging between 1,600 to 2,000 seconds, and an internal temperature between 3,000K and 5,000K

    Droplet Core

    Droplet Core
    Reactor inner diameter1 m
    Reactor outer diameter2 m
    Reactor inner length3 m
    Reactor outer length4 m
    Engine length13 m
    T/W
    (no shadow shield)
    5.0
    T/W
    (with shadow shield)
    1.6
    Engine mass
    (no shadow shield)
    6,800 kg
    Engine mass
    (with shadow shield)
    21,200 kg
    Engine pressure500 atm
    Internal temp6,000K
    Isp2,000 sec
    Exhaust velocity19,600 m/s
    Engine power1,500 MWth
    Thrust333,000 N

    The data is from Droplet Core Nuclear Rocket (1991).

    The main draw-back is that developing such an engine will be just as hard as developing a gas core nuclear thermal engine. But it has much lower performance. So why bother?

    This propulsion system straddles the line between liquid-core and vapor-core. Much like how vapor-core straddles the line between liquid-core and gas-core. Instead of the uranium fuel being in the form of gaseous vapor, it is instead in the form of a fog of droplets.

    Droplet core engines have a specific impulse between 1,500 and 3,000 seconds and an internal temperature between 5,000K and 7,000K. The specific impulse is enhanced because the nuclear energy is strong enough to dissociate some (20%) of the hydrogen molecules of propellant into atomic hydrogen. The propellant flow rate can be between 1 to 1,000 kilograms per second.

    The temperature depends upon the pressure inside the chamber. The design shown assumes a pressure of 500 atmospheres, where the melting point of uranium is 1,400K and the boiling point is 9,500K. This is enough to heat the hydrogen propellant to 6,000K and gives a specific impulse of 2,000 seconds.

    The chamber is about one meter in diameter and three meters tall.

    At the top molten uranium with a temperature of around 2,000K is injecting through the unfortunately named "atomizer." In this case the term has nothing to do with nuclear physics, but more to do with Victorian perfume spray bottles. The droplets are from five to ten microns in size, and enough are sprayed into to create a critical mass. The upper 1.5 meters of the chamber is clad in neutron reflectors, so about 70 to 80% of the power generated occurs here. The next meter has only partial neutron reflectors, and the lower half meter has no neutron reflectors at all. Naturally the neutron flux is highest in the part with the most reflectors.

    In the upper half of the chamber hydrogen propellant bleeds in from the walls, but in the lower half high pressure tangential jets spray a flood of hydrogen. Like vapor-core and open-cycle-gas-core the frantically fissioning uranium is intimately mixed with the hydrogen propellant. This gives an almost three orders of magnitude improvement on heat transfer area (i.e., about a thousand times better than a solid-core nuclear engine). The propellant is heated not only by heat radiation, but also by heat conduction of hydrogen gas in direct contact with the uranium drops. A whopping 30% to 40% of the fission energy is transferred to the propellant.

    The tangential spray in the lower half of the chamber does two things: [1] help keep the blasted uranium drops from splattering on the walls and [2] create a vortex that will assist capturing uranium so it can be re-used instead of losing it out the exhaust nozzle. That stuff is both deadly and expensive, you don't want any un-burnt uranium escaping. The report calculates that the uranium loss will be less than 50 kilograms per mission.

    About half a meter from the bottom of the chamber the tangential hydrogen jets are replaced with molten lithium-6 jets. The vortex makes the hot uranium drops hit the relatively cool lithium layer. This chills the uranium so the drops mix with the lithium. The mixture is captured at the bottom and sent to a fuel separator. The unburnt uranium is sent back to the top for another trip through the chamber while the lithium is sent back to the lithium jets.

    The engine has a very high thrust-to-weight ratio. A 1,500 MWth engine with 333,000 Newtons of thrust would have a T/W of 5.0. Though actually that drops to 1.6 once you add the radiation shadow shield so the crew doesn't die. If my slide rule is not lying to me, this means the described engine has a mass of 6.8 metric tons with no radiation shield, and a mass of 21.2 metric tons with (or a shield mass of 14.4 metric tons).

    This particular engine would have about 20 kg of uranium in the reaction chamber at any given time, and 100 kg total fuel. As mentioned before the report predicts it will lose about 50 kg out the exhaust nozzle over an entire mission.

    Vapor Core

    Vapor Core
    Thrust Power1.6 GW
    Exhaust velocity9,800 to
    11,800 m/s
    Thrust330,000 n
    Propellant mass flow30 kg/sec
    Reactor thermal power1,400 to
    1,800 MW
    Total engine mass6.83 tonne
    Fuel element mass total1.35 tonne
    Forward reflector mass0.60 tonne
    Aft reflector mass0.51 tonne
    Radial reflector mass2.47 tonne
    Radiation shield mass0.9 tonne
    Total reactor mass5.83 tonne
    Misc. engine
    component mass
    0.9 tonne
    T/W5
    FuelFission:
    Uranium Hexafluoride
    ReactorVapor Core
    RemassLiquid Hydrogen
    Remass AccelThermal Accel:
    Reaction Heat
    Thrust DirectorNozzle
    Specific Power4 kg/MW

    This is sort of an intermediate step in learning how to design a full-blown Gas Core Nuclear Thermal Rocket. It is basically a solid core NTR where the solid nuclear fuel elements are replaced by chambers filled with uranium235 tetrafluoride vapor. The engine is admirably compact with a nicely low critical mass, and an impressive thrust-to-weight ratio of 5-to-1. However the specific impulse / exhaust velocity is only slightly better than a solid core.

    In other words, the system is not to be developed because it has fantastic performance, but because it will be an educational step to building a system that does.

    The specific impulse is around 1,280 seconds and the internal temperature is between 6,000K and 8,000K.

    The uranium fuel is kept physically separate from the hydrogen propellant, so the exhaust is not radioactive.

    A 330,000 newton thrust NVTR would have a core with almost 4,000 fuel elements, with a core radius of 120 cm, core height of 150 cm, and 1,800 MW. Criticality can be achieved with smaller cores: a core volume five times smaller with radius of 60 cm, height of 120 cm, and power of 360 MW.

    Data is from Conceptual Design of a Vapor Core Reactor Rocket Engine for Space Propulsion by E.T. Dugan, N.J. Diaz, S.A. Kuras, S.P. Keshavmurthy, and I. Maya (1996).

    Reflectors
    SideCompositionThicknessMass
    ForwardBeryllium oxide15 cm0.60 tonne
    AftC-C Composite25 cm0.51 tonne
    RadialBeryllium oxide15 cm2.47 tonne
    CORE: 2000 fuel elements
    Radius0.5 m
    Height1.5 m
    Fuel channel per element12 to 32
    Hydrogen channel per element12 to 32
    Critical mass20 kg
    Hydrogen pressure100 atm
    UF4 pressure100 atm
    Fuel center temperature4,500 K
    Design Values
    Pump Flowrate (Total)75.20 lbm/s
    Pump Discharge Pressure3,924 psia
    Pump Efficiency80.01%
    Turbopump RPM70,000 RPM
    Turbopump Power (each)9,836 HP
    Turbine Inlet Temperature481 deg-R
    Turbine Pressure Ratio1.69
    Turbine Flow Rate (each)33.77 lbm/s
    Reactor Thermal Power1,769 MW
    Fuel Element and Reflector Power1,716 MW
    Nozzle Chamber Temperature5,580 deg-R
    Chamber Pressure (Nozzle Stagnation)1,500 psia
    Nozzle Expansion Area Ratio500:1
    Vacuum Specific Impulse (Delivered)997.8 sec
    Heat Loads
    Nozzle-con (total)30.05 MW
    Nozzle-div (total)22.97 MW
    Reflector (total)35.0 MW
    Typical NVTR Engine Parameters
    Nozzle Area Ratio500
    Fuel Pressure100 atm
    Average Fuel Temperature4000 K
    Maximum Element Heat Flux420 W/cm2
    Nomial Element Length150 cm
    Fuel Volume Fraction0.15
    Coolant Volume Fraction0.15
    Moderator Volume Fraction0.70
    Fuel Element Power0.9 MWt
    Element Heat Transfer Area2141 cm2
    Reactor Core L/D1.5
    Fuel Channel Diameter0.142 cm
    Fuel Channel Sectional Area0.0158 cm2
    Total Fuel Channel Area Per Element0.505 cm2
    Fuel Element Sectional Area3.464 cm2
    Element Diameter (across flats)2.2 cm
    Coolant Channel Diameter0.142 cm
    Coolant Channel Sectional Area0.0158 cm2
    Total Coolant Channel Area Per Element0.505 cm2
    Core Volume1.2 m3
    Core Volume Density1,500 MW/m3
    Fuel Element Mass, Total1.35 MT
    Forward Reflector Mass0.60 MT
    Aft Reflector Mass0.51 MT
    Radial Reflector Mass2.47 MT
    Radiation Shield Mass0.90 MT
    Total Reactor Mass5.83 MT
    Misc. Engine Components Mass0.9 MT
    Total Engine Mass6.83 MT
    Engine F/W5.0

    Gas Core

    Remember, all nuclear thermal rockets are using nuclear energy to heat hydrogen propellant for rocket exhaust. The hotter the reactor core, the more the propellant is heated, and the higher the specific impulse and exhaust velocity. That means the rocket has more delta-V go travel to more distant places, and also can carry more payload.

    The problem is that the reactor is made out of matter, and above a certain temperature the reactor melts. Go higher and the reactor vaporizes into gas. Solid-core nuclear thermal rockets keep the temperature below the melting point, which means they top out at a specific impulse of 1,200 seconds or so. Admittedly this is better than the pathetic 450 seconds you can squeeze out of a conventional chemical rocket. But it is still not high enough to really open up the exploration of the solar system.

    If you allow the uranium to reach a temperature where it melts you can get up to a specific impulse of 2,000 seconds or so. This is a liquid-core nuclear thermal rocket. You spin the reaction chamber around the thrust axis to make the hot bubbling liquid uranium stick to the chamber walls instead of escaping out the exhaust.

    But if you want to crank it up to the max you have to let the uranium reach temperatures where it vaporizes into white-hot gas. This can get up to a whopping 3,500 seconds of specific impulse.

    The drawback is trying to keep all that expensive and deadly gas from shooting out the exhaust bell. Which isn't easy.

    Closed-Cycle gas-core NTR try to have it both ways. They enclose the nuclear fury of gaseous uranium in solid quartz-crystal containers to keep the exhaust non-radioactive. Which is counter-productive since the whole idea was to let everything vaporize for maximum heat output. The end result is the specific impulse will be about half of what it could be.

    Open-cycle gas-core NTR just let it all hang out. Radioactive fission-products vapor escapes out the exhaust making it very unhealthy to be anywhere near the rocket when it is thrusting. But it has the maximum specific impulse. Since that enriched uranium is hideously expensive you want to at least make a cursory effort to keep it in the reaction chamber as long as possible. You do not want un-burnt uranium escaping, you want it all burnt in the reaction chamber. The general rule is that as long as the hydrogen mass expelled is 25 to 50 times a high as the uranium mass expelled the uranium losses are within acceptable limits. The various open-cycle designs use different strategies to make the hydrogen to uranium exhaust flow ratio as high as possible.

    Closed Cycle

    Gaseous Core NTR closed 1
    Exhaust Velocity20,405 m/s
    Specific Impulse2,080 s
    Thrust445,000 N
    Thrust Power4.5 GW
    Mass Flow22 kg/s
    Total Engine Mass56,800 kg
    T/W0.80
    FuelFission:
    Uranium Hexafluoride
    ReactorGas Core
    Closed-Cycle
    RemassLiquid Hydrogen
    Remass AccelThermal Accel:
    Reaction Heat
    Thrust DirectorNozzle
    Specific Power13 kg/MW
    Gaseous Core NTR closed 2
    Thrust Power0.6 to 231 GW
    Exhaust velocity10,800 to 31,400 m/s
    Thrust117,700 to 14,700,000 n
    Engine mass30 to 300 tonne
    Engine T/W0.4 to 5.0
    Operating Pressure400 to 1600 atm
    NASA report nuclear lightbulb
    Thrust Power3.7 GW
    Engine Power4.6 GW
    Exhaust velocity18,300 m/s
    Thrust409,000 n
    Engine mass32 tonne
    Engine T/W1.3
    Operating Pressure500 atm
    Propellant mass flow22.3 kg/s
    Liberty Ship
    Propulsion SystemNuclear Lightbulb
    Exhaust Velocity30,000 m/s
    Specific Impulse3,058 s
    Thrust/Engine5,340,000 N
    Number Thrustersx7
    Thrust37,380,000 N
    Thrust Power560.7 GW
    Mass Flow1,246 kg/s
    Total Engine Mass378,000 kg
    T/W10
    FuelFission:
    Uranium Hexafluoride
    Wet Mass2,700,000 kg
    Dry Mass1,600,000 kg
    Mass Ratio1.69 m/s
    ΔV15,697 m/s
    Specific Power0.67 kg/MW

    Closed-cycle gaseous core fission / nuclear thermal rocket AKA "Nuclear Lightbulb". Similar to an open-cycle gas core fission rocket, but the uranium plasma is confined in a fused quartz chamber. It is sort of like a child's classic Easy-Bake Oven. Except that there is propellant instead of cake mix and the light bulb is full of fissioning uranium instead of electricity.

    You can read more about this on the Unwanted Blog in the posts here, here, and here.

    The good news is that unlike the open-cycle GCNR it does not spray glowing radioactive death there is no uranium escaping in the exhaust. The bad news is that the maximum exhaust velocity is halved, as is the Delta-V. Yes, I did ask some experts if it was possible to make some kind of hybrid that could "shift gears" between closed and open cycle. Sorry, there would be no savings over just having two separate engines.

    The maximum exhaust velocity is halved because you are trying to have it both ways at once. The higher the propellant's temperature, the higher the exhaust velocity and rocket Delta-V. Unfortunately solid core nuclear reactors have a distressing habit of vaporizing at high temperatures (as do all material objects). Gas core reactors are attempting to do an end run around this problem, by having the reactor start out as high temperature vapor. But adding the quartz chamber is re-introducing solid material components into the engine, which kind of defeats the purpose. The only thing keeping this from utter failure is the fact that quartz does not heat up as much due to the fact it is transparent.

    Even with the restrictions, it seems possible to make a closed-cycle GCNR with a thrust to weight ratio higher than one. This would allow using the awesome might of the atom to boost truely massive amounts of payload into Terra orbit, without creating a radioactive wasteland with every launch. See the GCNR Liberty Ship for an example. The Liberty Ship can boost in one launch more payload than any given Space Shuttle does in the shuttles entire 10 year operating life. Then the Liberty Ship can land and do it again.

    The ideal solution would be to somehow constrain the uranium by something non-material, such as a mangnetohydrodynamic force field or something like that. Alas, currently such fields can only withstand pressures on the order of the breeze from a flapping mosquito, not the 500 atmospheres of pressure found here. But since researchers are working along the same lines in their attempts to make a fusion reactor, this may change. And I did find a brief reference to something called an "MHD choke" in reference to slowing the escape of uranium into the exhaust stream of an open-cycle gas core rocket. I'm still trying to find more information on that.

    The high pressure is to ensure the uranium vapor is dense enough to sustain a fission reaction.

    NUCLEAR COTV

    The nuclear Cargo Orbital Transport Vehicle (COTV) concept analyzed combined the desirable features of the chemical COTV and the electrical COTV — high thrust and high specific impulse, respectively. The stage, shown on Figure A-21, has a nuclear gas core, light bulb-shaped engine with a theoretical specific impulse of 2250 seconds and a thrust level of 890,000 newtons. The component mass breakdown is given in Table A-3.

    Although such a system could meet the short trip time requirement for personnel transfer and the high performance requirement for cargo transfer, the development risks and the presence of nuclear materials in LEO eliminated this system from further consideration.

    VCR light bulb fission
    VCR light bulb fission
    Exhaust Velocity19,620 m/s
    Specific Impulse2,000 s
    Thrust56,400 N
    Thrust Power0.6 GW
    Mass Flow3 kg/s
    Total Engine Mass72,566 kg
    T/W0.08
    FuelFission:
    Uranium Hexafluoride
    ReactorGas Core
    Closed-Cycle
    RemassSeeded Hydrogen
    Remass AccelThermal Accel:
    Reaction Heat
    Thrust DirectorNozzle
    Specific Power131 kg/MW

    Most fission reactors avoid meltdown, but the vapor core reactor (VCR) runs so hot (25000 K) that its core vaporizes.

    At this temperature, the vast majority of the electromagnetic emissions are in the hard ultraviolet range. A “bulb” transparent to this radiation, made of internally-cooled a-silica, bottles the gaseous uranium hexafluoride, while letting the fission energy shine through.

    The operating pressure is 1000 atm. The UF6 fuel is prevented from condensing on the cooled wall by a vortex flow field created by the tangential injection of a neon “buffer” gas near the inside of the transparent wall.

    In a generator mode, the UV uses photovoltaics to generate electricity. In a propulsion mode, the UV heats seeded hydrogen propellant, which exits at a specific impulse of 2000 seconds.

    From High Frontier by Philip Eklund
    NASA Report

    The pictured engine is the "reference engine" described in the report Studies of Specific Nuclear Light Bulb and Open-Cycle Vortex-Stabilized Gaseous Nuclear Rocket Engines. I will give the high-lights from the report, but for all the boring nitty-gritty details you'll have to read the report yourself. Please note that as always, "down" is the direction the thrust is going (to the right in the blueprint) and "up" is the opposite direction (to the left). I apologize for the use of imperial units instead of metric. The report is in imperial, and it is too much of a pain to change everything.

    The important statistics: Specific impulse is 1870 seconds (18,300 m/s), thrust 409,000 newtons, engine mass 32,000 kg, thrust-to-weight ratio 1.3.

    The other stats. The total volume of the reaction chambers (cavities) is 170 cubic feet. There are seven cavities, each six feet long. The cavity pressure is 500 atmospheres. The specific impulse is 1870 seconds (report says can theoretically be from 1500 to 3000 seconds). The total propellant flow (including seed and nozzle transpirant coolant flow) is 49.3 pounds per second. The thrust is 92,000 pounds. The engine power is 4600 megawatts. The engine weight is 70,000 pounds. If one can design a variable-throat-area nozzle (instead of fixed-area) this will result in a major decrease in the required chamber pressure during startup.

    Configuration

    The basic configuration is seven separate unit cavities surrounded by moderator-reflector material in between each cavity (beryllium oxide) and surrounding the entire cavity array (graphite). Each cavity is 6.0 feet long and the total volume of all seven cavities is 169.8 cubic feet. The cavity pressure is 500 atmospheres due to criticality and fuel density considerations.

    Lightbulbs

    In each lightbulb, a critical mass of gaseous uranium creates thermal radiation. The thermal radiation can pass through the transparent quartz crystal walls of the lightbulb, but the uranium vapor cannot. This means no lethal uranium enters the exhaust. Hydrogen propellant flowing over the lightbulb is heated to high temperatures by the thermal radiation and is expelled out the rocket nozzles, producing thrust. The hydrogen is "seeded" with tungsten dust because it too is ordinarily transparent to thermal radiation. The seeding makes it opaque, and allows it to be heated. Seven "lightbulbs" are used instead of one, since that increases the total lightbulb radiating area by about 2.2 times.

    Transparent quartz walls

    The transparent quartz wall of the lightbulb contains lots of coolant channels. This is because the quartz is mostly transparent to thermal radiation, but not totally. And fissioning uranium produces an awful lot of thermal radiation. I told you that nuclear lightbulb designers were trying to have it both ways. The coolant channels are marked "circumferential coolant tubes" in the diagram below.

    Inside a lightbulb

    Inside the lightbulb, neon buffer gas is used to create a vortex ring to suspend the gaseous nuclear fuel (a "radial inflow" vortex). The vortex ring looks like an elongated donut (I know it looks like two separate blobs above, that's due to the fact the diagram is a cross-section). One of the important jobs done by the neon buffer gas is to prevent the 42,000°R uranium plasma from making contact with the lightbulb walls. This would be very bad, as the walls would be instantly vaporized. The neon passes along the lightbulb walls, bends round the end caps, then travels down the long axis of the lightbulb (right down the center of the vortex ring). When it reaches the fore end cap, it is removed from the lightbulb through a port (marked "thru-flow" in diagram above).

    The removed neon is very hot, and contains unburnt uranium and fission products. It is cooled by mixing with low-temperature neon, which condenses the unburnt uranium vapor into hot liquid uranium. The liquid uranium is separated from the neon by a centrifuge and sent back into the vortex (at point marked "fuel injection"). The neon is cooled further then it too is sent back into the vortex (at point marked "buffer gas injection"). While examining the blueprint, I noticed that the centrifuges, and indeed the entire uranium fuel delivery system is conspicuous by its absence. Probably classified.

    Note that the centrifuges is a neat solution to the problem of fission fragments clogging up the fuel. In essence, this design has its own built-in nuclear fuel reprocessing plant. Of course the nasty fission fragments will have to be stored and eventually disposed of.

    Lightbulb dimensions

    The total volume inside all the lightbulbs is 84.9 cubic feet, which is 12.1 cubic feet per lightbulb. The radius of the uranium fuel containing region is 85% of the radius of the transparent wall. While the fissioning uranium fuel has a core temperature of 42,000° Rankine, the outer surface is only at 15,000° Rankine.

    Propellant flow in a lightbulb

    The propellant is assumed to exit with a temperature of 80% of the fuel temperature, or 12,000° Rankine. This is because the quartz transparent walls will reflect about 15% of the thermal radiation back inside. By some compilcated reasoning that you will find in the report, the total thermal radiation from the lightbulbs is 4.37 x 106 BTU/sec. The hydrogen propellant has an "enthalpy" of 1.033 x 105 BTU/pound at 12,000°R. So by dividing the two, one discovers that the entire engine can support a propellant flow rate of 42.3 pounds per second, which means 6.07 lb/sec for each of the seven cavities.

    If that last paragraph confused you, let me explain. As a simple example, if a pound of hydrogen at 5°R contains 2 BTUs ("enthalpy"), and the engine puts out 6 BTU per second, then obviously the engine can heat up 6 / 2 = 3 pounds of hydrogen per second. Why do we care? If you multiply the propellant flow rate by the exhaust velocity you will discover the engine's thrust value. And that's a number we do care about.

    The tungsten dust that the propellant is seeded with has a particle diameter of 0.05 microns. The seed density is 1.32 x 10-2 lb/ft3, which is about 3.9 percent of the inlet propellant density. This can probably be reduced if tungsten dust was in the form of thin flat plates instead of spherical particles.

    The hydrogen propellant enters the pressure shells from the fore end (see "Primary Circuit Inlet" in pressure shell diagram below). A bit is bled off from small H2 flow ports in order to pressurize the interior of the shells, circulating to provide coolant to the engines and machinery. But most of it is fed into the turbopump, then injected into the cavities. Since the fore end of each cavity is almost blocked off by the butt end of the lightbulb, there is only a narrow rim to inject the hydrogen.

    In the diagram to the right, you can see how the propellant is fed from the pink pipe into the pink-and-gold wedge-shaped injectors. I presume there are three injectors per cavity, spraying into the clear area between the transparent wall's coolant manifolds and buffer gas injectors.

    Uranium fuel

    The total fissioning uranium in all seven vortexes be about 25.2 pounds of uranium (about 3.6 pounds per cavity). You would ordinarily need more to ensure nuclear criticality, but the required amount is brought down by the beryllium oxide neutron reflector encasing each cavity. The average uranium fuel density is 0.409 lb/ft3. The total density of the neon-uranium mix inside the vortex is about 0.56 lb/ft3. A unit of neon gas will spend about 3.8 seconds inside the cavity. A unit of uranium will spend about 19 seconds inside the cavity. This implies a uranium fuel flow rate of 0.19 lb/sec per cavity.

    According to my slide rule, if the array of seven cavities is producing 4,600 megawatts, it means that the array is burning a miniscule total of 0.055 grams (0.00012 pounds) of uranium fuel per second (0.0079 grams per cavity per second). It still needs the full 3.6 pounds per cavity to be present in order to burn the fraction of a gram.

    The theoretical maximum specific impulse possible is 2230 seconds. Due to this designs incomplete expansion, transpiration coolant flow in the nozzle, presence of tungsten seeding, and friction losses the specific impulse is reduced to 84% or 1870 seconds. Total propellant flow (allowing for tungsten seeds and transpiration cooling) is 49.3 lb/sec. This would result in a thrust of 92,000 pounds force. For complicated reasons you can find in the report, this implies that the exhaust nozzles are 0.0875 feet in diameter at the throat expanding to 2.04 feet diameter at the exit.

    Uranium refueling

    Careful readers may have noticed how the description avoids mentioning the details on how one gets the uranium into the lightbulbs. This is because it is quite a difficult problem, and each of the proposed solutions has drawbacks. The basic problem is old reliable: all the atomic fireworks inherent in 235U will happen if you merely let too much of it accumulate in one place. You have to store it diffuse and somehow bring it together in the lightbulb.

    Method #1 Store it as uranium hexafluoride gas. This would be in large tanks of low pressure (i.e., low density) and with the tanks full of neutron absorbing foam. Pump enough into the lightbulb, a chain reaction will start, and well before the reaction reaches 13,000°R the uranium will have separated from the fluorine.

    The problem is that now you have the insanely dangerous task of dealing with 13,000°R fluorine gas. At room temperature the blasted stuff will violently react with any element in the known universe except helium and neon. A temperature of 13,000°R makes it about 13,000 times as deadly. It will explosively corrode away anything solid in its path like molten lead on facial tissue. Chemist Derek Lowe sarcastically notes that "At seven hundred freaking degrees, fluorine starts to dissociate into monatomic radicals, thereby losing its gentle and forgiving nature." You can read more about the suicidal risk of dealing with hot fluorine in his amusing blog post.

    Method #2 Store it as sub-critical chunks of uranium, melt them, and inject the molten uranium into the lightbulb. Uranium melts at 1403°K, which is difficult but not impossible. The plan is to somehow turn the molten uranium into a sort of aerosol mist suspended in hot neon.

    The problem is that the molten uranium wants to plate itself all over the melter and the aerosol spray equipment. Which is annoying if the material in question is something like lead, but disasterous if the material is radioactive and fissionable.

    Method #3 is to store the uranium cold as finely divided dust. As dust it is pumpable, injectable, and it will not plate over everything. Inside the lightbulb the uranium dust will be rapidly heated to vaporization by the nuclear reaction. This method does not have any major problems, except for the common problem of how to protect the transparent wall from being vaporized by the heat.

    Again, the uranium delivery system seems to be totally missing from the blueprint. The only bit present is the short stub of the injector at the top of each lightbulb.

    Pressure shells

    The entire engine is encased in two nested pressure shells constructed of filament-wound fiberglass. The inside of the inner shell is pressurized to 500 atmospheres. Hydrogen propellant enters through a 0.5 foot diameter duct at the fore end (aka "Primary Circuit Inlet"). There are seven 0.4 foot diameter holes in the aft end for the engine nozzles, one at zero degrees off-axis, the other six at 60°. The pressure shell can be separated into two parts along the flange at the point of maximum diameter, to allow an engineer or waldo manipulator access to the engine interior. This point is also where the rear structural grid protrudes from the interior, this is where the engine bolts onto the structural frame of the spacecraft to transmit the engine thrust.

    If you look at the large blueprint, you will see that parts of the rear structural grid penetrate the cavities to support the end-caps of the quartz lightbulbs.

    Coolant system

    The plumbing for the coolant system is rather complicated (translation: I don't understand it all). Click for larger image. You can use this diagram along with the large blueprint to attempt to puzzle out what all the pipes are for. Basically the propellant enters the system through the "Primary circuit inlet" (at lower left of plumbing diagram, and in the pressure shell diagram above) and leaves the system via the "Propellant injection" arrow, where the propellant is heated by the lightbulbs in the cavity and jets out the exhaust nozzles. In between, the propellant frantically threads its way over every single other engine component in a desperate attempt to cool them off.

    Cross sections

    Here are a set of cross sections through the cavities. The one on the left is zoomed in on the cavity interior, the other two gradually zoom out.

    UAC Report

    The information comes from a series United Aircraft Corporation reports written mostly by Thomas L. Latham. There are more reports than the ones I've used.

    The reference design had seven cells with six surrounding the center cell. The entire engine was sized to fit into the Space Shuttle cargo bay. It was also sized at 4.6 gigawatts, 409,000 Newtons, and a specific impulse of 1,860 seconds in order to avoid the need for external heat radiators. At this level no radiators are required for the moderator or pressure vessel, open-cycle cooling will suffice. Above a specific impulsle of 1,860 seconds radiators will be needed or the engine will melt.

    If the specific impulse is above 2,500 seconds the nozzle throats will require their own cooling system.

    The hydrogen propellant is seeded with tiny tungsten particles due to the unfortunate fact that hydrogen is transparent to the frequencies emitted by the nuclear reaction. Otherwise the chamber walls would be heated instead of the propellant, which is the exact opposite of what we want. The fissioning U235 or U233 fuel also emits ultraviolet light that degrades the transparency of the enclosing quartz "lightbulb." The researchers were experimenting with seeding the uranium with something that would turn the UV into infrared in order to protect the quartz. Happily the ionizing radiation does expose the degraded quartz to a radiation damage annealing effect that restores transparency to some extent.

    The fuel is in the form of Uranium Hexafloride.

    The average dose rate in the filament-wound fiberglas pressure vessel was calculated to be 0.17 mrad/sec. This would allow about six full-power runs of 1000-sec duration (about 17 minutes) before the total dose became 1000 mrad, the estimated allowable dosage before degradation of the laminate strength commences.


    SYSTEMS


    PRIMARY HYDROGEN PROPELLANT CIRCUIT
         This is basically the propellant, passing from the propellant tanks to be heated by the nuclear light bulbs, and then rushing through the exhaust nozzles to provide thrust. Along the way it provides some cooling for various items.
         Starting at the tank, the primary hydrogen pump sends it through a H2-H2 heat exchanger for preheating (and providing additional heat rejection for the Secondary Hydrogen Circuit). It passes through a H2-Ne heat exchanger to cool off the neon gas in the Neon And Fuel Circuit. It passes through the Fuel And Neon Separator. A turbine then sends it through the Solid Moderator and End-Wall Liners. Somewhere along the line it is seeded with tungsten microparticles so the hydrogen will be heated by the nuclear light bulbs.
         Finally it experiences extreme Direct Heating from the nuclear light bulbs, and exits through the exhaust nozzles.
    SECONDARY HYDROGEN CIRCUIT
         Basically the coolant system. It runs cooling hydrogen over the pressure vessel, nozzles, flow divider, tie rods, liner tubes, and the transparent walls of the quartz light bulbs (during shutdown it also cools the Fuel And Neon Separator).
         The now-hot hydrogen passes through a H2-H2 heat exchanger to give the heat to the space radiator. The lukewarm hydrogen passes through a second H2-H2 heat exchanger to cool down further and preheat the propellant hydrogen.
    NEON AND FUEL CIRCUIT
         The Neon Make-Up supply keeps the neon pressure in the circuit at the required level. The uranium-235 Fuel Make-Up keeps the amount of fuel droplets in the circuit at the required level. Both are fed into the Fuel Cavity in the interior of the quartz light bulbs to create the furious nuclear reaction (unless engine shut-down is in progress, then the Fuel Control Valve closes to shut off the uranium). The reaction provides the direct heating to the Primary Hydrogen Propellant Circuit. Some of the neon goes through the Cavity Bypass Flow.
         Only a fraction of the uranium undergoes fission. So the neon/uranium that comes out of the Fuel Cavity is sent through the Neon and Fuel Separator to strain the uranium out of the neon gas. The neon is cooled which makes the uranium gas condense into liquid droplets. The two are separated by a centrifuge. The neon is cooled further by the H2-Ne heat exchanger.
         The neon goes to the Neon Pump, the uranium goes to the Fuel Pump and the cycle begins anew.

    For additional details see Ref. 5 (Nuclear studies of the nuclear light bulb rocket engine).

    Neon supply is the Neon Make-Up supply, keeping the neon pressure in the circuit at the required level. It is fed into the Fuel Cavity (Unit Cavity) tangentally just inside the quartz light bulb Transparent Wall. This creates the neon-uranium vortex.

    The Fuel distillation canister is the Fuel Make-Up. It is fed by the Fuel Pump into the fuel injection duct, introducing it into the Fuel Cavity (Unit Cavity). This creates the furious nuclear reaction inside the quartz light bulb, providing the direct heating to the Primary Hydrogen Propellant Circuit.

    The mixture of hot neon, unburnt gaseous uranium fuel, and fission products exits the Fuel Cavity via the Exhaust Duct (about two meters long). Not shown is how cool neon is introduced into the entire length of the exhaust duct to [1] cool the exhaust from 6550 K to 1500 K, [2] prevent the exhaust from severely damaging the exhaust duct, [3] condense the gaseous uranium into liquid uranium droplets, and [4] ensuring that the uranium droplets condense inside the neon gas, instead of on the walls of the exhaust duct causing a nuclear reaction.

    The 1500 K neon-uranium droplet flow is sent to the Neon and Fuel Separator (Separator) where the two are isolated by a centrifuge. The neon is cooled by the H2-Ne heat exchanger and goes to the Neon Pump. The uranium fuel goes to the Fuel Pump. Alternatively the uranium is distilled to separate out the silicon seeding and the uranium is deposited in the fuel distillation canister.

    Values for weight flow rates, temperature, and volume flow rates are indicated at various stations in the system.

    In the Neon and Fuel Separator, the seven exhaust duct inlet pipes from the seven nuclear light bulb unit cavities enter from the left. They enter two inlet plenums: four inlet pipes on the top plenum and three on the bottom. Each plenum has an injection slot delivering the gas mix into the separator cavity, with a velocity of 500 m/s at a steep angle designed to spin the gas. The spin centrifugally separates the uranium from the neon, at about 100,000 g's. The uranium is harvested by uranium collector tubes on the separator wall, while the neon is harvested by an outlet pipe on the separator's long axis. The separator cavity and uranium collector tubes have to be maintained at or above 1,500 K, or the uranium will condense on them. This will not only clog the thing up, but if enough uranium plates out it will accumulate a critical mass with regrettable results.


    START-UP

    Startup Sequence

    1. Fill hydrogen ducts and neon system from storage to a pressure equal to approximately 20 atmospheres
    2. turn on neon recirculation pump
    3. inject fuel until critical mass is reached
    4. increase power level and adjust flow rates and cavity pressure to maintain criticality and limit component temperatures to tolerable level
    5. inject propellant seeds when 10 percent of full power is reached
    6. increase power to desired operating leve

    The paper looks at two "power ramps", going from cold to full power in 60 seconds or a more leisurely 600 seconds. Below a temperature of 15,000°R the fusing uranium is heating up the hydrogen propellant mainly by convection. Above 15,000°R the uranium heats the propellant by infrared thermal radiation.

    Since convection does such a pathetic job of transfering heat, most of the fission energy goes to heating up the uranium dust instead of the propellant. In about five seconds flat the uranium reaches 12,000°R, and vaporizes from dust into red-hot gas. Then at 15,000°R thermal radiation takes over and the uranium temperature rises more slowly (which you can see by the way the curve starts flattening out). At 60 or 600 seconds (depending upon which power ramp you used) the uranium is at the nominal temperature of 45,000°R. It won't rise any higher unless the engine is exploding or something rude like that.

    As previously mentioned the hydrogen propellant is pretty much transparent to thermal radiation, which is most unhelpful. Normally the infrared will shoot right through the hydrogen without heating it up. So tungsten dust is seeded into the propellant to soak up the thermal radiation and heat the propellant by conduction. Any thermal radiation that misses the seeding will hit the far wall of the propellant chamber, which is also the beryllium oxide moderator (BeO) helping to keep the uranium fissioning. The thermal heating of the BeO is nothing but wasted energy but the seeding is doing the best it can. The BeO is designed so it can handle up to 2,400°R.

    Since the BeO moderator outweighs the uranium dust by several orders of magnitudue, it takes far longer to heat up. As you can see from the graph the uranium fuel starts heating up after only 0.03 seconds but the BeO doesn't even start heating until 10 seconds, about 300 times longer. The uranium gets up to nominal temperature in 60 seconds but the BeO takes 300 seconds. And the BeO only gets up to 2,400°R while the uranium is smokin' at 45,000°R. That is for the 60 second ramp. The 600 second ramp has both the uranium and BeO all warmed up at the same time, only because 600 seconds gives the BeO time to catch up.

    However, the shorter 60 second ramp is desireable, because the 600 second ramp wastes precious propellant. Take the propellant mass required for a standard 20 minute burn at full power. The 60 sec ramp requires an additional 2.7% propellant as startup wastage. The 600 sec ramp requires a whopping 27% additional, which is totally unacceptable. What, do I look like I am made of propellant? The paper says it might be possible to reduce the ramp time down to 6 seconds, in the interest of reducing the propellant startup wastage even further (presumably to 0.27%).

    The critical mass of uranium-235 fuel required in the quartz tubes increases during the ramp up. It requires 18.6 pounds at zero power up to 30.9 lbs at full power. For the 60 second ramp up full power initially happens at 28.2 lbs, but rises to 30.9 lbs at 300 seconds. This is because at 60 seconds the BeO moderator has only warmed up about two-thirds of the way to its max temperature. Apparently once the BeO is fully warmed up the critical mass rises.

    When the paper was read, one of the attendees was skeptical about pressure. Specifically if the pressure of the uranium/neon mix is not the exact same as the pressure of the hydrogen propellant, the pressure differential will shatter the quartz tube like dropping an old-school incandescent lightbulb on a concrete floor. The paper authors insisted that the two pressures could be balanced rapidly enough to prevent that unhappy state of affairs. They say that a differential of two or three atmospheres will shatter the blasted tube, so they want to keep the diff under 2/3rds atm. Yikes, I didn't know that! That would instantly ruin the propulsion system, and spray everybody and everything close by with fissioning uranium.


    PERFORMANCE


    SHUTDOWN

    Shutdown Sequence

    1. Close Fuel Injection Control Valve (turn off the uranium)
    2. Begin Linear Decrease in Propellant Flow Rate (propellant flow past light bulbs to exhaust nozzles)
    3. Begin Linear Increase in Radiator Flow Rate (flow from coolant heat exchanger to radiator)
    4. Maintain Secondary Circuit (flow of hydrogen coolant) and Cavity Neon Flow (buffer gas flow inside the quartz light bulbs) at Full Power Value.

    Once the engine shut-down sequence is initiated, it takes six seconds for the power level to drop to zero. It only takes 0.8 seconds for power level to drop to 0.01 of full power, during which time the contained uranium fuel drops from the steady-state level of 13.65 kg down to 11.5 kg.


    Pulsed Close Cycle

    This is from Pulsed Plasma-Core Rocket Reactors (from Research on Uranium Plasmas and their Technological Applications page 52) (1970)

    This is actually quite clever. Dr. Winterberg was trying to address the two main problems with open-cycle gas core reactors: preventing unburnt U235 from escaping out the exhaust nozzle, and dealing with wear and tear on the engine from the horrifically high operating temperatures. His solution was to pulse the reaction.

    Now remember nuclear fission 101: when a thermal neutron crashes into a uranium 235 nucleus, the nucleus is split into fission fragments, and nuclear energy is released. Oh, and it also emits several neutrons, which keep the chain reaction going.

    You want to burn as much of the U235 as possible, that stuff's expensive. If you can't burn it all in the rocket chamber, the next best thing is to try and catch the unburnt U235 before it escapes out the exhaust and re-use it.

    where ΔNu/Nu is the percent of U235 that was successfully burnt in a fission reaction, σf is the fission neutron cross section, φ is the neutron flux, and τ is the fuel confinement time (or lifetime in the reactor if engine is a solid core NTR).

    In other words, improving the amount of U235 burnt means increasing the the amount of uranium atoms getting in the way of neutrons, increasing the number of neutrons for the uranium to get in the way of, and increasing how long the uranium atoms are playing demolition derby with the neutrons. Which is kind of obvious if you think abou it.

    So if a bog-standard nuclear power reactor had a neutron cross section σf of 10-22 cm3, a neutron flux φ of 1015, and was turned on τ of 103 seconds (16.6 minutes); then the ΔNu/Nu u235 burnup would be 0.0001 or 0.01%.

    Open-cycle gas core nuclear rockets are really bad at confining the fuel for any reasonable length of time. τ is really low. To make up for this you have to increase the neutron cross section or the neutron flux. Or both. Increasing the neutron cross section means drastically increasing the chamber pressure to make the U235 cloud more dense, which means more mass for a heavy-duty pressure chamber, which sends the engine's thrust-to-weight ratio gurgling down the toilet. Increasing the neutron flux means more neutron heating of the engine, or even enough neutron heating to actually vaporize the engine.

    Dr. Winterberg noted that while increasing the neutron cross section is probably out of the question, there might be a way to manage an increase in neutron flux. The neutron heating of the engine relies upon duration. The longer the engine is exposed to the neutron flux, the hotter it gets. Reduce the exposure time and you reduce the engine temperature rise. In other words: Pulse the reaction. You can use a fantastically high neutron flux as long as the duration of the flux is short enough so that the engine does not overheat. Wait for the engine to cool off then you can pulse again.

    Taken to extremes, you'll have the equivalent of an Orion drive, where the reaction is less a slow energy release and more like an Earth-Shattering Kaboom. A bomb in other words. But Dr. Winterberg saw there was a lot of performance improvement possible using pulses much less violent than bomb-level. More to the point, improvements that would allow the engine to get away with having very short confinment times.

    The engine will use a high neutron flux to pulse a series of "soft" nuclear detonations. This will have the following advantages:

    • The high neutron flux will increase the U235 burnup rate to the point where you can get away with a shorter required fuel confinement time. The short pulse will ensure that the neutron flux does not vaporize the engine.
    • The higher temperatures created in the reaction chamber will increase the exhaust velocity and specific impulse something wonderful. Again the short pulse will prevent the temperatures from damaging the engine
    • Pulse operation allows starting the chain reaction from a uranium-propellant mixture at high density with a small critical mass. This allows the reaction chamber and the rest of the engine to be smaller than other gas-core designs.
    • Using pulsed operation allows using a dynamic system to separate the fuel from the propellant, meaning to prevent uranium from escaping out the exhaust so the engine will be more closed-cycle than open cycle. Details to follow.

    Figure (a)

    The reactor vessel is surrounded by a conventional nuclear reactor (not shown). It is designed to be powered up then powered down rapidly, to create an intense pulse of neutron flux (something like φ = 1014/cm2 sec) inside the reactor vessel.

    Valve V opens, and into the reactor vessel is injected a slug of hydrogen propellant, containing a subcritical piece of U235. The valve snaps shut behind the slug.

    Note that the U235 is off-center inside the slug, further away from the exhaust nozzle than most of the propellant. This is so when the U235 explodes, most of the hydrogen propellant will be blown out the exhaust nozzle before any of the fissioning U235 reaches the nozzle exit.

    The U235 is still fully embedded in the propellant, none of the U235 is exposed. This is so all the nuclear explosion energy hits the propellant, instead of frying the interior of the reactor vessel.

    A tiny "trigger" piece of U235 is injected at high velocity down pipe T.

    Figure (b)

    When the trigger enters the subcritical U235, the surrounding nuclear reactor simultaneously pulses an intense neutron flux. The assembly becomes prompt critical and a small nuclear explosion ensues. This heats the hydrogen propellant which is pushed out the exhaust nozzle, creating thrust. Propellant on the other sides of the explosion protecting the reactor vessel from thermal radiation.

    Figure (c)

    Just before the unburnt U235 and fission fragment cloud escapes through the exhaust nozzle, the nozzle plug P closes the nozzle. The nozzle plug has to close at a rate of about 104 cm/sec, which can be done with a plug driven by pressurized gas. The hot propellant / unburnt U235 / fission fragment cloud is trapped inside the reactor vessel. This is sucked out of the reactor vessel through pipe E.

    The gases are sent through a heat radiator to be cooled off. Then they enter a fuel-propellant reprocessing plant. This separates the three ingredients. The fission fragments are disposed of. The hydrogen propellant is sent to the propellant tank. The unburnt U235 is carefully fabricated into subcritial fuel masses, being very careful not to let a critical mass accidentally accumulate. The subcritical masses are sent to the fuel storage unit.

    Open Cycle

    The open-cycle gas core engine has a radioactive exhaust, there is no getting around it. So the first thing you have to do is estimate the radiation hazard and ensure the crew has adequate radiation shielding.

    The second thing to do is find a design that does not wastefully allow expensive un-burnt uranium to escape out the tailpipe. Again the general rule is that as long as the hydrogen mass expelled is 25 to 50 times a high as the uranium mass expelled the uranium losses are within acceptable limits. The various open-cycle designs use different strategies to make the hydrogen to uranium exhaust flow ratio as high as possible.

    Crew radiation dose from plume of Gas-Core rocket

    In the open-cycle gas-core nuclear rocket concept the heat source is fissioning uranium gas. This released heat is radiated to and absorbed by the hydrogen propellant, The heated propellant is exhausted through a nozzle, producing thrust. The fission fragments that are formed and the unfissioned uranium fuel are also exhausted into the vacuum of space. As the plume is formed, the crew is exposed to gamma radiation from the fission fragments in the plume.

    The radiation dose to the crew from the fission fragments in the plume can be separated into two components. Component one results from the fact that there is a microscopic amount of plume material that has sufficient kinetic energy to flow back towards the vehicle. Some of this material will strike and stick to the vehicle. Since this material will contain fission fragments, these gamma radiation sources will stay with the crew throughout the entire trip and this dose could represent a significant source of radiation. Masser(3) has estimated this dose and has concluded it would be less than 10-3 rem for a typical manned Mars mission.

    Component two of the dose results from the fission fragment distribution throughout the entire plume volume and is potentially much larger than component one. Since the plume contains over 99 percent of the exhausted material, 99 percent of the fission fragments will be in the plume. It is the purpose of this paper to estimate the radiation dose rate and total dose to the crew from the fission fragments in the plume for four specific missions to the planet Mars.

    Another source of radiation is caused by the delayed decay of the fission fragments that are passing through the nozzle. This includes delayed neutrons which can cause secondary fissioning and gamma's. This source, however, has not been included. There is another radiation source associated with the gas-core reactor, that of the reactor core. This radiation source, along with solar radiation, must be ultimately considered when total dose rates to the crew are evaluated. This study, however, is concerned only with that part of the total radiation problem that arises from the fission fragments in the plume volume.


    3. Masser, C. C., "Radiation Hazzard from Backflow of Fission Fragments from the Plume of a Gas-Core Nuclear Rocket," Research on Uranium Plasmas and Their Technological Applications, SP- 236, 1971, NASA, Washington, D.C.

    (ed note: the equations used to draw these graphs are in the document. I didn't bother to include them since they involve calculus. The radiation doses in the graphs give spacecraft designers the radiation shielding requirements)

    1. For the most probable fission fragment retention, time of 100 seconds, and crew nozzle separation of 100 meters, the radiation dose varied from 170. to 36. rem for the 80 and 200 day round trip times respectively. Five centimeters of lead shielding would reduce the radiation dose by two orders of magnitude, thereby protecting the crew. The increase in vehicle weight would be insignificant. For example, a shield of five centimeters thickness and four meters in diameter would add 7120 kilograms to the vehicle gross weight of 0.94 million kilograms. Also additional attenuation is available In the form of liquid hydrogen propellant, spacecraft structure, nuclear fuel, equipment, and stores.

    2. For the trip times included in this analysis the total radiation dose to the crew is proportional to the energy required for the mission. Therefore, within the ranges used in this analysis one can estimate the crew radiation dose by knowing the energy needed for the mission.

    3. For the crew-nozzle separation of 100 meters, approximately 50 percent of the plume radiation is received from the first 0.1 kilometer into the plume. This percentage is increased to 90 percent for 1 kilometer and 100 percent for 100 kilometers into the plume.

    4. For an 80 day round trip to Mars, with a crew-nozzle separation distance of 100 meters, the radiation dose varied from about 0.5 to 1670. rem for fission fragment retention times of 10,000 and 10 seconds, respectively.

    5. For all cases, increasing the crew distance from 100 to 200 meters from the nozzle exit reduced the unshielded radiation dose by half.

    General Open Cycle
    Open Cycle
    Propulsion SystemGas Core NTR
    Exhaust Velocity35,000 m/s
    Specific Impulse3,568 s
    Thrust3,500,000 N
    Thrust Power61.2 GW
    Mass Flow100 kg/s
    Total Engine Mass200,000 kg
    FuelFission:
    Uranium Hexafluoride
    ReactorGas Core
    Open-Cycle
    RemassLiquid Hydrogen
    Remass AccelThermal Accel:
    Reaction Heat
    Thrust DirectorNozzle
    Specific Power3 kg/MW
    Engine mass30-200 tonne
    T/W 11.9 to 1.8
    Open Cycle 2
    Propulsion SystemGas Core NTR
    Exhaust Velocity50,000 m/s
    Specific Impulse5,097 s
    Thrust5,000,000 N
    Thrust Power0.1 TW
    Mass Flow100 kg/s
    FuelFission:
    Uranium Hexafluoride
    RemassLiquid Hydrogen
    Specific Power2 kg/MW
    Engine mass30-200 tonne
    T/W 17.0 to 2.5
    Open Cycle 3
    Thrust Power GW
    Exhaust velocity25,000 to 69,000 m/s
    Thrust19,600 to 108,000 n
    Engine mass40 to 110 tonne
    T/W0.05 to 0.10
    Operating Pressure400 to 2000 atm
    Open Cycle MAX
    Exhaust Velocity98,000 m/s
    Specific Impulse9,990 s
    Thrust3,000,000 N
    Thrust Power0.15 TW
    Mass Flow31 kg/s
    Total Engine Mass15,000 kg
    T/W20
    FuelFission:
    Uranium Hexafluoride
    Tanker
    Propulsion SystemGas Core NTR
    Open-cycle
    Exhaust Velocity35,316 m/s
    Specific Impulse3,600 s
    Thrust3,500,000 N
    Thrust Power61.8 GW
    Mass Flow99 kg/s
    FuelFission:
    Uranium Hexafluoride
    RemassLiquid Hydrogen
    Wet Mass433,000 kg
    Dry Mass268,000 kg
    Mass Ratio1.62 m/s
    ΔV16,943 m/s

    Gaseous core fission / nuclear thermal rocket AKA consumable nuclear rocket, plasma core, fizzer, cavity reactor rocket. The limit on NTR-SOLID exhaust velocities is the melting point of the reactor. Some engineer who obviously likes thinking "outside of the box" tried to make a liability into a virtue. They asked the question "what if the reactor was already molten?"

    Gaseous uranium is injected into the reaction chamber until there is enough to start a furious chain reaction. Hydrogen is then injected from the chamber walls into the center of this nuclear inferno where it flash heats and shoots out the exhaust nozzle.

    The trouble is the uranium shoots out the exhaust as well. This not only makes the exhaust plume dangerously radioactive but it also wastefully allows expensive unburnt uranium to escape before it contributes to the thrust.

    The reaction is maintained in a vortex tailored to minimize loss of uranium out the nozzle. Fuel is uranium hexaflouride (U235F6), propellant is hydrogen. However, in one of the designs, U235 is injected by gradually inserting into the fireball a long rod of solid uranium. The loss of uranium in the exhaust reduces efficiency and angers environmentalists.

    In some designs the reaction chamber is spun like a centrifuge. This encourages the heavier uranium to stay in the chamber instead of leaking into the exhaust. This makes for a rather spectacular failure mode if the centrifuge's bearings seize.

    You can find more details here.


    The thermal radiation from the fission plasma is intended to heat the propellant. Alas, most such engines use hydrogen as the propellant, which is more or less totally transparent to thermal radiation. So the thermal stuff goes sailing right through the hydrogen (heating it not at all) then striking the reaction chamber walls (vaporizing them).

    To remedy this sorry state of affairs, gas-core designers add equipment to "seed" the propellant with something opaque to thermal radiation. Most of the reports suggest tungsten dust, with the dust size about the same as particles of smoke, about 5% to 10% seeding material by weight. The seeding absorbs all but 0.5% of the thermal radiation, then heats up the hydrogen propellant by conduction. The chamber walls have to cope with the 0.5%.


    Most of the reports I've read estimate that the reaction chamber can withstand waste heat up to 100 megawatts per square meter before the chamber is destroyed. For most designs this puts an upper limit on the specific impulse at around 3,000 seconds.

    However, if you add a heat radiator to cool the reaction chamber walls and the moderator surrounding the reaction chamber, you can handle up to about 7,000 seconds of specific impulse. The drawback is the required heat radiator adds lots of mass to the engine. A typical figure is of the total mass of a gas core engine with radiator, about 65% of the mass is the radiator.

    Another fly in the ointment is that the proposed seeding materials turn transparent and worthless at about the 10,000 second Isp level. To push the specific impulse higher a more robust seeding material will have to be discovered. Since current heat radiators cannot handle Isp above 7,000 seconds, robust seeding is not a priority until better radiators become available.


    Yet another challenge is that 7% to 10% of the fission plasma power output is not in the form of thermal radiation, but instead neutrons and gamma rays. Which the propellant will not stop at all, seeded or not. This will penetrate deep into the chamber walls and moderator (since gamma-rays are far more penetrating than x-rays), creating internal waste heat.

    Sub 3,000 Isp designs deal with radiation heat with more regenerative cooling. Higher Isp need even more heat radiators.


    Most designs in the reports I've read use 98% enriched uranium-235 (weapons-grade). The size of the reaction chamber can be reduced somewhat by using uranium-233 according to this report.

    The reaction chamber size can be reduced by a whopping 70% if you switch to Americium-241 fuel according to this report. The drawback is the blasted stuff is $1,500 USD per gram (which makes every gram that escapes un-burnt out the exhaust financial agony). The short half-life means there is no primordial Americium ore, you have to manufacture it in a reactor via nuclear transmutation. The report estimates that for a 6 month brachistochrone trajectory the spacecraft would need about 2,000 kilograms of the stuff. Which would be a cool three million dollars US. I'm sure the price would drop if dedicated manufacturing sites were established to create it.


    If used for lift off it can result in a dramatic decrease in the property values around the spaceport, if not the entire country. An exhaust plume containing radioactive uranium is harmless in space (except to the crew) but catastrophic in Earth's atmosphere.


    Amusingly enough, this is the best match for the propulsion system used in the TOM CORBETT: SPACE CADET books. However the books are sufficiently vague that it is possible the Polaris used a nuclear lightbulb. According to technical advisor Willy Ley, "reactant" is the hydrogen propellant, but the books imply that reactant is the liquid uranium.


    POROUS WALL GAS CORE ENGINE

    GAS CORE FISSION THERMAL ROCKETS

    The temperature limitations imposed on the solid core thermal rocket designs by the need to avoid material melting can be overcome, in principle, by allowing the nuclear fuel to exist in a high temperature (10,000 — 100,000 K), partially ionized plasma state. In this so-called "gaseous- or plasma-core" concept, an incandescent cylinder or sphere of fissioning uranium plasma functions as the fuel element. Nuclear heat released within the plasma and dissipated as thermal radiation from its surface is absorbed by a surrounding envelope of seeded hydrogen propellant that is then expanded through a nozzle to provide thrust. Propellant seeding (with small amounts of graphite or tungsten powder) is necessary to insure that the thermal radiation is absorbed predominantly by the hydrogen and not by the cavity walls that surround the plasma. With the gas core rocket (GCR) concept Isp values ranging from 1500 to 7000 s appear to be feasible [Ref. 26]. Of the various ideas proposed for a gas core engine, two concepts have emerged that have considerable promise: an open cycle configuration, where the uranium plasma is in direct contact with the hydrogen propellant, and a closed-cycle approach, known as the "nuclear light bulb engine" concept, which isolates the plasma from the propellant by means of a transparent, cooled solid barrier.

    Porous Wall Gas Core Engine

    The "open cycle," or "porous wall," gas core rocket is illustrated in Fig. 9. It is basically spherical in shape and consists of three solid regions: an outer pressure vessel, a neutron reflector/moderator region and an inner porous liner. Beryllium oxide (BeO) is selected for the moderator material because of its high operating temperature and its compatibility with hydrogen. The open cycle GCR requires a relatively high pressure plasma (500 — 2000 atm; 1 atm = 1.013 × 105 N/m2 ) to achieve a critical mass. At these pressures the gaseous fuel is also dense enough for the fission fragment stopping distance to be comparable to or smaller than the dimensions of the fuel volume contained within the reactor cavity. Hydrogen propellant, after being ducted through the outer reactor shell, is injected through the porous wall with a flow distribution that creates a relatively stagnant non-recirculating central fuel region in the cavity. A small amount of fissionable fuel (1/4 to 1 % by mass of the hydrogen flow rate) is exhausted, however, along with the heated propellant.

    Because the uranium plasma and hot hydrogen are essentially transparent to the high energy gamma rays and neutrons produced during the fission process, the energy content of this radiation (~7—10% of the total reactor power) is deposited principally in the solid regions of the reactor shell. It is the ability to remove this energy, either with an external space radiator or regeneratively using the hydrogen propellant, that determines the maximum power output and achievable Isp for the GCR engines. To illustrate this point, an open cycle engine with a thrust rating of 220 kN (50,000 lbf) is considered. We assume that 7% of reaction energy Prx reaches the solid, temperature-limited portion of the engine and that the remainder is converted to jet power at an isentropic nozzle expansion efficiency of ηj. Based on the realtionships between Isp, reactor power, and propellant flow rate (ṁp) given below.

    (ed note: elsewhere in this website, ṁ is called "m-dot")

    0.93·Prx(MW) = 4.9×10-6·F(N)·Isp(s) / ηj

    0.93·Prx(MW) = 4.9×10-5·ṁp(kg/s)·Isp2(s) / ηj

    a 5000 s engine generating 7500 MW of reactor power will require a flow rate of 4.5 kg/s at rated thrust. If the hydrogen is brought into the cavity at a maximum overall operating temperature of 1400 K, no more than 1.2% of the total reactor power (~17% of the neutron and gamma power deposited in the reactor structure) can be removed regeneratively (ṁp cp ΔT ≈ 90 MW). Total removal requires either (1) operating the sold portions of the engine at unrealistically high temperatures (>11,000 K at ṁp = 4.5 kg/s) or (2) increasing the propellant flow rate substantially to 36.8 kg/s (at 1400 K), which reduces the engine's Isp to 1750 s. "Closed cooling cycle" space radiator systems have been proposed [Ref. 27] as a means of maintaining the GCR's operational flexibility. With such a system, adequate engine cooling is possible even during high Isp operation when the hydrogen flow is reduced. Calculations performed by NASA/Lewis Research Center [Ref. 28] indicate that specific impulses ranging from 3000 to 7000 s could be attained in radiator-cooled, porous wall gas core engines.

    The performance and engine characteristics for a 5000 s class of open cycle GCRs are summarized in Table 4 for a range of thrust levels. The diameter of the reactor cavity and the thickness of the external reflector/moderator region are fixed at 2.44 m and 0.46 m, respectively, which represents a near-optimum engine configuration. The engine weight (Mw) is composed primarily of the pressure vessel (Mpv); radiator (Mrad); and moderator (Mmod).

    Table 4
    Characteristics of 5000 s Porous Wall Gas Core Rocket Engines
    Thrust


    F(kN)
    Engine
    Power

    Prx(MW)
    Radiator
    Power

    Prad(MW)a
    Engine
    Weight

    Mw(mT)
    Pressure
    Vessel
    Weight
    Mpv(mT)b
    Radiator
    Weight

    Mrad(mT)c
    Moderator
    Weight

    Mmod(mT)d
    Alpha


    αp(kW/kg)
    Thrust
    to
    Weight
    F/Mw
    2275043.552.3106.33610.34.3×10-2
    4415008761.61312.63617.57.3×10-2
    11037502188618323631.30.13
    220750043512324633643.80.18
    44015,000870193311263655.90.23
    1. For a hydrogen cavity inlet temperature of 1400 K and a heat deposition rate that is 7% of the reactor power, the ratio of radiated to total reactor power is a constant equal to 5.8%.
    2. The weight of the spherical pressure vessel is based on a strength-to-density value of 1.7×l05 N-m/kg [Ref. 29] which Is characteristic of high strength steels.
    3. Used in these estimates is a radiator specific mass of 145 kg/MW [Ref. 28] which is based on a heat rejection temperature of 1225 K and a radiator weight per unit surface area of 19 kg/m2
    4. Density of BeO is 2.96 mT/m3.

    By fixing the engine geometry in Table 4 the mass of the BeO moderator remains constant at 36 mT. However, the pressure vessel and radiator weights are both affected by the thrust level. While the radiator weight increases in proportion to the extra power that must be dissipated at higher thrust, the reason for the increase in pressure vessel weight is slightly more subtle. For a constant Isp engine an increase in thrust is achieved by increasing both the reactor power and hydrogen flow rate. In order to radiatively transfer this higher power to the propellant, the uranium fuel temperature increases, necessitating an increase in reactor pressure to maintain a constant critical mass in the engine. Accommodating this increased pressure leads to a heavier pressure vessel. (In going from 22 kN to 440 kN, the engine pressure rises from 570 atm to 1780 atm).

    As Table 4 illustrates, the moderator is the major weight component at lower thrust levels (<110 kN) while the radiator becomes increasingly more important at higher thrust. At thrust levels of 220 kN and above, the radiator accounts for more than 50% of the total engine weight. There is therefore a strong incentive to develop high temperature (~1500 K) liquid metal heat pipe radiators that could provide significant weight reductions in the higher thrust engines.

    Table 4 also shows an impressive range of specific powers (alphas) and engine thrust-to-weight ratios for the thrust levels examined. The F/Mw ratio for the 22 kN engine is over two orders of magnitude higher than the 5000 s nuclear-powered MPD electric propulsion system proposed in the Pegasus study [Ref. 30]. For manned Mars missions the higher acceleration levels possible with the GCR can lead to significant (factor of 5) reductions in trip time compared to the Pegasus system.

    HIGH SPECIFIC IMPULSE GAS CORE REACTORS

    (ed note: calculated estimates of gas core nuclear rocket engine weights for specific impulses ranging from 3000 to 7000 seconds and for engine thrusts ranging from 4400 to 440,000 newtons. Contains useful equations for calculating the mass of various engine components.)

    SUMMARY

    Virtually all existing or proposed rocket propulsion engines can be categorized as either high-thrust systems or high-specific-impulse systems. What is really needed for fast interplanetary travel is both characteristics, namely a high specific impulse (3000 sec or greater), and an engine thrust-weight ratio that is in the range from to 10-1. The characteristics of a gas-core nuclear rocket engine are examined in this study to see how closely it meets these requirements.

    Calculations were carried out to estimate gas-core engine weights for specific impulses ranging from 3000 to 7000 seconds and thrust levels from 4.4×103 to 4.4×105 newtons. A vapor-fin space radiator operating at 1100 K was incorporated into the engine system to dispose of waste heat not regeneratively removed by the hydrogen propellant. The total engine weight was composed of the individual weights of the radiator, the reactor moderator-reflector materials, the pressure shell, the nozzle, and the propellant turbopump. The study produced the following results and conclusions:

    1. Gas-core engines have the potential of producing a specific mass in the range 0.6 to 0.02 kilogram of weight per kilowatt of thrust power.

    2. For a specific impulse of 5000 seconds and a thrust of 1.1×105 newtons, engine weight is estimated to be 91 000 kilograms. This weight is composed of about equal proportions of radiator, moderator, and pressure shell weights. For the entire range of specific impulses and thrust levels of this study, engine weight varied from 35 000 to 380 000 kilograms.

    3. Engine weight increases with increasing specific impulse and with increasing thrust level. For a given specific impulse, higher thrust-weight ratios occur at higher thrust levels because engine weight does not increase as fast as the thrust does.


    Figure 1(a) illustrates schematically how this basic notion might be translated into a rocket engine. It is not unreasonable to picture this kind of engine as a nuclear "sun" with the central fireball and surrounding gas flow contained within a chamber' surrounded by structural materials. The analogy is not exact, of course, because the heat generation is due to nuclear fission rather than fusion. However, in both cases tha amount of energy that can be generated in, and released from, the fireball is essentially unlimited. There is, however, a limitation on how much energy can be absorbed by the hydrogen and turned into thrust without overheating the cavity wall or the exhaust nozzle. It is the amount of energy that reaches various solid, temperature-limited regions of the engines that ultimately limits the power generation and therefore the specific impulse.

    The proposed reactor shown in figure 1(a) is basically spherical. It is composed of an outer pressure vessel, a region of heavy-water reflector, a high-temperature beryllium moderator region, an inner heavy-water moderator, and finally a porous or slotted cavity liner. Approximately 7 to 10 percent of the reactor power is deposited in these solid regions of the reactor due to attenuation of high-energy gamma and neutron radiation. This heat is removed either by a coolant in an external space radiator loop, or regeneratively by the hydrogen propellant before it enters the central reactor cavity, The beryllium region is operated at a temperature of about 1300 K and the radiator at 1100 K.

    Uranium metal would have to be injected into this high-pressure region. Once inside the cavity, the uranium vaporizes and rises to temperatures sufficient to thermally radiate the energy that is generated by the fissioning uranium. A possible fuel injection technique might consist of pushing a thin rod of solid uranium metal at a high velocity through a shielded pipe (perhaps made of cadmium oxide) that penetrates the moderator. Some cooling of the uranium fuel and the shielded passage may be required to remove the heat that would be generated in the fuel as it passes through the moderator region. A 100-kilogram force would be required to drive a 0.15-centimeter diameter wire into a cavity with a pressure of 5.07×107 newtons per square meter. As it enters the cavity, the uranium instantly vaporizes and rises in temperature to about 55 000 K. Reactor startup could be achieved by first establishing the hydrogen flow. Next uranium particles would be blown into the dead cavity region to achieve nuclear criticality. The power would then be increased to a level sufficient to vaporize the incoming uranium rod.

    The seeded hydrogen is heated solely by absorbing the thermal radiation from the fissioning uranium fireball. The cavity walls receive only about 1 or 0.5 percent of the thermal radiation from the fireball. This wall protection is accomplished by introducing about 1 percent by weight of a seeding material such as graphite or tungsten particles into the hydrogen. This same technique is used in the nozzle region to reduce the hydrogen radiation heat load and the hydrogen temperature near the nozzle wall to tolerable levels. Seed concentrations of about 1 to 10 percent are required here. Figure 1 shows that some cold hydrogen can be introduced through the nozzle walls directly from the plenum at the downstream end of the engine if it is required. This would tend to reduce the specific impulse.


    SPECIFIC IMPULSE

    The specific impulse of a gas-core rocket engine is limited by the fraction of the reactor power that reaches the solid, temperature-limited portions of the engine, and by how that heat is removed. It is an unavoidable characteristic of the nuclear fission process that about 7 to 10 percent of the energy release is high-energy gamma and neutron radiation that will go through the hydrogen gas but be stopped in the surrounding solid reactor structure.

    This energy that is deposited in the moderator can be regeneratively removed by the incoming hydrogen propellant. There is, however, a limit to how much heat the hydrogen can accommodate. For a 3000-second specific impulse engine, 7 percent of the reactor power will heat all the hydrogen propellant to 2800 K before it enters the reactor cavity. To achieve a higher specific impulse would require the solid parts of the engine to operate at an unrealistically high temperature. If the reactor materials, including the porous cavity wall, were limited to a little over 1000 K and if only regenerative cooling were used, the specific impulse would be limited to 2000 seconds.

    Higher specific impulses are possible by using an external radiator to reject part of the moderator heat to space. The radiator is shown schematically in figure 1. To bring the hydrogen into the reactor cavity at 1000 K for a specific impulse of 5000 seconds would require that the hydrogen remove no more than about 1 percent of the reactor power from the moderator, as shown in figure 2. The remaining 6 to 9 percent would have to be removed by the radiator loop.

    It appears that the ultimate limitation on specific impulse of a gas-core engine will depend on the ability to absorb the thermal radiation from the fuel in the hydrogen so that the cavity wall and the nozzle wall do not receive an excessive heat flux. Based on current estimates of the optical absorption and emission properties of the gases involved, a recent Lewis in-house study indicates that the maximum specific impulse is in the range 5000 to 7000 seconds.


    ENGINE WEIGHT

    The engine weight analysis used for this study is the same as was presented in reference 4, except for the addition of a space radiator and the elimination of a specific equation for fuel volume as a function of the hydrogen-to-uranium-mass-flow ratio (how many units of hydrogen propellant are expended in the exhaust before one unit of uranium is lost). The engine weight is taken to be the sum of the individual weights of the moderator, pump, nozzle, pressure shell, and radiator:

    (1)

    An initial series of calculations were made to select a "best" cavity diameter and moderator thickness combination. This preliminary optimization was done at values of specific impulse (5000 sec) and thrust (4.4×104 N) that are centered in the ranges covered in this study. One cavity diameter and one moderator thickness were selected on this basis, and then held constant for all subsequent variations of specific impulse and thrust. Thus, after this initial reactor optimization, the moderator weight was not a variable in this study.


    Engine Pressure

    In order to calculate the weights of the nozzle, turbopump, and pressure shell, it was necessary to calculate the pressure required to have a critical mass in the engine. This was obtained from the following equation:

    (2)

    where P is the reactor pressure in atmospheres, Mc, is the critical mass in kilograms, F is the engine thrust in newtons, Isp is the specific impulse in seconds, Dc is the reactor cavity diameter in meters, and VF is the fraction of the reactor cavity filled with fuel. Equation (2) is more general than the form used in reference 4 where a specific relation between fuel volume fraction and hydrogen-touranium-mass-flow ratio was used to eliminate VF from equation (2). The present study was carried out for a fuel volume fraction of 0.25. Recent fluid mechanics experiments using air/air indicate that this value should be attainable for hydrogen-to-uranium-flow ratios in the range 100 to 400.


    Nozzle, Turbopump, And Pressure Shell

    Nozzle:
    (3)
    Pump:
    (4)
    Shell:
    (5)

    where the component weights are in kilograms, F is thrust in newtons, Isp is specific impulse in seconds, P is reactor pressure from equation (2) in atmospheres, and Rs is the inside radius of the pressure shell in meters.

    The radiator weight estimate was based on a recent study of a vapor-fin for space power systems. The vapor-fin design would weigh 290 kilograms per megawatt of radiated power, based on operating the radiator at 945 K. For this study it was assumed that the same radiator, or at least one of the same weight per unit surface area (19 kg/m2 of plan form area), could be operated at 1100 K. This gives a weight of 145 kilograms per megawatt of radiated power:

    (6)

    Equations (2) to (6) were used to obtain the weight of each engine component. Equation (1) was used to obtain the total engine weight. For this study, calculations were carried out for specific impulses of 3000, 5000, and 7000 seconds, and for engine thrusts from 4.4×103 to 4.4×105 newtons.

    It may be necessary to operate the radiator at a pressure less than that of the reactor cavity in order to keep the lightweight vapor-fin design. For example, the pressure stress in the radiator tube walls would range from 10.14×107 to 50.7×107 newtons per square meter for internal tube pressures ranging from 10.14×106 to 5.07×107 newtons per square meter, respectively. This same pressure stress range could be reduced by a factor of 3 by increasing the tube wall thickness such that the overall radiator weight would increase by about 20 percent. In an actual engine design, one might not choose to do this, but instead operate the radiator at a lower pressure than that of the reactor. This would then require a pump to increase the radiator discharge pressure to that inside the reactor pressure vessel.


    RESULTS AND DISCUSSION

    The engine weight results are presented and discussed in this section. First, the effect of varying the cavity diameter and the moderator thickness is presented. Based on these results, one cavity diameter and one moderator thickness are selected for the remainder of the calculations. For this fixed engine geometry, the effect of thrust level on engine weight is determined for a specific impulse of 5000 seconds. Next, the effect of specific impulse on engine weight is presented over a range of thrust levels. Finally, these results are presented in terms of a parameter commonly used to describe lowthrust propulsion devices, engine specific mass, which is the ratio of engine weight to thrust power (in kg/kW).


    Effect of Cavity Diameter and Moderator Thickness

    Changes in cavity diameter or in moderator thickness cause two effects on engine weight. One effect is that the weight of moderator material is changed. The other effect is that the uranium density required for criticality is changed. This changes the required reactor pressure, which, in turn, results in a change in the pressure shell weight.

    These two influences on engine weight tend to oppose each other. For example, reducing the moderator thickness reduces the moderator weight, but increases the pressure required for criticality. Thus, there is some optimum moderator thickness that gives a minimum engine weight. It is possible, however, that the engine pressure at this minimum-weight geometry would be unrealistically high, so that one might choose to operate at some near but off-optimum configuration that has a somewhat lower pressure.

    Engine weight was calculated for five combinations of cavity diameter and moderator thickness. The results are shown in figure 3. The critical mass requirements are listed in table I. These engine weight calculations were carried out for a specific impulse of 5000 seconds and a thrust level of 4.4×104 newtons. Both of these values are centered within the ranges covered in this study.

    Cavity diameters of 2.4, 3.6, and 4.9-meters were used with a constant moderator thickness of 0.76 meter. Moderator thicknesses of 0.61, 0.76, and 0.91 meter were used with a constant cavity diameter of 3.6 meters. Within these ranges, reductions in either parameter caused a decrease in engine weight but an increase in engine pressure. A cavity diameter of 2.4 meters with a moderator thickness of 0.76 meter produced the lightest engine, which weighed 64 000 kilograms. The reactor pressure for this engine was 7.8×107 newtons per square meter.

    Further reduction of cavity diameter below 2.4 meters would probably have produced a slightly lighter engine, but at the expense of an extremely high pressure. This is shown in figure 4. On the basis of these results, a 2.4-meter cavity diameter and a 0.76-meter moderator thickness were selected as representing a near-optimum engine configuration. The remaining calculations were carried out using this one engine geometry.


    Effects of Thrust Level on Engine Weight

    Higher thrust requires a heavier engine. The component weights are shown in figure 5 for engine thrust varying from 0 to 1.1×105 newtons at a specific impulse of 5000 seconds. For a thrust below about 5×104 newtons, the radiator weight is not too important, compared to the moderator and the pressure shell weights. At a thrust of 1.1×105 newtons, the radiator, pressure shell, and moderator each contribute about one-third of the total engine weight.

    For higher thrusts, the radiator weight begins to dominate. This is shown in table II. At a thrust of 2.2×104 newtons, the radiator only contributes 6400 kilograms to the total engine weight of 51 000 kilograms, or about 12 percent. At a thrust of 2.2×105 newtons, the radiator accounts for 64 000 kilograms out of 133 000 kilograms, or almost 50 percent. This indicates that for thrusts above 2.2×105 newtons, at this specific impulse of 5000 seconds, significant weight reductions can be achieved if higher temperature radiators can be developed. For example, the radiator weight could be cut in half by operating at 1300 K instead of 1100 K. All the calculations of this study were done for a radiator temperature of 1100 K.


    Effect of Specific Impulse on Engine Weight

    Higher specific impulses require heavier engines, at a given thrust level. This is shown in figure 6. For a thrust of 4.4×104 newtons, engine weights of 50 000, 64 000, and 73 000 kilograms are required for specific impulses of 3000, 5000, and 7000 seconds, respectively.

    At a specific impulse of 3000 seconds, a radiator may not be necessary. If the hydrogen propellant enters the reactor at 2800 K, it can regeneratively remove all the gamma and neutron heat deposition from the moderator region. This produces a lighter engine, as shown by the dashed curve in figure 6. Whether one would actually choose to operate the moderator at a little over 2800 K in order to achieve the lower weight would depend on a number of factors, such as the particular mission involved and the effect of moderator temperature on engine reliability and life. The solid curves in figure 6 are based on a hydrogen cavity inlet temperature of 1400 K. Table III lists the percent of reactor power that must be radiated away for this temperature.

    Gas-Core Specific Mass

    For low-acceleration systems such as electric thrusters, it is useful to characterize the propulsion device in terms of its specific mass. This parameter α is in kilograms of powerplant weight per kilowatt of thrust power. It can be related to the engine thrust-weight ratio as follows. The thrust power, or jet power as it is sometimes called, is given by 1/2 (F×Isp×g), which is simply the kinetic energy in the jet exhaust. SP Using this relation, the specific mass α, in kilograms per kilowatt, is

    (7)

    where the specific impulse is in seconds and the engine thrust-weight ratio is dimensionless.

    Figure 7 shows the results of the present study presented on this basis. The specific mass of a gas-core engine varies from a high of 0.6 to a little less than 0.02 for specific impulses from 3000 to 7000 seconds and thrust levels from 4.4×10+3 to 4.4×10+5 newtons. Higher specific impulse or higher thrust produces a lower, and therefore better, specific mass.


    SUMMARY OF RESULTS

    An analysis has been carried out to determine the characteristics of a low-thrust, high-specific-impulse, gas-core, nuclear rocket engine. The latest information on reactor critical mass requirements, radiant-heat-transfer properties, and fluid mechanics were used. For specific impulses above 3000 seconds, it was necessary to incorporate a space radiator as an engine system component. Engine weight was calculated for specific impulses ranging from 3000 to 7000 seconds, and for thrust levels from 4.4×103 to 4.4×105 newtons. Radiator weight estimates were based on an operating temperature of 1100 K. The calculations indicate the following results:

    1. Gas-core engines have the potential of producing a specific mass in the range 0.6 to 0.02 kilogram of weight per kilowatt of thrust power.

    2. For a specific impulse of 5000 seconds and a thrust of 1.1×105 newtons, engine weight is estimated to be 91 000 kilograms. This weight is composed of about equal proportions of radiator, moderator, and pressure shell weights. For the entire range of specific impulses and thrust levels of this study, engine weight varied from 35 000 to 380 000 kilograms.

    3. Engine weight increases with increasing specific impulse and with increasing thrust level. For a given specific impulse, higher thrust-weight ratios occur at higher thrust levels because engine weight does not increase as fast as the thrust does.

    Hybrid-Fuel

    This is from Mini Gas-Core Propulsion Concept by R. E. Hyland (1971) and A Study Of The Potential Performance And Feasibility Of A Hybrid-Fuel Open Cycle Gas Core Nuclear Thermal Rocket by Lucas Beveridge (2016).

    As previously mentioned open-cycle gas core engines solve the "reactor got so hot it vaporized" problem by starting out with the reactor already vaporized. The primary problem is how to prevent the uranium gas from prematurely escaping out the exhaust nozzle, but the secondary problems are pretty bad as well.

    To start the uranium fissioning, you need a certain amount of uranium at a certain density surrounded by enough neutron reflectors to kick stray neutrons back into play. Sadly, by definition, gaseous uranium has a much lower density than solid uranium. As it works out, for the engine to require a non-outrageous critical mass of uranium and a non-outrageous reaction chamber volume, the core pressure has to be very very high. Which will require a massive pressure vessel. Which makes the engine mass skyrocket. Which savagely cuts into the available payload mass and seriously degrades the engine's thrust-to-weight ratio.

    Oh, calamity and woe! How can this problem be remedied?


    HYLAND MINI-GAS CORE
    Isp1,600 sec
    Exhaust Velocity15,696 m/s
    Thrust450 N
    Reactor Mass2,200 kg
    Pressure Shell Mass3,100 kg
    Radiator Mass4,930 kg
    Total Mass10,230 kg
    T/W0.0045
    Fuel233U
    PropellantLH2
    Outer Diameter1.22 m
    Cavity Diameter0.61 m
    233U Plasma Diameter0.43 m
    233U Plasma Mass1.42 kg
    233U Plasma Power
    (Pgas)
    4.5 MW
    233U Driver Power
    (Psolid)
    15.9 MW
    Total Engine Power
    (Ptotal)
    20.4 MW
    Radiator Alpha310 kg/MW
    Pressure51 MPa
    Exhaust Temp4,000 to
    5,000 K

    HYLAND MINI-GAS CORE

    Robert Hyland pondered the problem until the question arose "is it really necessary for all the uranium to be gaseous?"

    Hyland's solution was to embed a small solid core reactor in the walls of the chamber, as sort of a reactor layer. This is called the "driver core." It is far enough from the furious heat raging inside the chamber so it wouldn't melt. The driver core produces heat, but the important part is it produces neutrons. This makes the interior of the chamber so neutron-rich that the gaseous uranium does not have to be under such high pressure. In other words, the extra neutrons from the driver core lower the required critical mass of uranium gas inside the chamber.

    This allows the engine to get away with using a much less massive pressure vessel, which lowers the engine mass, which reduces the payload reduction and increases the thrust-to-weight ratio.

    Hyland said "I shall call him 'Mini-Gas Core.'" Lucas Beveridge called it the hybrid-fuel engine, since it uses both solid and gaseous uranium.

    Hyland scaled this to have an engine power of 20.4 MW, which implied a meager thrust of only 450 N. He thought it might be useful for unmanned space probes.

    So part of the total engine power is produced by the driver core (233U Driver Power or Psolid) and part of the total engine power is produced by the uranium plasma inside the chamber (233U Plasma Power or Pgas). Only Pgas is used to heat up the propellant to create thrust. Most of Psolid is just waste heat, a fraction of it is used to create neutrons to supercharge the uranium plasma. So heat radiators will be needed to get rid of the 15.9 megawatts worth of Psolid waste heat.

    Ptotal = Pgas + Psolid = 20.4 MW

    εgas = Pgas / Ptotal = 0.221

    εsolid = Psolid / Ptotal = 0.780

    εgas is the ratio of power in the 233U Plasma to the total. Hyland's Mini-Gas Core has a εgas of 0.221, or only 1/5th of the power is in the plasma. Beveridge found that was too low, and was focusing on a Low-ε engine with εgas = 0.51 and a High-ε engine with εgas = 0.673.


    BEVERIDGE HYBRID-FUEL

    BEVERIDGE
    HYBRID-FUEL
    Engine Common
    Thrust300,000 N
    Total Engine
    Power (Ptotal)
    3 GW
    Engine Mass<36,000 kg
    T/W0.85
    Low-ε Engine
    εgas0.51
    εsolid0.49
    Isp1,600 sec
    Exhaust Vel15,700 m/s
    High-ε Engine
    εgas0.673
    εsolid0.327
    Isp1,950 sec
    Exhaust Vel19,100 m/s
    MARS MISSION
    MissionConjunction
    (one-way)
    EngineHigh-ε
    Inert Mass36,000 kg
    Payload Mass
    (incl. crew)
    62,800 kg
    Dry Mass98,800 kg
    Propellant Mass33,620 kg
    Wet Mass132,420 kg
    Mass Ratio1.34
    Exhaust Vel19,100 m/s
    ΔV5,590 m/s
    Initial Accel2.27 m/s
    (0.23 g)

    Remember that εgas is the ratio of power in the 233U Plasma to the total. Hyland's Mini-Gas Core has a εgas of 0.221, or only 1/5th of the power is in the plasma. Beveridge focused on a Low-ε engine with εgas = 0.51 and a High-ε engine with εgas = 0.673.

    Beveridge found that it was not optimal if εsolid is larger than 0.50, that is, if more than 50% of the total engine power comes from the driver core. Hyland's design had εsolid = 0.780, or almost 80%. This means the Hyland's driver core needed more cooling than the cavity wall.

    The obvious solution won't work. Rockets in general use cold propellant to cool off engine components. So one would think the solution is to cool off the driver core with propellant, then send it into the chamber to be superheated by the uranium plasma. But since Hyland's engine only had about 20% of the total energy generated by the uranium plasma, the plasma would not significantly heat the propellant more than the driver core already had. Bottom line is the performance would be about the same as a garden-variety NERVA solid core reactor, but with an engine that was much more expensive.

    Example

    In Hyland's engine the driver core produces 78% of the power. Since the driver core is a solid-core reactor, it cannot go above 3,000K or it will melt. Since the uranium plasma is only 22% it can only heat the propellant about 500K more for a total exhaust temperature of 3,500K. Which is about the same as a bog-standard solid-core NTR.

    But if both the driver core and the uranium plasma produce 50% of the power, then the gas core can add about 2,400K more for a total exhaust temperature of 5,400K which is much better than a solid-core NTR. But wait! There's more! Above a temperature of about 5,000K, molecular hydrogen propellant dissociates into monoatomic hydrogen (single-H). This could increase the exhaust velocity and specific impulse by up to a factor of 1.4 (i.e., √2).

    To avoid that unhappy state of affairs, you have to use the un-obvious solution of using a heat radiator to cool the driver core. The trouble is that heat radiators add literally tons of penalty-mass to the engine. You will have to dial down the total engine power to control the heat radiator mass. The end result would be an engine with about the same mass as a standard nuclear-electric propulsion engine (NEP), fractionally more thrust, and drastically less specific impulse (Isp of 2,000 sec instead of 6,000 sec.) In which case it would be more advantageous to use NEP.

    Since neither of those solutions works, Beveridge found a third option. Design the engine so that the driver core power is less than 50% of the total. This means the driver core can be cooled by propellant, and the uranium plasma will most certainly heat the propellant more than the driver core did. A heat radiator is used to cool the chamber from uranium plasma heat. Bottom line: high specific impulse and high power.

    Beveridge did comparison studies on a pure open-cycle gas core, a Low-ε hybrid engine with εgas = 0.51 and a High-ε engine hybrid with εgas = 0.673. For comparison purposes they were all scaled to have a power level of 3 gigawatts. Unsurprisingly the low-ε had the lowest critical mass, the pure open-cycle had the highest, and the high-ε was somewhere in the middle.

    Coaxial
    Coaxial
    Exhaust Velocity17,658 m/s
    Specific Impulse1,800 s
    Thrust17,800,000 N
    Thrust Power0.2 TW
    Mass Flow1,008 kg/s
    Total Engine Mass127,000 kg
    T/W14
    FuelFission:
    Uranium Hexafluoride
    ReactorGas Core
    Open-Cycle
    RemassLiquid Hydrogen
    Remass AccelThermal Accel:
    Reaction Heat
    Thrust DirectorNozzle
    Specific Power1 kg/MW
    NASA-Lewis
    Thrust Power0.495GW
    Exhaust velocity22,000 m/s
    Specific Impulse2,200 s
    Thrust45,000 n
    Engine mass66,000 kg
    T/W0.68
    Diameter5 m
    Length5 m
    Fuel Temp20,000° R
    Propellant Temp10,000° R

    Gaseous core coaxial flow fission / nuclear thermal rocket.

    The basic problem of gas core nuclear rockets is ensuring that the hot propellant escapes from the exhaust nozzle, but the nuclear fuel does not. In this concept, the propellant and fuel are kept separate by a velocity differential. That is, a central, slow moving stream of fission fuel heats an annular, fast moving stream of hydrogen.

    Yes, the uranium jet is aimed straight at the exhaust nozzle. But they figured the uranium loss would be acceptable as long as 25 to 50 times as much hydrogen propellant escapes compared to uranium fuel (measured by mass).

    No, the concept does not work very well. In theory the difference in velocity should keep the uranium/plutonium and the hydrogen separate. Unfortunately the velocity differential at the boundry between the propellant and fuel generates shear forces. The fast hydrogen strips off uranium atoms from the slow fuel plume like a carpenter's plane (laminar and turbulent mixing processes). This means the hydrogen to uranium escape ratio drops below 25.

    The concept seems to have been abandoned.

    Vortex Confined
    Vortex Confined
    Vortex Confined
    Exhaust Velocity19,620 m/s
    Specific Impulse2,000 s
    Thrust50,400 N
    Thrust Power0.5 GW
    Mass Flow3 kg/s
    Total Engine Mass114,116 kg
    T/W0.04
    Frozen Flow eff.75%
    Thermal eff.70%
    Total eff.53%
    FuelFission:
    Uranium Hexafluoride
    ReactorGas Core
    Vortex Confined
    RemassSeeded Hydrogen
    Remass AccelThermal Accel:
    Reaction Heat
    Thrust DirectorNozzle
    Specific Power231 kg/MW

    The hotter the core of a thermodynamic rocket, the better its fuel economy. If it gets hot enough, the solid core vaporizes.

    A vapor core rocket mixes vaporous propellant and fuel together, and then separates the propellant out so it can be expelled for thrust. Energy is efficiently transferred from fuel to propellant by direct molecular collision, radiative heat, and direct reaction fragment deposition.

    The open-cycle arrangement illustrated accomplishes this by spinning the plasma mixture in a vortex maintained by tangential injection of preheated propellant from the reactor walls. The denser material is held to the outside of the cylindrical reactor vessel by centrifugal force. The fuel is subsequently cooled in a heat exchanger and recirculated for re-injection at the forward end of the reactor, while the propellant is exhausted at high velocity.

    The plasma source can be fission, antimatter, or fusion.

    For fission reactions, the outer annulus of the vortex is high-density liquid uranium fuel, and the low-density propellant is bubbled through to the center attaining temperatures of up to 18500 K. A BeO moderator returns many reaction neutrons to the vortex. Prompt feedback actuators maintain a critical fuel mass in spite of the turbulent flow of water or hydrogen propellant. Since the core has attained meltdown, reaction rates must be maintained by fuel density variation rather than with control rods or drums.

    For antimatter reactions, swirling liquid tungsten (about 4 cm thick) is used instead of uranium, for absorbing anti-protons.

    For fusion reactions, it is the propellant that is cooler and higher in density, and thus it is the reacting fuel ball that resides at the center of the vortex.

    N. Diaz of INSPI, 1990.

    From High Frontier by Philip Eklund
    Wheel Flow

    This is from Wheel-flow gaseous-core reactor concept (1965).

    John Evvard figures this gas-core rocket will have (like all the others) an upper limit of about 3,000 seconds of specific impulse, exhaust velocity of about 29,400 m/s. The design is trying to increase the propellant to fuel mass flow ratio to something between 25 and 50. Since uranium has something like 238 times the molecular weight of hydrogen increasing the mass flow ratio is very hard to do.

    The brute-force approach does not work. If you increase the engine pressure to 2,000 psi with a partial-pressure ratio of 80, preventing the reaction chamber from exploding will increase the reactor mass to something between 250,000 to 500,000 pounds. With that penalty weight the propellant load will have to exceed 500,000 to 1,000,000 pounds to capitalize on the increase specific impulse the engine enjoys over a conventional solid-core NTR. And even then the fuel mass flow ratio would be below 25. So this is a dead end.

    So the standard solution is to somehow make an incredibly high hydrogen-uranium volume flow ratio.

    There are numerous schemes to increase the volume flow.

    The vortex-confined GCR makes a vortex of gaseous uranium (sort of a smoke ring) with the center hole aligned with the thrust axis. Hydrogen is injected around the outer edge of the vortex, travels radially across the furiously fissioning uranium being heated all the way, enters the hole in the center of the smoke ring, turns 90 degrees and goes rushing out of the hole and out of the exhaust nozzle.

    The pious hope was that the centrifugal forces acting on the heavier uranium atoms would counteract the diffusion drag of the inwardly moving hydrogen. Sadly the drag produced by the flowing hydrogen is so great that it carries along too much of the valuable uranium.

    The coaxial-flow reactor was another idea that failed even harder. The uranium gas in the center moved really slow while the hydrogen gas around the rim moved really fast. The regrettable result was the velocity difference caused shear forces which allowed the dastardly hydrogen to drag uranium along with it right out the exhaust nozzle.


    John Evvard had a fresh idea: the Wheel-Flow Confined GCR.

    The problem with the vortex confined GCR was that the hydrogen moves through the uranium. This allows the hydrogen to drag along some uranium. The problem with the coaxial-flow is that though the hydrogen doesn't move through the uranium, it is moving at a vastly different velocity. This causes shear forces that allow the hydrogen to drag along some uranium.

    So Evvard tried to find a geometry where the hydrogen does not move through the uranium and it moves at the same velocity as the uranium.

    In the Wheel-flow there is a cylinder of gaseous fissioning uranium in the center of the chamber, spinning around its long axis.

    Hydrogen is injected at the outer surface of the cylinder and moves along the surface, not moving through the uranium. This avoid the vortex-confined GCR's problem. The hydrogen moves at the same velocity as the uranium gas cylinder. This avoids the coaxial-flow GCR's problem. The uranium and the hydrogen rotate as one, as if they were a solid wheel.

    After one rotation of the cylinder the hydrogen is good and hot. It then exits tangentally from the chamber into an array of exhaust nozzles. And there is your thrust.

    Uranium will be lost due to fission and some unavoidable diffusion into the hydrogen. Fresh uranium will be injected from the two end walls, entering the long axis of the uranium cylinder. The end wall will also rotate to match the wheel, to avoid stirring up turbulence.

    The main drawback is that the boundary layer between the hydrogen and uranium is unstable. Any blob of uranium entering the hydrogen blanket will be accelerated outward by simple boyancy. This could possibly be stablized by an axial magnetic field. The fissioning uranium is more ionized than the hydrogen so the magentic field will grab the uranium more firmly.

    Since the temperature inside the reaction chamber is hot enough to vaporize any material object the ions are moving like microscopic bats from hell. You'd think the high uranium molecular velocities would make the uranium cloud instantly explode to fill the chamber. Luckily the mean free path of individual atoms is a microscopic 10-7 meters or less (one micrometer, about the length of a bacteria). Since the hot uranium atoms cannot move further than the span of a typical e coli germ without crashing into other atoms their effective speed is slowed down about the same as the wheel rotational velocity.


    The report is a little vague about this design. It says that if the wheel-flow engine is used in a gravitational field, the spinning cylinder of fissioning uranium might settle to the bottom of the chamber, which is bad. However, unless you were using an open-cycle gas core nuclear engine spraying radioactive death from the nozzle as an aircraft engine I don't see the application.

    The idea seems to be that while some hydrogen is injected around the uranium gas cylinder for coolant, most of the propellant hydrogen goes across the top along the axial line. I guess the propellant lowers the gas pressure enough to levitate the uranium cylinder.


    In the standard wheel design, the end walls will have to be cooled since they are exposed to the fury of fissioning uranium. This can be avoided by bending the uranium gas cylinder so the ends meet, converting the cylinder into a torus donut shape. Since it is now a ring there are no end walls and no need to cool them.

    The problem is that the end walls were where the fresh uranium was injected, and it is unclear how to refresh the torus.


    This design makes a bit more sense. It uses a torus of uranium gas. The rocket rotates around the thrust axis to make artificial gravity. This pulls the torus outward, making it expand. Meanwhile the propellant hydrogen is roaring down the thrust axis, being heated and expelled out the exhaust nozzle. This lowers axial gas pressure and pulls the torus inward, making it contract.

    Between the artificial gravity and Bernoulli's principle the torus of uranium is held in place.

    Of course there is still the unsolved problem of how to refresh the torus.

    MHD Driven Rotation
    MHD Driven Rotation
    Design
    LowMedHigh
    Isp
    sec
    1,7921,7701,740
    Thrust
    tonnes
    46.835.830.4
    Thrust
    kiloNewtons
    459351298
    T/W ratio1:1211:1121:135
    H2/U235
    mass flow ratio
    106.428.414.2
    Mass flow
    kg/sec
    23.818.415.9
    Radiator area
    m2
    1.39e51.06e58.83e5
    Fission Power
    MW
    14,76011,1509,300
    Mass Schedule
    (metric tons)
    LowMedHigh
    Cavity Struct1246942
    Moderator-reflector2,1501,5202,150
    Cryogenic Magnet12898128
    Turbo-electric Gen999634482
    Radiator2,0901,5801,330
    Misc925239
    TOTAL ENGINE5,6904,0104,110

    This is from Gas-Core Nuclear Rocket With Fuel Separation by MHD-Driven Rotation (from Research on Uranium Plasmas and their Technological Applications page 155) (1970)

    The major problem with open-cycle gas core NTR is keeping the blasted uranium from escaping out the exhaust nozzle. Or at least only escaping after all the expensive uranium has been burnt in nuclear fission.

    The researchers noted that injecting gas tangentially at high velocity (Figure 1 (a)) would confine the U235 fuel to the outer region of the cavity yet allowing the propellant to diffuse radially into the center region was the great hope. The supersonic rotation would develop high centrifugal force, forcing the heavy U235 to the outer while permitting the light hydrogen into the middle. Nope, this was tested and it don't work no-way, no-how (though they put it "this configuration does not result in effective separation of the two gases").

    The researchers noted the next great hope was vortex-stabilization. The idea here was to exploit the high stability of the rotation flow instead of centrifugal force. The flow was subsonic, so the centrifugal force was negligible. A donut-shaped vortex of U235 floats in the center of the chamber, while hydrogen propellant flows around the edge of the chamber. The idea is that the hydrogen will stay in the outer regions due to the inherent stability of the rotation flow.

    This didn't work either.

    Looking more closely at the scheme of injecting gas tangentally, it was noticed that the centrifugal separation worked best in the part of the flow that resembled solid-body rotation. That is, rotating as if it was a solid brick of matter instead of rotating gas. So investigation focused on making the U235 and hydrogen gas rotate as if it was a solid body.

    The trouble with tangential gas injection is it develops into what is called an "inviscid vortex flow field". I don't know that that is either, but apparently it makes TGI about as effective as trying to push spaghetti uphill, when it comes to making a centrifuge. So a different means of rotating the gas will be needed.

    In Figure 1 (b) the entire cavity chamber will be spun mechanically to induce the centrifugal effect. Alas, in order to separate the uranium from the hydrogen you need about 1,000,000 gs of centrifugal force. No known construction material can withstand that sort of force so the chamber would explode like a bomb. To keep it from exploding you'd have to apply an external gas pressure of at least 10,000 atmospheres, which is rather excessive. What's worse is the friction loss from the external gas would become prohibitively large. Another failed concept.

    The study authors had an idea. How about spinning the uranium and hydrogen using electromagnetic forces? See Figure 1 (c)

    This uses the magic of Magnetohydrodynamics.

    If you send electrical current J in a direction parallel to the thrust axis (z-axis), a magnetic field B will be created radially at 90° (r direction). This is called J×B. The important point is the magnetic field will be pushing the gas towards the chamber walls, allowing the gases to rotate as if it was a solid body. Rotating such that the blasted U235 separates from the propellant, and is kept away from the exhaust nozzle.

    No chambers rotating so fast they explode, no friction loss from external gas at 10,000 atm, this design looks like it would actually work.


    The report presents a prototype engine.

    The cavity is typically seven to eight meters in both diameter and length. The radial mangetic field is produced by cryogenically cooled magnetic coils, and has a strength of about 1.0 tesla near the cavity walls. The coils draw a negligible amount of power. The total electrical current is about 20,000 amps, flowing through 200 pairs of segmented electrodes. The chamber pressure is 20 to 60 atmospheres. The maximum tangential rotational velocity is about 1.6 to 1.8 kiometers per second.

    The hydrogen propellant is introduced along the centerline of the cavity and flows through the center at low velocity. The propellant is heated mainly by radiation, plus a bit by conduction on the part of any propelant that brushes the hot uranium. Hydrogen propellant is regrettably mostly transparent to infrared heat rays, which is why most gas core designs seed the hydrogen with microscopic tungsten particles or something. In this design they seem to be relying upon uranium atoms for seeding, since some will diffuse into the propellant (about 0.00015 mole fraction).

    The chamber temperature varies from 10,000K at the chamber walls (in the hot uranium) to 6,000K at the centerline (in the propellant). This averages out to a specific impulse of approximately 1,770 seconds, which is actually pretty good. The thrust is about 40 metric tons or 392 kiloNewtons.

    The liquid hydrogen first flows through the superconducting magnetic coils to help keep them at cryogenic temperatures. It then passes through a pump to pressurize it to about 640 atmospheres. Now the propellant travels through the moderator-reflector wall heat exchanger, simultaneously cooling it off and getting real hot. The hot hydrogen enters the first-stage turboelectric generator, which supplies half the required MHD power. The hydrogen leaves the turbogenerator at about 107 atmospheres of pressure. It then passes through the moderator-reflector heat exchanger a second time, and enters the second-stage turboelectric generator. This produces the other half of the required MHD power. Finally the propellant enters the chamber to be superheated and exhausted to create thrust.

    The propellant only removes about 3% of the waste heat in the moderator-reflector. The other 97% of the waste heat is removed by a liquid-metal cooling system which expells the heat out of a heat radiator with a surface temperature of 1,200K. A fraction of this is diverted to an auxiliary power generator for other power needs.

    Nuclear Salt Water
    NSWR
    20% UTB
    Exhaust Velocity66,000 m/s
    Specific Impulse6,728 s
    Thrust12,900,000 N
    Thrust Power425.7 GW
    Mass Flow195 kg/s
    Total Engine Mass33,000 kg
    T/W40
    FuelFission:
    Uranium Tetrabromide
    ReactorGas Core
    Open-Cycle
    RemassWater
    Remass AccelThermal Accel:
    Reaction Heat
    Thrust DirectorPusher Plate
    Specific Power0.08 kg/MW
    90% UTB
    Exhaust Velocity4,700,000 m/s
    Specific Impulse479,103 s
    Thrust13,000,000 N
    Thrust Power30.6 TW
    Mass Flow3 kg/s

    This concept by Dr. Zubrin is considered far-fetched by many scientists. The fuel is a 2% solution of 20% enriched Uranium Tetrabromide in water. A Plutonium salt can also be used.

    Just to make things clear, there are two percentages here. The fuel is a 2% solution of uranium tetrabromide and water. That is, 2 molecules of uranium tetrabromide per 100 molecules of water.

    But the uranium tetrabromide can be 20% enriched. This means that out of every 100 atoms of uranium (or molecules of uranium tetrabromide), 20 are fissionable Uranium-235 and 80 are non-fissionable uranium. If it is 90% enriched, then 90 atoms are Uranium-235 and 10 atoms are non-fissionable. As a side note, 90% enriched is considered "weapons-grade".


    The fuel tanks are a bundle of pipes coated with a layer of boron carbide neutron damper. The damper prevents a chain reaction. The fuel is injected into a long cylindrical plenum pipe of large diameter, which terminates in a rocket nozzle. Free of the neutron damper, a critical mass of uranium soon develops. The energy release vaporizes the water, and the blast of steam carries the still reacting uranium out the nozzle.

    It is basically a continuously detonating Orion type drive with water as propellant. Although Zubrin puts it like this:

    As the solution continues to pour into the plenum from the borated storage pipes, a steady-state conditions of a moving detonating fluid can be set up within the plenum.

    He also notes that it is preferable to subject your spacecraft to a steady acceleration (as with the NSWR) as opposed to a series of hammer-blow accelerations (as with Orion).

    The controversy is over how to contain such a nuclear explosion. Zubrin maintains that skillful injection of the fuel can force the reaction to occur outside the reaction chamber. He says that the neutron flux is concentrated on the downstream end due to neutron convection. Other scientists are skeptical.

    Naturally in such a spacecraft, damage to the fuel tanks can have unfortunate results (say, damage caused by hostile weapons fire). Breach the fuel tubes and you'll have a runaway nuclear chain reaction on your hands. Inside your ship.

    The advantage of NSWR is that this is the only known propulsion system that combines high exhaust velocity with high thrust (in other words, it is a Torchship). The disadvantage is that it combines many of the worst problems of the Orion and Gas Core systems. For starters, using it for take-offs will leave a large crater that will glow blue for several hundred million years, as will everything downwind in the fallout area.

    Zubrin calculates that the 20% enriched uranium tetrabromide will produce a specific impulse of about 7000 seconds (69,000 m/s exhaust velocity), which is comparable to an ion drive. However, the NSWR is not thrust limited like the ion drive. Since the NSWR vents most of the waste heat out the exhaust nozzle, it can theoretically produce jet power ratings in the thousands of megawatts (meaning it is not power limited, like other nuclear propulsion). Also unlike the ion drive, the engine is relatively lightweight, with no massive power plant required.

    Zubrin suggests that a layer of pure water be injected into the plenum to form a moving neutron reflector and to protect the plenum walls and exhaust nozzle from the heat. One wonders how much protection this will offer.

    Zubrin gives a sample NSWR configuration. It uses as fuel/propellant a 2% (by number) uranium bromide aqueous solution. The uranium is enriched to 20% U235. This implies that B2 = 0.6136 cm-2 (the material buckling, equal to vΣfa)/D) and D = 0.2433 cm (diffusion coefficent).

    Radius of the reaction plenum is set to 3.075 centimeters. this implies that A2 = 0.6117 cm-2 and L2 = 0.0019. Since exponential detonation is desired, k2 = 2L2 = 0.0038 cm-2. Then k = U / 2D = 0.026 cm-1 and U = 0.03.

    If the velocity of a thermal neutron is 2200 m/s, this implies that the fluid velocity needs to be 66 m/s. This is only about 4.7% the sound speed of room temperature water so it should be easy to spray the fuel into the plenum chamber at this velocity.

    The total rate of mass flow through the plenum chamber is about 196 kg/s.

    Complete fission of the U235 would yield about 3.4 x 1012 J/kg. Zubrin assumes a yield of 0.1% (0.2% at the center of the propellant column down to zero at the edge), which would not affect the material buckling during the burn. This gives an energy content of 3.4 x 109 J/kg.

    Assume a nozzle efficiency of 0.8, and the result is an exhaust velocity of 66,000 m/s or a specific impules of 6,7300 seconds. The total jet power is 427 gigawatts. The thrust is 12.9 meganewtons. The thrust-to-weight ratio will be about 40, which implies an engine mass of about 33 metric tons.

    For exponetial detonation, kz has to be about 4 at the plenum exit. Since k = 0.062 cm-1, the plenum will have to be 65 cm long. The plenum will be 65 cm long with a 3.075 cm radius, plus an exhaust nozzle.

    Zubrin then goes on to speculate about a more advanced version of the NSWR, suitable for insterstellar travel. Say that the 2% uranium bromide solution used uranium enriched to 90% U235 instead of only 20%. Assume that the fission yield was 90% instead of 0.1%. And assume a nozzle efficency of 0.9 instead of 0.8.

    That would result in an exhaust velocity of a whopping 4,725,000 m/s (about 1.575% c, a specific impulse of 482,140 seconds). In a ship with a mass ratio of 10, it would have a delta V of 3.63% c. Now you're talkin...

    Ken Burnside: In my game universe, the engineers call the pumps that feed Uranium Tetrabromide solution into the reaction chamber "Wileys", reputedly after the engineer who first made them safe to use and maintain.

    More than likely, it's after the coyote of the same name...


    Winchell Chung: An appropriate name for what are basically atomic squirt-guns.

    From a thread in SFConSim-l (2002)
    Zubrin NSWR
    Zubrin NSWR
    Exhaust Velocity78,480 m/s
    Specific Impulse8,000 s
    Thrust8,696,900 N
    Thrust Power0.3 TW
    Mass Flow111 kg/s
    Total Engine Mass495,467 kg
    T/W1.79
    Frozen Flow eff.80%
    Total eff.80%
    FuelFission:
    Uranium Tetrabromide
    ReactorGas Core
    Open-Cycle
    RemassWater
    Remass AccelThermal Accel:
    Reaction Heat
    Thrust DirectorPusher Plate
    Specific Power1.45 kg/MW

    The illustration shows the vision of Robert Zubrin: a rocket riding on a continuous controlled nuclear explosion just aft of a nozzle/reaction chamber.

    The propellant is water, containing dissolved salts of fissile uranium or plutonium. These fuel-salts are stored in a tank made from capillary tubes of boron carbide, a strong structural material that strongly absorbs thermal neutrons, preventing the fission chain reaction that would otherwise occur.

    To start the engine, the salt-water is pumped from the fuel tank into an absorber-free cylindrical nozzle. The salt-water velocity is adjusted as it exits the tank so that the thermal neutron flux peaks sharply in the water-cooled nozzle.

    At critical mass (around 50 kg of salt water), the continuous nuclear explosion produces 427 GWth, obtaining a thrust of 8600 kN and a specific impulse of 8 ksec at a thermal efficiency of 99.8% (with open-cycle cooling). Overall efficiency is 80%.

    Robert Zubrin, "Nuclear Salt Water Rockets: High Thrust at 10,000 sec ISP," Journal of the British Interplanetary Society 44, 1991.


    You need much more propellant than fuel, 22,000 times more in the case of the Zubrin without open cycle cooling, and 44,000 times more if open cycle cooling is used.

    The Zubrin drive exhaust (without open cycle cooling) contains 108 kg/sec of water, but only about 5 grams/sec of uranium.

    (This is from a quick calculation: mass flow equals the Zubrin thrust (8.7 meganewtons) divided by the exit velocity (80 km/sec) = 108 kg/sec. But the fissioning energy can be estimated from the Zubrin total power of 427 GW divided by the energy content of Uranium 235 of 83 TJ/kg.)


    Dr. Zubrin responded, and he defends the performance of the Zubrin drive as depicted in the game (as high thrust & high specific impulse rocket with low mass and low radiators).

    1). In U235 fission, only about 2% of the energy goes into neutrons (unlike D-T fusion).

    2). The design uses a pusher plate or open nozzle, like an Orion drive. Or magnetic confinement (since most of the energy is released as a plasma). Therefore, the opportunity to absorb heat is low.

    3) Many of the neutrons that are intercepted would sail through the pusher plate, rather than be absorbed as waste heat.

    4) No lithium should be in the outer water, because this would poison the fission reactions.

    5). Because the design does not use a heat engine cycle, the radiators could be far hotter than ones in the game. He suggested graphite at 2500 K°. That would drop the required radiating area by a factor of 40 (2.5 to the fourth power), which means that the radiator could be the first wall itself.

    Dr. Zubrin went on to say the chief disadvantage is the expense of the fuel (like He3-D and antimatter drives).

    Philip Eklund, from a discussion on the High Frontier Yahoo group about the NSWR drive in High Frontier

         "So anyway, we were passing through the outer Kirkwood Gap, totally the a** end of nowhere. I'm trying to catch some rack time, XO has the conn, nice boring trip to Europa." The CO of U.S.N.A.S. Saskatchewan tipped back another shot of Scotch and continued his story. "Totally routine, right? No problems at all. So then, all of the sudden, the whole ship gets racked. Meteoroid. Big one, too, maybe a centimeter across."

         The captains seated around the table, two Americans including Fitzthomas, an Indian, three Chinese, and the South African, all clucked and groaned.

         "Well, we got lucky and it missed the crew compartment, but by the time I get to command the chief engineer is screaming over the intercom that it holed tank one, busted three tubes, and we've got nuke juice pooling and we have to dump the tank. Problem is, we're running at top speed and if we dump the tank, we don't have enough propellant to stop at Europa. We'd have to ride all the way out to Neptune, sling around, and hope someone from the inner solar system has dispatched a tanker to intercept us on the return trip, and we don't have near enough consumables for that."

         "So what did you do, mate?" said the South African.

         "I told the chief he had to fix the tank or we'd all starve before we could stop the damn ship. Well, he screams some more that we don't have time, and I tell him his choice is fix the tank or die real fast in a runaway, because we're not going to die slow in the void. So he grabs a crew, stuffs them into suits, and crawls out onto the tank. They punch some holes in it to let the juice drain instead of pool, but it's still leaking like a f***** and the water's evaporating and leaving uranium crusted all over everything. So he radios command and says, 'It's still leaking, and all this uranium crud is going to accumulate into a critical mass somewhere, so we still have to drop the tank.' Meteoroid busted open three valves, you see. No way to stop the leak. And I tell him again, that's no good, and by now astrogation has confirmed it and the XO has tallied up the consumables and I know for sure we don't have enough for an unscheduled trip to Neptune.

         "So he says something about how he's not a miracle worker, and I tell him he damn well has to be. Lo and behold, he and his crew go ahead and do something crazy and it works."

         "What was that?" said the South African.

         "They take torches to the tank. The plug up the broken pipes as best they can, and then they go ahead and cut away the smashed cells. Just cut it off and jettison it into space, and suddenly the propellant that's still leaking is leaking right into space. We have lousy flow through the tank and the braking burn is going to be real tricky, but we can make Europa. I put the chief up for a commendation medal for figuring that out on the fly and saving our asses."

         The other captains nodded their approval at the chief's quick thinking. Good chiefs prevented accidents; great ones prevented disasters.

         "Is the chief's name Mr. Scott, by any chance?" said one of the Chinese captains.


         Commander George Allen, New Jersey's full blooded Cherokee XO, drifted into the command deck from astrogation, where he'd been monitoring the final approach to Hektor. He took his place at the copilot station and put on his headset. Fitzthomas toggled his direct channel to Allen's station.

         "How was the approach?"
         "We wasted too much propellant before the chain reaction started. I think Pennai should inspect the nozzles and pumps before we get underway again."
         "What does Pennai say about it?"
         Pause. "Pennai thinks the fuel is dirty."
         "Is it?"
         "It was certified 90% enriched at Roosevelt Station."
         "Is there any way to test it here?"
         "No sir. Not without a centrifuge."
         "How does Pennai know, then?"
         "Some engineering technobabble about neutron flux and reaction rate. I couldn't follow a tenth of what she said."
         Fitzthomas considered that. "Have her inspect the pumps and nozzle alignment. If they pass, then we might have a fuel problem."

         "Captain," said Allen, "Thought you'd like to know: Pennai just inspected the entire fuel line. Everything there is in order."
         "So what are you telling me, George?"
         "I think we have dirty fuel."
         "What's her recommendation?"
         "She wants to drain the tanks and top up with the good stuff. But I can't—"
         "Write that request, I know. The CO has to. Where's Pennai now?"
         "Racked out. She has the midwatch tonight."
         "After her watch tonight, she has four days of leave."
         "Sir, she's supposed to be OOW all day Wednesday."
         "I'll take that shift. She was right, we were wrong. She deserves to be rewarded. When I get back I'll write up a request and have it to the fuelmaster by tomorrow AM."

         "Do you have to return to your ship?"
         "Yeah. Dirty fuel, God damn it. Wait until I get my hands on the fuelmaster at Roosevelt."

         (Admiral Castro said) "Anyway, I saw your chief engineer's report. I passed it back to Fleet. The fuelmaster at Roosevelt Station is going to have a lousy day tomorrow. There's also a bulletin going out to the entire fleet. Everyone who tanked up at Roosevelt near the same time you did should keep a close eye on his reaction rate. Your Lieutenant Pennai might be up for a commendation letter in her file."


         Duvalier left Ortiz main engineering and vaulted down the access tube to the reactor room. The tube ran down the ship's spine, surrounded by megaliters of water enriched with uranium salts in highly complex tanks made of neutron absorbing material. In his head, he knew the tube was the safest part of the ship, shielded from the worst the universe could throw at it by dozens of meters of water. In his head, he knew the fuel, so long as it didn't pool into a critical mass somewhere in the thousands of kilomters of pipes on all sides of him, emitted only low intensity alpha rays which couldn't penetrate his own skin, let alone the aluminum skin of the pressure tube. It was all perfectly safe, so far as anything in space could be safe. He knew that in his head.

         His b***s, however, hadn't gotten the memo. His testicles tried to crawl up into his body every time he climbed through the hatch.

    From The Last Great War by Matthew Lineberger (not yet published)

    Fission Fragment

    Fission Fragment

    George Chapline
    Exhaust velocity980,000 m/s

    All of the other nuclear thermal rockets generate heat with nuclear fission, then transfer the heat to a working fluid which becomes the reaction mass. The transfer is always going to be plagued by inefficiency, thanks to the second law of thermodynamics. What if you could eliminate the middleman, and use the fission heat directly with no transfer?

    That what the fission fragment rocket does. It uses the hot split atoms as reaction mass. The down side is that due to the low mass flow, the thrust is minuscule. But the up side is that the exhaust velocity is 5% the speed of light! 15,000,000 kilometers per second, that's like a bat out of hell. With that much exhaust velocity, you could actually have a rocket where less than 50% of the total mass is propellant (i.e., a mass ratio below 2.0).

    The fission fragment is one of the few propulsion systems where the reaction mass has a higher thermal energy than the fuel elements. The other notable example being the Pulsed NTR.

    Dr. Chapline's design use thin carbon filaments coated with fission fuel (coating is about 2 micrometers thick). The filaments radiated out from a central hub, looking like a fuzzy vinyl LP record. These revolving disks were spun at high speed through a reactor core, where atoms of nuclear fuel would undergo fission. The fission fragments would be directed by magnetic fields into an exhaust beam.

    The drawback of this design is that too many of the fragments fail to escape the fuel coat (which adds no thrust but does heat up the coat) and too many hit the carbon filaments (which adds no thrust but does heat up the filaments). This is why the disks spin at high speed, otherwise they'd melt.

    Dusty Plasma
    550AU
    Thrust22 N
    Thrust Power0.2 GW
    Mass Flow1.00e-06 kg/s
    T/W2.49e-04
    Specific Power55 kg/MW
    0.5LY
    Thrust344 N
    Thrust Power2.6 GW
    Mass Flow2.30e-05 kg/s
    T/W4.00e-03
    Specific Power3 kg/MW
    All
    Exhaust Velocity15,000,000 m/s
    Specific Impulse1,529,052 s
    Total Engine Mass9,000 kg
    FuelFission:
    Uranium 235
    ReactorGas Core
    MHD Choke
    RemassReaction
    Products
    Remass AccelFission-Fragment
    Thrust DirectorMagnetic Nozzle

    Rodney Clark and Robert Sheldon solve the problem with their Dusty plasma bed reactor (report).

    You take the fission fuel and grind it into dust grains with an average size of 100 nanometers (that is, about 1/20th the thickness of the fuel coating in dr. Chapline's design). This does two things [A] most of the fragments escape and [B] the dust particles have such a high surface to volume ratio that heat (caused by fragments which fail to escape) readily dissipates, preventing the dust particles from melting.

    The dust is suspended in the center of a reaction chamber whose walls are composed of a nuclear moderator. Power reactors will use beryllium oxide (BeO) as a moderator, but that is a bit massive for a spacecraft. The ship will probably use lithium hydride (LiH) for a moderator instead, since is only has one-quarter the mass. Probably about six metric tons worth. The dust is suspended electrostatically or magnetically by a containment field generator. The dust is heated up by radio frequency (RF) induction coils. The containment field generator will require superconductors, which will probably require a coolant system of its own.

    The dust particles are slow and are relatively massive, while the fission fragments are fast and not very massive at all. So the magnetic field can be tailored so it holds the dust but allows the fission fragments to escape. Magnetic mirrors ensure that fragments headed the wrong way are re-directed to the exhaust port.

    One valuable trick is that you can use the same unit for thrust or to generate electricity. Configure the magnetic field so that the fragments escape "downward" through the exhaust port and you have thrust. Flip a switch to change the magnetic field so that the fragments escape upward into deceleration and ion collection electrodes and you generate electricity. As a matter of fact, it is so efficient at generating electricity that researchers are busy trying to adapt this for ground based power plants. But I digress.

    The dust is only sufficient for a short period of critical nuclear reaction so it must be continuously replenished. The thermal energy released by fission events plus heat from collisions between fission fragments and dust grains create intense heat within the dust cloud. Since there is no core cooling flow, the reactor power is limited to the temperature at which the dust can radiatively cool itself without vaporizing. The interior of the reaction chamber walls will protected by a mirrored (95% reflection) heat shield attached to a heat radiator. The outer moderator layer will have its own heat shield.

    Clark and Sheldon roughed out a propulsion system. It had six tons for the moderator, 2 tons for radiators and liquid metal cooling, 1 ton for magnets, power recovery, and coils, for a grand total of 9 tons. The reaction chamber will be about 1 meter in diameter and 10 meters long. The moderator blanket around the chamber will be about 40 centimeters thick. The thrust is a function the size of the cloud of fissioning dust, and is directly related to the power level of the reactor. There is a limit to the maximum allowed power level, set by the coolant system of the reaction chamber. Clark and Sheldon estimate that only about 46% of the fission fragments provide thrust while the rest are wasted. See the report for details.

    In the table, the 550AU engine is for a ten year journey to the Solar gravitational lensing point at 550 astronomical units (so you can use the sun as a giant telescope lens). The 0.5LY engine is for a thirty year trip to the Oort cloud of comets. These are constant acceleration brachistochrone trajectories, the 550AU mission will need a reactor power level of 350 MW and the 0.5LY mission will need 5.6 GW. Don't forget that the engine power is only 46% efficient, that's why the table thrust values are lower.

    Werka FFRE
    First Generation
    Exhaust Velocity5,170,000 m/s
    Specific Impulse527,013 s
    Thrust43 N
    Thrust Power0.1 GW
    Mass Flow8.00e-06 kg/s
    Total Engine Mass113,400 kg
    T/W3.90e-05
    FuelFission:
    Plutonium 239
    ReactorGas Core
    MHD Choke
    RemassReaction
    Products
    Remass AccelFission-Fragment
    Thrust DirectorMagnetic Nozzle
    Specific Power1,020 kg/MW
    HOPE FFRE
    Propulsion SystemWerka FFRE
    Wet Mass303,000 kg
    Dry Mass295,000 kg
    Mass Ratio1.03 m/s
    ΔV138,336 m/s

    Robert Werka has a more modest and realistic design for his fission fragment rocket engine (FFRE). He figures that a practical design will have an exhaust velocity of about 5,200,000 m/s instead of his estimated theoretical maximum of 15,000,000 m/s. His lower estimate is still around 1.7% the speed of light so we are still talking about sub 2.0 mass ratios. Collisions between fission fragments and the dust particles is responsible for the reduction in exhaust velocity.

    Incidentally the near relativistic exhaust velocity reduces radioactive contamination of the solar system. The particles are traveling well above the solar escape velocity (actually they are even faster than the galactic escape velocity) so all the radioactive exhaust goes shooting out of the solar system at 0.017c.

    The dusty fuel is nanometer sized particles of slightly critical plutonium carbide, suspended and contained in an electric field. A moderator of deuterated polyethylene reflects enough neutrons to keep the plutonium critical, while control rods adjust the reaction levels. The moderator is protected from reaction chamber heat by a heat shield, an inner layer composed of carbon-carbon to reflect infrared radiation back into the core. The heat shield coolant passes through a Brayton cycle power generator to create some electricty, then the coolant is sent to the heat radiator.

    The details of Werka's initial generation FFRE can be found in the diagram below. The reaction chamber is about 5.4 meters in diameter by 2.8 meters long. The magnetic nozzle brings the length to 11.5 meters. The fuel is uranium dioxide dust which melts at 3000 K, allowing a reactor power of 1.0 GW. It consume about 29 grams of uranium dioxide dust per hour (not per second). Of the 1.0 GW of reactor power, about 0.7 GW of that is dumped as waste heat through the very large radiators required.

    The second most massive component is the magnetic mirror at the "top" of the reaction chamber. Its purpose is to reflect the fission fragments going the wrong way so they turn around and travel out the exhaust nozzle. Surrounding the "sides" of the reaction chamber is the collimating magnet which directs any remaining wrong-way fragments towards the exhaust nozzle. The exhaust beam would cause near-instantaneous erosion of any material object (since it is electrically charged, relativistic, radioactive grit). It is kept in bounds and electrically neutralized by the magnetic nozzle cage.

    Afterburner Fission Fragment

    AFFRE
    EngineAFFRE
    Engine Mass
    (reactor)
    107,000 kg
    Engine Mass
    (mod oil)
    91,000 kg
    Engine Mass
    (total)
    268,961 kg
    Reactor Power2.5 GW
    Thrust4,651 N
    Thrust Power730 MW
    Specific
    Impulse
    32,000 sec
    Exhaust
    Velocity
    313,900 m/s
    Mass Flow
    (FF)
    3.12×10-5 kg/s
    Mass Flow
    (Hydrogen)
    0.0179 kg/s
    Mass Flow
    (Total)
    0.018 kg/s
    T/W0.002

    Robert Werka has apparently figured out a new configuration for his fission-fragment rocket engine (FFRE).

    As with most engines that have high specific impulse and exhaust velocity, the thrust of a FFRE is pathetically small. Ah, but there is a standard way of dealing with this problem: shifting gears. What you do is inject cold propellant into the exhaust ("afterburner"). The fission fragment exhaust loses energy while the cold propellant gains energy. The combined exhaust velocity of the fission fragment + propellant energy is lower than the original pure fission fragment, so the specific impulse goes down. However the propellant mass flow goes up since the combined exhaust has more mass than the original pure fission fragment. So the thrust goes up.

    Now you have an Afterburner fission-fragment rocket engine (AFFRE).

    As you are probably tired of hearing, this means the engine has shifted gears by trading specific impulse for thrust.

    Shifting Gears
    EngineIspThrust
    FFRE527,000 sec43 Newtons
    AFFRE32,000 sec4,651 Newtons

    The heart of the engine is a standard "dusty plasma" fission fragment engine. A cloud of nanoparticle-sized fission fuel is held in an electrostatic field inside a neutron moderator. Atoms in the particles are fissioning like crazy, spewing high velocity fission products in all directions. These become the exhaust, directed by a magnetic nozzle.

    The AFFRE alters this a bit. Instead of a cylindrical reactor core it uses half a torus. Each end of the torus has its own magnetic nozzle. But the biggest difference is that cold hydrogen propellant is injected into the flow of fission fragments as an afterburner, in order to shift gears.

    In the diagram above, the magnetic nozzles are the two frameworks perched on top of the reactor core. It is a converging-diverging (C-D) magnetic nozzle composed of a series of four beryllium magnetic rings (colored gold in the diagram). Note how each frame holding the beryllium rings is shaped like an elongated hour-glass, that is the converting-diverging part. The fission fragment plume emerges from the reactor core, is squeezed (converges) down until it reaches the midpoint of the magnetic nozzle, then expands (diverges) as it approaches the end of the nozzle. At the midpoint is the afterburner, where the cold hydrogen propellant is injected.

    The semi-torus has a major and minor radius of 3 meters. The overall length of the engine is 13 meters. The reactor uses 91 metric tons of hydrocarbon oil as a moderator. This means the heavy lift vehicle can launch the engine "dry" with no oil moderator. In orbit the oil moderator can be easily injected into the reactor, at least easier than building the blasted thing in free fall out of graphite bricks.

    Fission Sail

    Fission Sail

    Antimatter-Driven Sail

    The sail is made of graphite and carbon-carbon fiber, infused with a tiny amount of uranium. It is subjected to a misting of antiprotons. These induce uranium atoms to fission, with the recoil pushing the sail. Since this is nuclear powered, the sail does not have to be kilometers in diameter, five meters will do. 30 miligrams of antiprotons could push the sail to the Kuiper Belt.

    Pulse

    Orion

    Fission Orion
    Exhaust Velocity43,000 m/s
    Specific Impulse4,383 s
    Thrust263,000 N
    Thrust Power5.7 GW
    Mass Flow6 kg/s
    Total Engine Mass200,000 kg
    T/W0.13
    FuelFission:
    Uranium 235
    ReactorPulse Unit
    RemassTungsten
    Remass AccelThermal Accel:
    Reaction Heat
    Thrust DirectorPusher Plate
    Specific Power35 kg/MW
    Fusion Orion
    Exhaust Velocity73,000 m/s
    Specific Impulse7,441 s
    Thrust292,000 N
    Thrust Power10.7 GW
    Mass Flow4 kg/s
    Total Engine Mass200,000 kg
    T/W0.15
    FuelD-D Fusion
    Specific Power19 kg/MW
    1959 Orion 1st Gen
    Thrust Power1,600 GW
    Exhaust velocity39,000 m/s
    Thrust80,000,000 n
    Engine mass1,700 tonne
    T/W >1.0yes
    1959 Orion 2nd Gen
    Thrust Power24,000 GW
    Exhaust velocity120,000 m/s
    Thrust400,000,000 n
    Engine mass3,250 tonne
    T/W >1.0yes
    ORION USAF 10m
    Exhaust Velocity32,900 m/s
    Specific Impulse3,354 s
    Thrust2,000,000 N
    Thrust Power32.9 GW
    Mass Flow61 kg/s
    Total Engine Mass107,900 kg
    T/W2
    Wet Mass475,235 kg
    Dry Mass180,975 kg
    Mass Ratio2.63 m/s
    ΔV31,763 m/s
    Specific Power3 kg/MW
    ORION 4K ton battleship
    Exhaust Velocity39,000 m/s
    Specific Impulse3,976 s
    Thrust80,000,000 N
    Thrust Power1.6 TW
    Mass Flow2,051 kg/s
    Total Engine Mass1,700,000 kg
    T/W4.80
    Specific Power1.09 kg/MW
    ΔV 10 km/s
    Wet Mass4,000,000 kg
    Dry Mass3,100,000 kg
    Mass Ratio1.29 m/s
    ΔV9,941 m/s
    ΔV 21 km/s
    Wet Mass4,000,000 kg
    Dry Mass2,353,000 kg
    Mass Ratio1.70 m/s
    ΔV20,694 m/s
    ΔV 30 km/s
    Wet Mass4,000,000 kg
    Dry Mass1,852,000 kg
    Mass Ratio2.16 m/s
    ΔV30,031 m/s
    ORION 10k ton adv
    Exhaust Velocity120,000 m/s
    Specific Impulse12,232 s
    Thrust400,000,000 N
    Thrust Power24.0 TW
    Mass Flow3,333 kg/s
    Total Engine Mass3,250,000 kg
    T/W13
    Specific Power0.14 kg/MW
    ΔV 10 km/s
    Wet Mass10,000,000 kg
    Dry Mass9,199,000 kg
    Mass Ratio1.09 m/s
    ΔV10,019 m/s
    ΔV 15.5 km/s
    Wet Mass10,000,000 kg
    Dry Mass8,772,000 kg
    Mass Ratio1.14 m/s
    ΔV15,722 m/s
    ΔV 20 km/s
    Wet Mass10,000,000 kg
    Dry Mass8,403,000 kg
    Mass Ratio1.19 m/s
    ΔV20,880 m/s
    ΔV 30 km/s
    Wet Mass10,000,000 kg
    Dry Mass7,813,000 kg
    Mass Ratio1.28 m/s
    ΔV29,616 m/s
    ΔV 100 km/s
    Wet Mass10,000,000 kg
    Dry Mass4,348,000 kg
    Mass Ratio2.30 m/s
    ΔV99,944 m/s
    Orion MAX
    Exhaust Velocity9,800,000 m/s
    Specific Impulse998,981 s
    Thrust8,000,000 N
    Thrust Power39.2 TW
    Mass Flow0.82 kg/s
    Total Engine Mass8,000 kg
    T/W102
    FuelProton-Proton
    Fusion
    RemassTungsten
    Specific Power2.04e-04 kg/MW

    Orion AKA "old Boom-boom" is the ultimate consumable nuclear thermal rocket, based on the "firecracker under a tin can" principle. Except the tin can is a spacecraft and the firecracker is a nuclear warhead.

    This concept has the spacecraft mounted with shock absorbers on an armored "pusher plate". A stream of small (5 to 15 kiloton) fission or fusion explosives are detonated under the plate to provide thrust. While you might find it difficult to believe that the spacecraft can survive this, you will admit that this will give lots of thrust to the spacecraft (or its fragments). On the plus side, a pusher plate that can protect the spacecraft from the near detonation of nuclear explosives will also provide dandy protection from any incoming weapons fire. On the minus side I can hear the environmentalists howling already. It will quite thoroughly devastate the lift-off site, and give all the crew bad backs and fallen arches. And they had better have extra-strength brassieres and athletic supporters.

    Mathematician Richard Courant viewed an Orion test and said "Zis is not nuts, zis is super-nuts."


    This section is about the Orion propulsion system. If you want all the hot and juicy details about various versions of Orion spacecraft go here.

    Please note that Orion drive is pretty close to being a torchship, and is not subject to the Every gram counts rule. It is probably the only torchship we have the technology to actually build today.


    If you want the real inside details of the original Orion design, run, do not walk, and get a copies the following issues of of Aerospace Projects Review: Volume 1, Number 4, Volume 1, Number 5, and Volume 2, Number 2. They have blueprints, tables, and lots of never before seen details.

    If you want your data raw, piled high and dry, here is a copy of report GA-5009 vol III "Nuclear Pulse Space Vehicle Study - Conceptual Vehicle Design" by General Atomics (1964). Lots of charts, lots of graphs, some very useful diagrams, almost worth skimming through it just to admire the diagrams.


    The sad little secret about Orion is that the mission it is best suited for is boosting heavy payloads into orbit. Which is exactly the mission that the enviromentalist and the nuclear test ban treaty will prevent. Orion has excellent thrust, which is what you need for lift-off and landing. Unfortunately its exhaust velocity is pretty average, which is what you need for efficient orbit-to-orbit maneuvers.

    Having said that, there is another situation where high thrust is desirable: a warship jinking to make itself harder to be hit by enemy weapons fire. It is also interesting to note that the Orion propulsion system works very well with the bomb-pumped laser weapons system.


    Each pulse unit is a tiny nuclear bomb, encased in a "radiation case" that has a hole in the top. A nuclear blasts is initially mostly x-rays. The radiation case is composed of a material that his opaque to x-rays (depleted uranium). The top hole thus "channels" the flood of x-rays in an upwards direction (at least in the few milliseconds before the bomb vaporizes the radiation case).

    The channeled x-rays then strike the "channel filler" (beryllium oxide). The channel filler transforms the atomic fury of x-rays into an atomic fury of heat.

    Lying on top of the channel filler is the disc of propellant (tungsten). The atomic fury of heat flashes the tungsten into a jet of ionized tungsten plasma, traveling at high velocity (in excess of 1.5 × 105 meters per second). This crashes into the pusher plate, accelerating the spacecraft. It crashes hard. You will note that there are two stages of shock absorbers between the pusher plate and the spacecraft, preventing instant crew death.

    The ratio of beryllium oxide to tungsten is 4:1.

    The thickness of the beryllium oxide and tungsten should be such to serve as a shield to protect the engine and upper vehicle from the neutron and high-energy gamma radiation produced by the nuclear explosion. This sets a lower limit on the thickness of the propellant and channel filler for a particular design.

    The jet is confined to a cone about 22.5 degrees (instead of in all directions). The detonation point is positioned such that the 22.5 cone exactly covers the diameter of the pusher plate. The idea is that the wider the area of the cone, the more spread out the impulse will be, and the larger the chance that the pusher plate will not be utterly destroyed by the impulse.

    It is estimated that 85% of the energy of the nuclear explosion can be directed in the desired direction. The pulse units are popped off at a rate of about one per second. A 5 kiloton charge is about 1,152 kg. The pulses are so brief that there is no appreciable "neutron activation", that is, the neutron from the detonations do not transmute parts of the spacecraft's structure into radioactive elements. This means astronauts can exit the spacecraft and do maintenance work shortly after the pulse units stop detonating.

    The device is basically a nuclear shaped charge. A pulse unit that was not a shaped charge would of course waste most of the energy of the explosion. Figure that 1% at best of the energy of a non-shaped-charge explosion would actually hit the pusher plate, what a waste of perfectly good plutonium.

    Each charge accelerates the spacecraft by roughly 12 m/s. A 4,000 ton spacecraft would use 5 kiloton charges, and a 10,000 ton spacecraft would use 15 kiloton charges. For blast-off, smaller charges of 0.15 kt and 0.35 kt respectively would be used while within the Terra's atmosphere. The air between the charge and the pusher plate amplifies the impulse delivered (it is extra propellant), so if you are not in airless space you can get away with a smaller kt yield.


    How much weapons-grade plutonium will each charge require? As with most details about nuclear explosives, specifics are hard to come by. According to GA-5009 vol III , pulse units with 2.0×106 newtons to 4.0×107 newtons all require approximately 2 kilograms per pulse unit, with 1964 technology. It goes on to say that advances in the state of the art could reduce the required amount of plutonium by a factor 2 to 4, especially for lower thrust units. 2.0×106 n is 1 kiloton, I'm not sure what 4.0×107 n corresponds to, from the document I'd estimate it was about 15 kt. Presumably the 2 kg plutonium lower limit is due to problems with making a critical mass, you need a minimum amount to make it explode at all.


    According to Scott Lowther, the smallest pulse units were meant to propel a small ten-meter diameter Orion craft for the USAF and NASA. The units had a yield ranging from one-half to one kiloton. The USAF device was one kiloton, diameter 36 centimeters, mass of 86 kilograms, tungsten propellant mass of 34.3 kilograms, jet of tungsten plasma travels at 150,000 meters per second. One unit would deliver to the pusher plate a total impulse of 2,100,000 newton-seconds. Given the mass of the ten-meter Orion, detonating one pulse unit per second would give an acceleration well over one gee. According to my slide rule, this implies that the mass of the ten-meter Orion is a bit under 210 metric tons.

    Pulse UnitYieldMassDia.HeightPropellant
    (percent)
    Det.
    Interval
    Propellant
    Velocity
    Effective
    Exhaust
    Velocity
    (Isp)
    Thrust
    per unit
    Effective
    Thrust
    NASA 10m Orion
    (vacuum)
    141 kg0.86 s18,200 m/s
    (1,850 s)
    3.0×106 N3.5×106 N
    USAF 10m Orion
    (vacuum)
    1 kt79 kg
    (86 kg?)
    0.33 m0.61 m34.3 kg
    (40%)
    1 s1.5×105 m/s25,800 m/s
    (2,630 s)
    2.0×106 N2.0×106 N
    20m Orion
    (vacuum)
    450 kg0.87 s30,900 m/s
    (3,150 s)
    1.4×107 N1.6×107 N
    4000T Orion
    (atmo)
    0.15 kt1,152 kg0.81 m0.86 m1.1 s1.17×105 m/s42,120 m/s
    (4,300 s)
    8.8×107 N8.0×107 N
    4000T Orion
    (vacuum)
    5 kt1,152 kg0.81 m0.86 m415 kg
    (36%)
    1.1 s1.17×105 m/s42,120 m/s
    (4,300 s)
    8.8×107 N8.0×107 N
    10,000T Orion
    (atmo)
    0.35 kt118,000 m/s
    (12,000 s)
    4.0×108
    10,000T Orion
    (vacuum)
    15 kt118,000 m/s
    (12,000 s)
    4.0×108
    20,000T Orion
    (vacuum)
    29 kt1,150 kg0.8 m
    • Pulse Unit: The type of Orion spacecraft that uses this unit, and whether it is an atmospheric or vacuum type.
    • Yield: Nuclear explosive yield (kilotons)
    • Mass: Mass of the pulse unit
    • Dia.: Diameter of pulse unit
    • Height: Height of pulse unit
    • Propellant (percent): Mass of tungsten propellant in kilograms, as percentage of pulse unit mass in parenthesis.
    • Det. Interval: Time delay interval between pulse unit detonations.
    • Propellant Velocity: The velocity the tungsten propellant plasma travels at. Do not use this for delta V calculations.
    • Effective Exhaust Velocity (Isp): A value for exhaust velocity suitable for delta V calculations. Specific impulse in parenthesis.
    • Thrust per unit: Amount of thrust produced by detonating one pulse unit.
    • Effective Thrust: Thrust per second. Calculated by taking Thrust per unit and dividing by Det. Interval.

    Tungsten has an atomic number (Z) of 74. When the tungsten plate is vaporized, the resulting plasma jet has a relatively low velocity and diverges at a wide angle (22.5 degrees). Now, if you replace the tungsten with a material with a low Z, the plasma jet will instead have a high velocity at a narrow angle. The jet angle also grows narrower as the thickness of the plate is reduced. This makes it a poor propulsion system, but an effective weapon. Instead of a wall of gas hitting the pusher plate, it is more like a directed energy weapon. The military found this to be fascinating, who needs cannons when you can shoot spears of pure nuclear flame? The process was examined in a Strategic Defense Initiative project called "Casaba-Howitzer", which apparently is still classified. Which is not surprising but frustrating if one is trying to write a science fiction novel or spacecraft combat game.

    NASA has been quietly re-examining ORION, under the new name of "External Pulsed Plasma Propulsion". As George Dyson observed, the new name removes most references to "Nuclear", and all references to "Bombs."

    For details about spacecraft using Orion propulsion, go here.


    Oh, and another thing. ORION is fantastic for boosting unreasonably huge payloads into orbit and it is pretty great for orbit to orbit propulsion. But trying to use it to land is not a very good idea. At least not on a planet with an atmosphere.

    Project Orion
    Project Orion
    Exhaust Velocity19,620 m/s
    Specific Impulse2,000 s
    Thrust2,215,200 N
    Thrust Power21.7 GW
    Mass Flow113 kg/s
    Total Engine Mass203,680 kg
    T/W1
    Frozen Flow eff.39%
    Thermal eff.99%
    Total eff.39%
    FuelFission:
    Curium 245
    ReactorPulse Unit
    RemassWater
    Remass AccelThermal Accel:
    Reaction Heat
    Thrust DirectorPusher Plate
    Specific Power9 kg/MW

    This fabled technology converts the impulses of small nuclear detonations into thrust.

    The small shaped-charge bombs each have a mass of 230 kg (including propellant) and a yield of a quarter kiloton (1 terajoule). The fissile material is curium 245, with a critical mass of 4 kg, surrounded by a beryllium reflector. The soft X-rays, UV and plasma from the external detonation vaporize and compress the propellant to a gram per liter, highly opaque to the bomb energies at the temperatures attained (67000 K).

    The propellant, a mixture of water, nitrogen, and hydrogen, interfaces with a pusher plate “nozzle”, which can be either solid or magnetic.

    Shown is a solid plate, which tapers to the edges (to maintain a constant net velocity of the plate given a greater momentum transfer in the center). Pressure on the plate reaches 690 MPa in the center. The impulse shock is absorbed by a set of pneumatic “tires”, followed by gas-filled pistons detuned to the 56 Hz detonation frequency.

    The shock plate system becomes a useful shield if pointed towards the enemy.

    The amount of blast energy utilized for thrust is 7%, and the amount of pulse mass that intercepts the plate is 39%. A 56 TWth design optimized for 1TJ bombs achieves a specific impulse of 2 ksec and a thrust of 2.2 MN.

    Ted Taylor’s classic design, optimized for low yield bombs and 2 ksec specific impulse: “Project Orion”, George Dyson, Henry Holt and Company, 2002.

    From High Frontier by Philip Eklund
    DO NOT LAND WITH ORION

    Interesting e-mail conversation I had with Rhys Taylor on the topic of Entry-Descent-Landing (EDL) as relevant to nuclear pulse propulsion.

    I was aware one of the concepts that came out of the 1958 Project Orion involved landing a surface installation and a 100 man crew on the surface of Mars. Two of the early large Orion's would be involved. One would enter a low Mars orbit and completely cancel its orbital velocity while well above the sensible Martian atmosphere. The crew would ride down in a number of smaller landing craft with individual return stages. A large section of the vehicle, the base structure carrying a cargo of surface rovers, scientific gear, and consumables, would separate from the Orion propulsion module and descend propulsively on rockets without undergoing meteoric entry. The propulsion module would be allowed to crash on the surface (presumably this would entail transferring any remaining pulse units to the second Orion remaining in orbit before cancelling its orbital velocity — so only the absolute minimum required number of pulse units would remain to be expended before its uncontrolled descent and crash landing).

    My interest was in regards to soft landing an Orion intact after a controlled descent, and I was unsure of how deep into the atmosphere the nuclear pulse propulsion system could be fired, if it could be fired in descent mode, or if this was even advisable.

    Rhys was kind enough to advise me on these particular points, which to sum up are:

    1. Orion is capable of completely cancelling its orbital velocity.
    2. Descent would be a matter of managing the free-fall velocity of the vehicle.
    3. Inside the atmosphere the pulse unit will generate a many-thousands degree fireball, this is not a problem during launch, or in the vacuum of space, but during descent flying into the fireball would not be a good thing for vehicle and crew.
    4. There is some point at very high altitude where you would have to trade off from nuclear pulse propulsion to rocket powered descent.

    The input Rhys provided went toward this spacecraft designed for my Orion's Arm future history, and will be applied to several related spacecraft to be posted in the near future. 

    Orion Thrust and Isp

    Even though only a fraction of the pulse unit's mass is officially tungsten propellant, you have to count the entire mass of the pulse unit when figuring the mass ratio. The mass of the Orion spacecraft with a full load of pulse units is the wet mass, and the mass with zero pulse units is the dry mass.

    The thrust is not applied constantly, it is in the form of pulses separated by a fixed detonation interval. Generally the interval is from about half a second to 1.5 seconds. This means to figure the "effective" thrust you take the thrust-per-pulse-unit and divide it by the detonation interval in seconds. So if each pulse unit gives 2×106 Newtons, and they are detonated at 0.8 second intervals, the effective thrust is 2×106 / 0.8 = 2.5×106 Newtons

    Obviously the converse is if you have the effective thrust, you multiply it by the detonation interval to find the thrust-per-pulse-unit. So if the effective thrust is 3.5×106 N and the units are detonated at 0.86 second intervals, the thrust-per-pulse-unit is 3.5×106 N * 0.86 = 3.01×106 Newtons


    There are some interesting equations in GA-5009 vol III on pages 25 and 26 on the subject of nuclear pulse units. These were developed in the study for the 10 and 20 meter NASA Orion spacecraft, and they heavily rely upon a number of simplifying assumptions. These were for first generation pulse units, with the assumption that second generation units would have better performance. So take these with a grain of salt.

    These equations are only considered valid over the range 3×106 < FE < 2×108

    You are given the amount of thrust you want to get out of the propulsion system: FE and the detonation interval time Dp. From those you calculate the amount of thrust each pulse unit has to deliver Fp:

    Fp = FE / Dp

    From this the specific impulse, nuclear yield, and the mass of the Orion propulsion module.

    Isp = 1 / ((5.30×102 / (Fp * (1 + (2.83×10-3 * Fp1/3)))) + ((4.32×10-2 * (1 + (2.83×10-3 * Fp1/3))) / Fp1/3))

    Ve = Isp * g0

    Y = 9.30×10-10 * Fp4/3

    ME = Fp / (3.6 * g0)

    where

    • FE = effective thrust (newtons)
    • Dp = delay between pulses (seconds)
    • Fp = thrust per pulse (newtons)
    • Isp = effective specific impulse (seconds)
    • Ve = exhaust velocity (m/s)
    • Y = size of nuclear yield in pulse unit (kilotons)
    • ME = mass of Orion propulsion module (kg)
    • g0 = acceleration due to gravity = 9.81 m/s2
    • x1/3 = cube root of x

    The results are close but do not exactly match the values given in the document, but they are better than nothing

    NASA 10-meter Orion
    Given Effective Thrust3.5×106 N
    Given Detonation Delay0.86 s
    ParameterDocument
    Value
    Equation
    Value
    Specific Impulse1,850 s1,830 s
    Yield1 kt0.4 kt
    Propulsion module mass90,946 kg85,245 kg
    NASA 20-meter Orion
    Given Effective Thrust1.6×107 N
    Given Detonation Delay0.87 s
    ParameterDocument
    Value
    Calculated
    Value
    Specific Impulse3,150 s3,082 s
    Yield5 kt3.1 kt
    Propulsion module mass358,000 kg394,223 kg

    For more in depth calculations of an Orion rocket's specific impulse, read page 1 and page 2. But be prepared for some heavy math.


    Orion Environmental Impact

    Naturally, some people freak out when you tell them about a rocket that rises into orbit by detonating Two! Hundred! Atom! Bombs!. But it actually isn't quite as bad as it sounds.

    First off, these are teeny-tiny atom bombs, honest. The nuclear pulse units used in space will be about one kiloton each, while the Nagasaki device was more like 20 kt. And in any event, the nuclear pulse units used in the atmosphere are only 0.15 kt ( about 1/130th the size of the Nagasaki device). This is because the atmosphere converts the explosion x-rays into "blast", increasing the effectiveness of the pulse unit so you can lower the kilotonnage.

    So we are not talking about zillions of 25 megaton city-killer nukes scorching the planet and causing nuclear winter.


    Some environmentalists howl that Orion should never be used for surface-to-orbit boosts, due to the danger of DUNT-dunt-Dunnnnnnnn Deadly Radioactive Fallout. However, there is a recent report that suggests ways of minimizing the fallout from an ORION doing a ground lift-off (or a, wait for it, "blast-off" {rimshot}). Apparently if the launch pad is a large piece of armor plate with a coating of graphite there is little or no fallout.

    By which they mean, little or no ground dirt irradiated by neutrons and transformed into deadly fallout and spread the the four winds.

    There is another problem, though, ironically because the pulse units use small low-yield nuclear devices.

    Large devices can be made very efficient, pretty much 100% of the uranium or plutonium is consumed in the nuclear reaction. It is much more difficult with low-yield devices, especially sub-kiloton devices. Some of the plutonium is not consumed, it is merely vaporized and sprayed into the atmosphere. Fallout, in other words. You will need to develop low-yield devices with 100% plutonium burn-up, or use fusion devices (with 100% burn-up fission triggers or with laser inertial confinement fusion triggers).

    The alternative is boosting the Orion about 90 kilometers up using a non-fallout chemical rocket. Which more or less defeats the purpose of using an Orion engine in the first place. Remember that Orions are best at boosting massive payloads into orbit.

    Most of the fallout will fall within 80 kilometers of the launch site. You can also reduce the fallout by a factor of 10 if you launch from near one of the two Magnetic Poles. You see, far from the magnetic poles, Terra's magnetic field traps fallout particles that would have been ejected into space, and returns them to the surface. At the magnetic poles are "holes" in the magnetic field which allows the fallout to travel unimpeded into deep space.

    One minor drawback is that if you launch from a magnetic pole, you pretty much have to launch into a polar orbit. In practice these are seldom used specialized orbits, of use mainly for military spy satellites, weather satellites, orbital bombardment weapons, and Google Earth. The Orion will probably have to change to a more useful equatorial orbit, which alas will require a change-of-plane maneuver of ninety freaking degrees. COPMs are notorious for being the most costly all maneuvers in terms of delta-V, and that is for changes of only a few degrees. This is still only a minor drawback because an Orion has delta-V to burn. It can do a 90° COPM and not even notice the delta-V is missing. Crazy nastya** Orions just don't give a sh*t.


    When fissionables like plutonium undergo fission, their atoms are split which produces atomic energy. The split atoms are called fission fragments.

    The good news is that they have very short half-lives, e.g., in 50 days pretty much all of the Strontium 94 has decayed away (because 50 days is 58,000 St94 half-lives).

    The bad news is that they have very short half-lives, this means they are hideously radioactive. Radioactive elements decay by emitting radiation, shorter half-life means more decays per second means a higher dose of radiation per second.

    The fragments that come screaming out of the detonation aimed at the sky are no problem. They are moving several times faster than Terra's escape velocity, you will never see them again (Terra's escape velocity is 11.2 km/s, the fragments are travelling like a bat out of hell at 2,000 km/s). The ones aimed towards Terra are a problem. The fragments can be reduced by using fusion instead of fission pulse units. The fragments can also be reduced by designing the pulse units to trade thrust in favor of directing more of the fragments skyward.


    A more sophisticated objection to using Orion inside an atmosphere is the sci-fi horror of EMP melting all our computers, making our smart phones explode, and otherwise ruining anything using electricity. But that actually is not much of a problem. EMP is not a concern unless the detonation is larger than one megaton or so, Orion propulsion charges are only a few kilotons (one one-thousandth of a megaton). Ben Pearson did an analysis and concluded that Orion charges would only have EMP effects within a radius of 276 kilometers (the International Space Station has an orbital height of about 370 kilometers). So just be sure your launch site is in a remote location, which you probably would have done anyway.


    Naturally watching an Orion blast-off is very bad for your eyes, defined as instant permanent blindness. This is called "eyeburn". While the Orion is below 30 km you definitely need protective goggles or you might be blinded. Above 90 km your eyesight it safe. In between 30 and 90 is the gray area, where prudent people keep their protective goggles on.


    Detonating pulse units in space near Terra can create nasty artificial radiation belts. The explosion can pump electrons into the magnetosphere, creating the belt.

    There are two factors: detonation altitude from Terra's surface, and magnetic latitude in Terra's magnetic field. If the detonation is within 6,700 kilometers of Terra's surface (i.e., closer than 2 Terran radii from Terra's center) and at a magnetic latitude from 0° to 40°, the radiation belt can last for years. Above 2 Terran radii the radiation belt will last for only weeks, and from latitude 80° to 90°, the radiation belt will last for only a few minutes.

    The military discovered this the hard way with the Starfish Prime nuclear test. The instant auroras were very pretty. The instant EMP was very scary, larger than expected (but the test was using a 1.4 megaton nuke, not a 0.001 megaton pulse unit). The artificial radiation belt that showed up a few days later was a very rude surprise. About one-third of all low orbiting satellites were eventually destroyed by the radiation belt.

    The radiation belts are harmless to people on Terra, but astronauts in orbit and satellites are at risk.


    There are three classes of pulse unit failure modes. Note that in this analysis the USAF had given up and had decided to boost the Orion on top of a chemical rocket.

    Class I - Pad Abort
    Typically occurs when the chemical booster burns or explodes on the pad. There will be no nuclear explosion. The pulse units contain chemical explosives, but there is much more explosive potential in the chemical booster fuel. Even if all the pulse units exploded simultaneously there would only be a 1 psi overpressure out to 300 meters and shrapnel hazard out to 2,000 meters.

    A chemical booster burn could aerosolize radioactive plutonium from booster units and create a downrange fallout hazard. The solution is to put the launch pad over a pool of water about 10 meters deep. In event of fire, collapse the pad into the pool. The fire would be extinguished and any escaped plutonium will be contained in the water. Many of the pulse units can be recovered and reused.
    Class II - Failure to Orbit
    The trouble is that the thousands of nuclear pulse units will fall down, probably into uncontrolled territory. As with Class I there will be no nuclear explosion, the chemical explosion will be impressive but not too huge, and there is a danger of radioactive fallout. All in what could very well be a foreign country.

    In addition, it will be scattering thousands of containers of weapons grade plutonium in convenient form to cause nuclear weapon proliferation. Or the pulse units could be used as is as impromptu terrorist devices. Though I'm sure the devices will contain fail-safes seven ways to Sunday, the same way nuclear warheads are in order to deal with the possibility of them falling into the Wrong Hands.

    Probably the best solution is to command all of the nuclear charges to detonate simultaneously while the spacecraft is at high altitude. This will make one heck of a fireworks display, and may cause an EMP, but nuclear devices in questionable hands is to be avoided at all costs.
    Class III - Misfire
    If a given pulse unit fails to detonate, the command can be resent repeatably, and/or there can be an automatic on-board destruct system. Otherwise the unit could survive reentry (due to the tungsten propellant plate) causing some damage to the country it hit and causing a foreign policy nightmare to the nation owning the Orion spacecraft.

    By about 1963 General Atomic had given up on designing an Orion to lift off from Terra's surface under nuclear power. They put together three plans for using chemical rocket boosters to get the Orion into orbit. Again this is throwing away the big advantage of the Orion, its ability to boost massive payloads.

    Mode I
    A fully loaded and fully fueled Orion is boosted to an altitude of 90 kilometers and 900 m/s by a chemical rocket. There it stages, and the Orion proceeds into orbit or into mission trajectory under nuclear power. The disadvantage is it requires a subobital start-up of the Orion engine. The Orion engine will need a thrust greater than the mass of the spacecraft, the standard was T/W of 1.25. But high thrust is never a problem with Orion.
    Mode II
    An empty Orion is loaded with just enough pulse units. It is boosted to an altitude of 90 kilometers and 900 m/s by a chemical rocket. There it stages, and the Orion proceeds into orbit. A second chemical booster rendezvous with the Orion to deliver the payload and a full load of pulse units.
    This was the worst plan. It combines the disadvantage of Mode I (by requiring suborbital start-up of the Orion engine) with the disadvantage of Mode III (by requiring orbital assembly).
    Mode III
    The Orion is boosted into orbit piecemeal as payload on a series of chemical boosters. The Orion is assembled in orbit, then departs on its mission under nuclear power. The main advantage is it avoids the possibility of the entire Orion spacecraft crashing to Terra in the event of a propulsion failure. The second advantage is it allowed a lower thrust Orion unit to be used, but with Orion thrust is never a problem. The main disadvantage is that orbital assembly is time consuming and difficult.

    Zeta-Pinch

    Zeta pinch is a type of plasma confinement system that uses an electrical current in the plasma to generate a magnetic field that compresses it. The compression is due to the Lorentz force.

    Zeta-Pinch Fission

    Mini-Mag Orion
    Mini-Mag Orion
    Exhaust Velocity157,000 m/s
    Specific Impulse16,004 s
    Thrust1,870,000 N
    Thrust Power0.1 TW
    Mass Flow12 kg/s
    Total Engine Mass199,600 kg
    T/W0.95
    FuelFission:
    Curium 245
    Specific Power1 kg/MW
    FuelFission:
    Curium 245
    ReactorZeta-Pinch
    RemassReaction
    Products
    Remass AccelThermal Accel:
    Reaction Heat
    Thrust DirectorMagnetic Nozzle
    Mini-Mag Orion (DRM-1)
    Exhaust Velocity93,164 m/s
    Specific Impulse9,497 s
    Thrust642,000 N
    Thrust Power29.9 GW
    Mass Flow7 kg/s
    Total Engine Mass119,046 kg
    T/W0.55
    Wet Mass731,924 kg
    Dry Mass250,300 kg
    Mass Ratio2.92 m/s
    ΔV99,967 m/s
    Specific Power4 kg/MW
    Mini-Mag Orion (DRM-3)
    Exhaust Velocity93,000 m/s
    Specific Impulse9,480 s
    Thrust642,000 N
    Thrust Power29.9 GW
    Mass Flow7 kg/s
    Total Engine Mass199,600 kg
    T/W0.33
    Wet Mass788,686 kg
    Dry Mass157,723 kg
    Mass Ratio5.00 m/s
    ΔV149,686 m/s
    Specific Power7 kg/MW

    The Mini-MagOrion is a sort of micro-fission Orion propulsion system. The idea was to make an Orion with weaker (and more reasonably sized) explosive pulses, using pulse charges that were not self contained (the full Orion pulse units were nothing less than nuclear bombs). Subcritical hollow spheres of curium-245 are compressed by a Z-pinch magnetic field until they explode. The sacrificial Z-pinch coil in each pulse charge is energized by an a huge external capacitor bank mounted in the spacecraft. So the pulse units are not bombs.

    The explosion is caught by a superconducting magnetic nozzle.

    More details are in the Realistic Designs section.

    Z-pinch Microfission
    Z-pinch Microfission
    Z-pinch Microfission
    Exhaust Velocity156,960 m/s
    Specific Impulse16,000 s
    Thrust8,500 N
    Thrust Power0.7 GW
    Mass Flow0.05 kg/s
    Total Engine Mass193,333 kg
    T/W4.00e-03
    Frozen Flow eff.74%
    Thermal eff.90%
    Total eff.67%
    FuelFission:
    Curium 245
    ReactorZeta-Pinch
    RemassReaction
    Products
    Remass AccelThermal Accel:
    Reaction Heat
    Thrust DirectorMagnetic Nozzle
    Specific Power290 kg/MW

    Electrodynamic zeta-pinch compression can be used to generate critical mass atomic bombs at very low yields. These detonations can be used to generate impulsive power or thrust.

    Exotic fission material (245Cm) is utilized to reduce the required compression ratio. The explosion of each low yield (335 GJ) atomic bomb energizes and vaporizes a set of low mass transmission lines, used to pump either another high current Z-pinch, or a bank of nanotube-enhanced ultracapacitors.

    Each bomb uses 40 grams of Cm fissile material and 60 grams of Be reflector material, with an aspect ratio of 5. A DT diode is used as a neutron emitter. The mylar transmission lines have a mass of 15 kg, and are replaced after each shot.

    The design illustrated is rated for a shot every 5.5 minutes, equivalent an output of 1000 MWth. If utilized for thrust, this provides 7.7 kN at a specific impulse of 17 ksec.

    Ralph Ewig & Dana Andrews, “Mini-MagOrion Micro Fission Powered Orion Rocket”, Andrews Space & Technology, 2002.

    From High Frontier by Philip Eklund
    n-Li6 Microfission
    n-Li6 Microfission
    n-6Li Microfission
    Exhaust Velocity156,960 m/s
    Specific Impulse16,000 s
    Thrust20,000 N
    Thrust Power1.6 GW
    Mass Flow0.13 kg/s
    Total Engine Mass106,667 kg
    T/W0.02
    Frozen Flow eff.87%
    Thermal eff.90%
    Total eff.78%
    FuelFission:
    Lithium 6
    ReactorUltracold Neutron
    Catalyzed
    RemassReaction
    Products
    Remass AccelThermal Accel:
    Reaction Heat
    Thrust DirectorMagnetic Nozzle
    Specific Power68 kg/MW

    The minimum explosive yield for fission bombs is about a quarter kiloton. Thus, rockets that fly using atomic explosions, such as Project Orion, require huge shock absorbers.

    The pulse energy can be brought down to microfission levels by the use of exotic particles. A n-6Li microfission thruster brings the lithium isotope 6Li to spontaneous microfission by interaction with particles with very large reaction cross sections such as ultracold neutrons. No “critical mass” is required. This clean reaction produces only charged particles (T and He), each at about 2 MeV.

    The system illustrated uses a 5-meter magnetic nozzle to transfer the microexplosion energy to the vehicle. This magnetic impulse transfer is borrowed from the MagOrion concept (combination of Orion and the magnetic sail).

    A fuel reaction rate of 60 mg/sec yields 3720 MWth. At a pulse repetition rate of one 224 GJ (0.05 kT) detonation each minute, the thrust is 12.8 kN at a 12 ksec specific impulse. A hydraulic fixture oscillates at a tuned frequency to provide a constant acceleration to the spacecraft. The combined frozen-flow and nozzle efficiencies are 21%, and the thermal efficiency is 96%.

    Ralph Ewig’s “Mini-magOrion” concept, modified for n-6Li fission, http://www.andrews-space.com/images/videos/PAPERS/Pub-MMOJPLTalk.pdf

    From High Frontier by Philip Eklund
    Ultracold Neutrons

    Neutrons are normally unstable particles, with a half life of 12 minutes.

    When polarized and ultra-cooled (using vibrators or turbines), they form a dineutron or tetraneutron phase. These “molecules” are believed to be stable and storable in total internal reflection bottles, lined with diamond-like carbon as the neutron reflector.

    Ultracold neutrons (UCN) have a huge quantum mechanical wavelength as a consequence of their slow movement (typically 0.4 μm @ 1 m/sec), and thus can spontaneously initiate fission reactions such as n-235U or n-6Li.

    If the neutron source is a nuclear reactor, the neutrons must be cooled from 2 MeV to 2 meV using a heavy water moderator, and then in a UCN turbine to 0.2 IeV.

    Robert L. Forward, “Alternate Propulsion Energy Sources”, 1983.

    From High Frontier by Philip Eklund

    Zeta-Pinch Fusion

    HOPE Z-Pinch
    Propulsion SystemZ-Pinch Fusion
    Exhaust Velocity189,780 m/s
    Specific Impulse19,346 s
    Thrust38,120 N
    Thrust Power3.6 GW
    Mass Flow0.20 kg/s
    Total Engine Mass95,138 kg
    T/W0.04
    FuelDeuterium-Tritium fusion
    + Lithium6 fission
    ReactorZeta-Pinch
    RemassReaction
    Products
    Remass AccelThermal Accel:
    Reaction Heat
    Thrust DirectorMagnetic Nozzle
    Wet Mass888,720 kg
    Dry Mass552,000 kg
    Mass Ratio1.61 m/s
    ΔV90,380 m/s
    Specific Power26 kg/MW
    Firefly Starship
    2013 design
    ΔV2.698×107 m/s
    (0.09c)
    Wet Mass17,800 metric tons
    Dry Mass2,365 metric tons
    Mass Ratio7.526
    Payload150 metric tons
    PropulsionZ-Pinch DD Fusion
    Exhaust Velocity1.289×107 m/s
    Thrust1.9×106 N
    Acceleration0.11 m/s
    (0.01 g)
    Accel time4 years
    Coast time93 years
    Decel time1 years

    PuFF Pulsed Fission Fusion

    Pulsed Fission-Fusion
    Specific
    Impulse
    20,000 sec
    Exhaust
    Velocity
    196,000 m/s
    Thrust29,400 N
    Thrust
    Power
    2.88 GW
    Specific
    Power
    96 kW/kg
    Fuel-
    Propellant
    U-235 + D-T

    This is from The Pulsed Fission-Fusion (PuFF) Propulsion System and Phase I Final Report.

    The study authors were going to take a Hope Z-Pinch Fusion spacecraft and swap out its drive for the PuFF drive.

    The idea is that while you can make some fuel undergo nuclear fission, and you can make other fuel undergo nuclear fusion, wouldn't it be nice to make some fuel do both? After all, a standard nuclear fusion warhead is a slug of fusion fuel that is ignited by the detonation of a small nuclear fission warhead.


    Refer to the diagram at right.

    The target is a charge of fission/fusion fuel, composed of Uranium-235 fission fuel and Deuterium-Tritium fusion fuel. The charge is held at the ignition point by some strong holder.

    A ring of liquid lithium sprayers (Li Injectors) are aimed at the target. They spray a cone-shaped plume of liquid lithium (Li Shell) with the cone apex located at the target. Oh, did I mention that the sprayers are connected to the anode of the power system capacitor (LTDs) so they and the lithium shell are charged to two mega-volts? The target holder is connected to the cathode.

    When the liquid lithium hits the target the circuit is closed, and the target is electrocuted by two mega-amps at two mega-volts (also totally draining the power system capacitor). This is 4 terawatts (4×1012 watts). Lorentz force (j×B) produced by the current and magnetic field savagely squeezes the fuel charge to one-tenth its original size. This makes the uranium achieve criticality.

    Only some of the uranium undergoes nuclear fission like an atom bomb (which it is). This heats the D-T fuel hot enough to initiate nuclear fusion.

    Neutrons from the fusion reaction ignites more of the uranium into a fission reaction. The heat from the fission boosts the fusion rate. Rinse-Lather-Repeat. This is called a Fission-Fusion Cascade. The fission to fusion cycle keeps cascading until all the fuel is burnt.

    The energy from the cascade turns the liquid lithium into plasma. The plume of charged plasma from the cascade is ejected by the magnetic exhaust nozzle. In addition to creating thrust, the nozzle also harvests some of the exhaust energy to charge up the primary power system capacitors for the subsequent pulse.


    Each fuel charge detonation takes several microseconds to cascade to full burnout. Detonations are repeated up to a rate of 100 Hz. The report notes that much analysis and experimentation is needed to find the optimum detonation frequency and fuel charge size.

    The specific impulse and thrust can shift gears by modifying the amount of lithium injected.

    Initially the power system capacitors are empty. For the first charge of the new burn an onboard SP-100 nuclear reactor laboriously charges them up. Subsequent capacitor recharges are by harvesting exhaust energy.

    Left as an exercise for the reader is what the heck do you make the target holder out of so it is not obliterated by the fission and fusion explosions.

    A - Target
    Charge of fission/fusion fuel
    B - Linear Transformer Drivers (LTD)
    Pulsed power storage (capacitors), discharge, and compression system
    C - Magnetic Nozzle (MN)
    Directs fission/fusion products into exhaust for thrust. Recovers energy for next pulse.
    D - Recharge System
    Pulse generation and onboard power storage/generation
    E - Lithium Injectors
    Lithium tankage / distribution system to provide target liner (cone of liquid lithium) and power conduction path (when it touches the target)
    F - Target Storage / Dispenser
    Maintains targets in non-critical configuration (so the uranium doesn't explode prematurely), injects into nozzle

    Medusa

    Medusa
    Exhaust velocity490,000 m/s
    to 980,000 m/s

    Medusa is driven by the detonation of nuclear charges like Orion, except the charges are set off in front of the spacecraft instead of behind. The spacecraft trails behind a monstrously huge parachute shaped sail (about 500 meters). The sail intercepts the energy from the explosion. Medusa performs better than the classical Orion design because its pusher plate intercepts more of the bomb's blast, its shock-absorber stroke is much longer, and all its major structures are in tension and hence can be quite lightweight. It also scales down better. The nuclear charges will be from 0.025 kilotons to 2.5 kilotons.

    The complicated stroke cycle is to smooth out the impulses from each blast, transforming it from a neck-braking jerk into a prolonged smooth acceleration.

    Jondale Solem calculates that the specific impulse is a function of the mass and yield of the nuclear charges, while the thrust is a function of the yield and explosion repetition rate. In this case, the mass of the nuclear charge is the mass of "propellant".

    Remarkably the mass of the spinnaker (sail) is independent of the size of its canopy or the number or length of its tethers. This means the canopy can be made very large (so the bomb blast radiation does not harm the canopy) and the tethers can be made very long (so the bomb blast radiation does not harm the crew). The mass of the spinnaker is directly proportional to the bomb yield and inversely proportional to the number of tethers.

    THE SAPPHIRE COLORATURA: REVEALED!

    Inspired by a passing comment on the Eldraeverse Discord, we now present a galari starship, the Sapphire Coloratura-class polis yacht; the favored interplanetary and interstellar transport of all sophont rocks of wealth and taste.

    SAPPHIRE COLORATURA-CLASS POLIS YACHT

    Operated by: Galari groups requiring luxurious private transit.
    Type: Executive polis yacht.
    Construction: Barycenter Yards, Galáré System

    Length: 96 m (not including spinnaker)
    Beam: 12 m (not including radiators)

    Gravity-well capable: No.
    Atmosphere-capable: No.

    Personnel: None required (craft is self-sophont). Can carry an effectively arbitrary number of infomorph passengers.

    Main Drive: Custom “dangle drive”; inertially-confined fusion pellets are detonated behind a leading spinnaker, the resulting thrust being transferred to the starship via a tether.
    Maneuvering Drive: High-thrust ACS powered by direct venting of fusion plasma from power reactors; auxiliary cold-gas thrusters.
    Propellant: Deuterium/helium-3 blend (pelletized aboard for main drive).
    Cruising (sustainable) thrust: 7.2 standard gravities
    Peak (unsustainable) thrust: 7.5 standard gravities
    Maximum velocity: 0.12 c (based on particle shielding)

    Drones:

    4 x galari body-crystals; since the galari are ergovores, any galari passenger or AI system may use these for EVA purposes.

    Sensors:

    1 x standard navigational sensor suite, Barycenter Yards
    1 x lidar grid and high-sensitivity communications laser grid, Barycenter Yards

    Weapons:

    Laser point-defense grid.

    Other Systems:

    • Cilmínár Spaceworks navigational kinetic barrier system
    • 4 x Bright Shadow secondary flight control systems
    • Kaloré Gravity Products type 1MP vector-control core
    • Systemic Integrated Technologies flux-pinned superthermal radiator system

    Small craft:

    5 x minipoleis (no independent drive systems; local accumulators only)

    DESIGN

    The Sapphire Coloratura was intended to be a shining jewel in the crown of galari starship design, so it is perhaps fitting that it indeed resembles a shining jewel, the translucent crystal of its main body throwing sparkles of rainbow light everywhere when it chooses to fly close to stars, or when it is illuminated by the fiery blasts of its main drive.

    The main body of the ship is similar to, in many ways, the galari themselves; a sixteen-faceted crystal, with eight long facets facing forward to the bow tip, and short, blunter facets facing aft towards the mechanical section, a gleaming metal cylinder with a rounded-off end taking up the remaining two-thirds of the starship’s length.

    To proceed from fore to aft, the bow tip of the ship is capped with metal, housing the core mechanisms of the dangle drive; the sail deployment system, tether terminus, pellet launcher, and ignition lasers.

    From our Earth perspective, this drive is very similar to the Medusa-type Orion; thrust is delivered to the starship via a 216 m diameter spinnaker “sail” on a tether ahead of the craft. Rather than dedicated pulse units, the drive projects pelletized D-3He charges ahead of the craft to the focal point of the spinnaker, where inertially-confined fusion is initiated by the ignition lasers, reflected to surround the pellet by the inner surface of the spinnaker. The resulting nuclear-pulse detonation accelerates the craft, smoothed out by the stroke cycle of the tether (see above link).

    The main crystal body of the craft is essentially a solid-state piece – save for cooling labyrinths and the axial passage required by the drive – of galari thought-crystal: a substrate which holds the ship’s own intelligence, those of all passengers and any crew needed, along with whatever virtual realms, simulation spaces, or other computational matrices they may require. As such, there is little that can be described by way of an internal layout; most polis-yachts are unique in this respect.

    The “waist” – broadest point – of the body is girdled by a machinery ring, containing within it the four fusion power reactors (multiple small reactors were preferred for extra redundancy by the designer) with the associated ACS, and at points between them, the backup flight control systems, navigational sensor suite, and other small auxiliary machinery.

    At the aftmost point of the main body, where the blunter end of the crystal joins the mechanical section, eight crystal spikes project, symmetrically, from the point of junction. These are left hollow by the manufacturer and equipped with tip airlocks to provide a small amount of volume for cargo space and aftermarket customization; if non-ergovore passengers are expected, two of these are typically converted into quarters and life-support. A central chamber where the spikes meet serves as a body and robot hotel.

    Entering the mechanical section, an accessible chamber at the forward end of the cylinder provides accommodation for the vector-control core and larger auxiliary machinery, including the thermal control system. The remainder of the section is entirely made up of bunkerage for the reactors and main drive.

    The galari have never, it should be noted, shied away from making maximal use of vector control technology. This is particularly notable in the Sapphire Coloratura‘s design in two areas:

    First, its radiators, which cloak the center of the mechanical section with a divided cylinder of gridwork, individual carbon-foam emitting elements held together and in place away from the hull by vector-magnetic couples, linked back to the ship itself only by the ribbons of thermal superconductor transmitting waste heat to them; and

    Second, by the minipoleis that the Coloratura uses as small craft. Resembling nothing so much as miniature duplicates of the starship’s main body, these auxiliary blocks of thought-crystal are held in place orbiting the main body of the ship – often in complex patterns, even under full acceleration – connected only by vector-magnetic couples and whisker-laser communication.

    That is pure ostentation.

    Inertial Confinement

    IC-Fusion
    Exhaust Velocity10,000,000 m/s
    Specific Impulse1,019,368 s
    Thrust100,000,000 N
    Thrust Power500.0 TW
    Mass Flow10 kg/s
    Total Engine Mass1,000,000 kg
    T/W10
    FuelProton-Proton
    Fusion
    Specific Power2.00e-03 kg/MW

    A pellet of fusion fuel is bombarded on all sides by strong pulses from laser or particle accelerators. Some use a two dimensional ring of lasers like a proverbial circular firing squad. Others expand it into a three dimensional spherical firing squad. The beams implode the pellet, raising the density and temperature to the point where a fusion reaction ignites.

    The inertia of the fuel holds it together long enough for most of it to undergo fusion, instead of using a magnetic bottle as in Magnetic Confinement fusion.

    The spherical arrangement of lasers would have a gap in it for the exhaust nozzle.

    D-D Fusion Inertial
    D-D Fusion Inertial
    Exhaust Velocity78,480 m/s
    Specific Impulse8,000 s
    Thrust3,200 N
    Thrust Power0.1 GW
    Mass Flow0.04 kg/s
    Total Engine Mass243,333 kg
    T/W1.00e-03
    Frozen Flow eff.50%
    Thermal eff.50%
    Total eff.25%
    FuelDeuterium-Deuterium
    Fusion
    ReactorInertial Confinement
    Laser
    RemassGraphite
    Remass AccelThermal Accel:
    Reaction Heat
    Thrust DirectorAblative Nozzle
    Specific Power1,938 kg/MW

    A “target” of fusion fuel can be brought to ignition by “inertial confinement”: the process of compressing and heating the fuel with beamed energy arriving from all sides. A snowflake of deuterium, the “heavy” isotope of hydrogen, can be imploded and fused with a combination of lasers and deuterium particle beams.

    The illustrated design uses combined input beam energy of 38 megajoules, arrayed in a ring surrounding the ejected iceball target. This energy operates at 1 Hz to blast a 2 gram ice pellet ejected each second. The outside 99% of the pellet is ablated away within 10 ns, super-compressing the deuterium fuel at the core to a density of a kilogram per cubic centimeter. The T and 3He products are catalyzed to undergo further fusion until all that remains is hydrogen, helium and some neutrons. (Neutrons comprise 36% of the reaction energy.) Fractional burn-up of the fuel (30%) is twice that of magnetic confinement systems, which implies a 40% higher fuel economy. The energy gain factor (Q) is 53.

    For a 500 MWth reactor, 320 MW of charged particles are produced, which can be used directly for thrust or metals refining. About 105 MW of fast neutrons escape to space, but another 75 MW of them are intercepted by the structure. About two thirds of this energy must be rejected as waste heat, but the remainder is thermally used to generate electricity or to breed tritium to be added to the fuel to facilitate the cat D-D pellet ignition.

    When used as a rocket, an ablative nozzle, made of nested layers of whisker graphite whose mass counts as propellant and shadow shield, is employed (much like the ACMF).

    “A Laser Fusion Rocket for Interplanetary Propulsion,” Hyde, R., 34th International Astronautical Conf., AIF Paper 83-396, Budapest, Hungary, Oct. 1983.

    (To keep radiator mass under control, I reduced the pellet repetition rate from 100 Hz to 1 Hz).

    From High Frontier by Philip Eklund
    VISTA
    Propulsion SystemIC Fusion
    Exhaust Velocity170,000 m/s
    Specific Impulse17,329 s
    Thrust240,000 N
    Thrust Power20.4 GW
    Mass Flow1 kg/s
    FuelDeuterium-Tritium
    Fusion
    ReactorInertial Confinement
    Laser
    RemassReaction
    Products
    Remass AccelThermal Accel:
    Reaction Heat
    Thrust DirectorMagnetic Nozzle
    Wet Mass6,000,000 kg
    Dry Mass1,835,000 kg
    Mass Ratio3.27 m/s
    Width170 m
    Height100 m

    Magneto Inertial Fusion

    Magneto Inertial Fusion
    Both
    Exhaust Velocity50,420 m/s
    Specific Impulse5,140 s
    FuelDeuterium-Deuterium
    Fusion
    ReactorMagneto-Inertial
    Confinement
    RemassLithium
    Remass AccelThermal Accel:
    Reaction Heat
    Low Gear
    Thrust103 N
    Thrust Power2.6 MW
    Mass Flow2.00×10-03 kg/s
    Delay between
    Fusion Pulses
    180 seconds
    High Gear
    Thrust13,800 N
    Thrust Power0.3 GW
    Mass Flow0.27 kg/s
    Delay between
    Fusion Pulses
    14 seconds

    There are two main approaches to utilizing nuclear fusion, magnetic confinement and inertial confinement. Magnetic confinement uses titanic magnetic fields, inertial confinement is how fusion bombs explode (a third way would be stars shining by gravitational confinement, but we don't know how to generate artificial gravitational fields).

    Inertial confinement ignites the fusion fuel by imploding a solid pellet of fuel with a circular firing squad of lasers or particle beams. This raises the density and temperature high enough for fusion ignition. It confines the burning fusion fuel by sheer inertia. That is, it is hoping that the burning fuel simply does not have enough time to expand below fusion density before all the fuel is burnt.

    Magnetic confinement ignites using a magnetic field to squeeze a cloud of fusion fuel plasma until it is hot and dense enough to ignite. It confines the burning fusion fuel with the same magnetic field. More like tries to confine, the blasted plasma keeps wiggling out of the cracks in the magnetic field before it is all burnt.

    As propulsion systems, both have major drawbacks.

    Problem 1

    Magnetic confinement requires huge (read: massive) electromagnets. The technique also has the problem of plasma instabilities (read: fusion plasma has thousands of different ways to wiggle out of the magnetic cage) which so far have defied any solution. Meaning that every time fusion researchers have devised a new magnetic cage, the blasted plasma finds two new ways of wiggling out.

    Inertial confinement works well in bombs, but trying to do it in a small controlled fashion (read: so the fusion reaction does not vaporize everything in a one kilometer radius) has also defied any solution. The compressing laser or particle beams have such low efficiencies that tons of excess power is required. Timing all the beams so they strike at the same instant is a challenge.

    Problem 2

    Both approaches have a problem with getting the fusion reaction energy to heat the propellant. Magnetic confinement tries to use the actual fusion plasma as propellant, resulting in a ridiculously small mass flow and thus a tiny thrust.

    Problem 3

    Also, there is nothing in between the fusion reaction and the chamber walls, leading to severe damage to the walls. The escaping radiation harms the crew as well.

    Magneto Inertial Fusion

    Dr. John Slough and his associates have come up with a new technique that sort of combines the two conventional approaches: magneto inertial fusion (MIF). You can find their published papers on the subject here

    A blob of FRC (field reversed configuration) plasma is created and injected axially into the chamber.

    Simultaneously injected into the chamber is a "liner". The liner is a foil ring composed of lithium, about 0.2 meters in radius. Each liner will have a mass of 0.28 kg (minimum) to 0.41 kg.

    As the liner travels axially down the chamber, electromagnets crush it down into a solid cylinder (the crush speed is about 3 kilometers per second, the cylinder will have a radius of 5 centimeters). This is timed so that the plasma blob (plasmoid) is in the center of the cylinder. The liner compresses the plasmoid and ignites the fusion reaction.

    The fusion reaction vaporizes the lithium liner. The ionized lithium (plus the burnt fusion fuel) exits through a magnetic nozzle, providing thrust.


    In other words it both ignites and confines the fusion fuel with a collapsing wall of solid metal. The metal is being squeezed by an external magnetic field even as the fusion reaction is raging, which does a much better job of confinent than simple inertia or a rubbery magnetic field.


    Liner compression is a heck of a lot more efficent than using huge magnetic fields or batteries of laser beams. Translation: it uses way less power and the equipment has a far smaller mass cost. Problem 1 solved.

    The lithium is also the propellant. Since it is tightly wrapped around the reaction, it is very efficient at getting the fusion reaction energy to heat the propellant. Problem 2 solved.

    The lithium stands in between the reaction and the chamber walls, protecting the walls. It also absorbs much of the radiation, protecting the crew. Problem 3 solved.

    So magneto inertial fusion solves the fusion ignition problem, the fusion heating the propellant problem, and the reaction damaging the chamber problem which are endemic to magnetic and inertial confinement fusion. And the engine has a far lower mass.


    Since this is an open-cycle system, the exhaust acts as the heat radiator, so the spacecraft can get by with only a tiny radiator. The energy to run the magnets can be supplied by solar cell arrays. Since the compression is so efficient, this will work with several types of fusion fuel: D-T, D-D, and D-3He. D-D is probably preferred, since tritium is radioactive with a short half-life, and 3He is rare.

    Please note that if you replace the magnetic nozzle with a magnetohydrodynamic (MHD) generator, the propulsion system is transformed into an electrical power generator. This could be used for ground based fusion power generators.

    Dr. Slough et al worked up two spacecraft for a Mars mission. The first was optimized to have a high payload mass fraction. The second was optimized to have the fastest transit time. Both were capable of a direct abort and return. The "Low Gear" engine is the study author's opinion of an engine easily achievable with current technology (that is, achievable fusion yields). The "High Gear" engine is a bit more speculative, but requiring only modest incremental improvements in technology.

    Fusion Drive Rockets (FDR)
    High Mass Fraction
    EngineLow Gear
    Transit Time90 days
    Initial Mass90 mT
    Payload Mass Fraction65%
    Specific Mass4.3 kg/kW
    Shortest Transit Time
    EngineHigh Gear
    Transit Time30 days
    Initial Mass153 mT
    Payload Mass Fraction36%
    Specific Mass0.38 kg/kW

    Plasma Jet Magneto Inertial

    Plasma Jet Magnetio Inertial
    ConMedOpt
    Base Parameters
    Mass of
    plasma (g)
    2.21.51.0
    Efficiency of rail
    & θ-pinch guns
    0.3
    Initial jet
    velocity (km/s)
    2007501500
    Heat fraction
    for 2nd power
    0.010.001
    Firing
    Frequency (Hz)
    200
    Fusion
    Gain
    50
    Target ΔV (c)0.08
    Target Burn
    Time (years)
    4
    Nozzle
    Efficiency
    0.84
    Resulting Ship Parameters
    Fuel Mass (t)55,50337,84325,228
    Exhaust
    Velocity (km/s)
    1189.794461.278922.48
    Specfic
    Impulse (s)
    121,284454,768909,529
    Thrust (MN)0.521.341.78
    Thrust/
    Fuel Mass (N/kg)
    0.03060.04490.0674
    Jet Power (GW)311.432985.457961.07
    Alpha (MW/kg)0.00560.07890.3156
    Waste
    Heat (GW)
    15.14145.13387
    Radiator
    Mass (t)
    30029007732

    This is from Project Icarus: Analysis of Plasma jet driven Magneto-Inertial Fusion as potential primary propulsion driver for the Icarus probe.

    This is basically the Magneto Inertial Fusion concept where the foil rings have been replaced by jets of plasma.

    A blob of fusion fuel plasma is injected into the center of the reaction chamber. It is bombarded by a spherical firing squad much like classic inertial confinement fusion. The difference is:

    1. The fusion fuel is a blob of plasma, not a solid pellet.
    2. The fusion fuel plasma blob is magnetized.
    3. The firing squad does not fire lasers or particle beams. Instead it fires cylindrical jets of plasma. The plasma is made from some element with a high atomic weight, so it has some serious momentum and inertia

    In the table there are three columns for three estimates of the performance of an actual engine. These are labeled CON (Conservative), MED (Medium), and OPT (Optimistic). The report notes that the Medium column is probably good enough for an unmanned interstellar probe. The Conservative column is probably good enough for missions within the solar system.

    • Mass Of Plasma: mass of the fusion fuel blob
    • Efficiency of rail & θ-pinch guns: efficiency of the railguns shooting the plasma liner jets and the theta-pinch guns creating the fusion fuel blob
    • Initial Jet Velocity: how fast the plasma liner jets are imploding
    • Heat Fraction for 2nd Power: fraction of the total rejected heat that is being used for the secondary power needs of the spacecraft. Meaning that some of the waste heat will be sent through a generator to make power for the ship's avionics and whatnot
    • Firing Frequency: how many fusion detonations are ignited per second
    • Fusion Gain: how many times bigger is the fusion energy compared to the input energy. The return on your investment, in other words
    • Target ΔV: the delta-V requirements the report assumes will be needed by the proposed interstellar mission
    • Target Burn Time: the burn time requirements the report assumes will be needed by the proposed interstellar mission
    • Nozzle Efficency: efficiency of the magnetic nozzle
    • Fuel Mass: The total mass of fuel needed for the mission. This is also a first approximation of the ship's wet mass, since with such outrageous delta-V requirements the fuel mass will dominate the total mass
    • Exhaust Velocity: what it says
    • Specific Impulse: what it says
    • Thrust: what it says
    • Thrust/Fuel Mass: Thrust to total fuel mass ratio, which is pretty darn close to thrust to mass ratio
    • Jet Power: what it says
    • Alpha: power to mass ratio
    • Waste Heat: amount of the power that turns up as waste heat and must be gotten rid of before the ship melts
    • Radiator Mass: mass of the heat radiators required to cope with the waste heat

    As the jets converge on the fuel at 750 kilometers per second they merge to form a spherical "liner". The liner collapses, squeezing the fusion fuel like a nutcracker from hell.

    Meanwhile as the fusion fuel is squeezed, so is its magnetic field. The density of the magnetic field increases to a point where is makes a conventional magnetic-confinement fusion engine look anemic.

    The shock where the imploding liner contacts the surface of the fuel blob heats it up. The liner also compresses the fuel blob, and soon fusion will be ignited. The internal magnetic field helps keep it confined long enough to burn all the fuel.


    The exploding fusion blob hits the magnetic nozzle, compressing the nozzle's magnetic field. This acts like a trampoline, making the fusion plasma rebound out the exhaust nozzle, creating thrust. Which is the purpose of all rocket engines. Meanwhile some of the energy in the nozzle field compression can be harvested to charge up the capacitors for the next round.


    The main advantage this propulsion system has over inertial or magnetic confinement is a drastically lower power requirement. Lasers, particle beam accelerators, or giant magnetics are power hogs. In this system the liner plasma jets can be lauched with relatively low powered rail-guns. This means you do not need tons and tons of capacitors to hold the huge jolts of electricity the other systems demand.

    I will admit I am a little fuzzy on what advantage this system has over the metal foil type Magneto Inertial Fusion. I'm looking into it.

    Antimatter Bottle

    This section has been moved here

    Antimatter catalyzed

    Nuclear fission pulse drives like Orion scale up well, since it is relatively easy to design a bigger bomb than the last one. However, physics seem to prevent the creation of a nuclear device with a yield smaller than about 1/100 kiloton (10 tons, 42 GJ) and a fissionable material mass under 25 kilograms. This is due to critical mass restraints.

    However, if a tiny sub-critical bit of fissionable material is bombarded by a few antiprotons, it will indeed create a tiny nuclear explosion. The antiprotons annihilate protons in uranium atoms, the energy release splits the atoms, creating a shower of neutrons, and a normal chain reaction ensues. Using antiprotons, yields smaller than 1/100 kiloton can be achieved. This can be used to create Antimatter catalyzed nuclear pulse propulsion

    AIM

    AIM
    Exhaust Velocity598,000 m/s
    Specific Impulse60,958 s
    Thrust55 N
    Thrust Power16.4 MW
    Mass Flow1.00e-04 kg/s
    FuelHelium3-Deuterium
    Fusion
    ReactorAntimatter Catalyzed
    RemassReaction
    Products
    Remass AccelThermal Accel:
    Reaction Heat
    Thrust DirectorMagnetic Nozzle

    Antiproton-initiated Microfusion. Inertial Confinement Fusion. See here.

    ACMF

    ICAN-II
    Propulsion SystemACMF
    Exhaust Velocity132,435 m/s
    Specific Impulse13,500 s
    Thrust180,000 N
    Thrust Power11.9 GW
    Mass Flow1 kg/s
    Total Engine Mass27,000 kg
    T/W0.68
    FuelFission:
    Uranium 235
    ReactorAntimatter Catalyzed
    RemassSilicon Carbide
    Remass AccelThermal Accel:
    Reaction Heat
    Thrust DirectorAblative Nozzle
    Wet Mass707,000 kg
    Dry Mass345,000 kg
    Mass Ratio2.05 m/s
    ΔV95,020 m/s
    Specific Power2 kg/MW

    Antiproton-catalyzed microfission, inertial confinement fission. See here.

    Fuel pellets have 3.0 grams of nuclear fuel (molar ratio of 9:1 of Deuterium:Uranium 235) coated with a spherical shell of 200 grams of lead. The lead shell is to convert the high energy radiation into a form more suited to be absorbed by the propellant. Each pellet produces 302 gigajoules of energy (about 72 tons of TNT) and are fired off at a rate of 1 Hz (one per second). The pellet explodes when it is struck by a beam containing about 1×1011 antiprotons.

    A sector of a spherical shell of 4 meters radius is centered on the pellet detonation point. The shell is the solid propellant, silicon carbide (SiC), ablative propellant. The missing part of the shell constitutes the exhaust nozzle. Each fuel pellet detonation vaporizes 0.8 kilograms of propellant from the interior of the shell, which shoots out the exhaust port at 132,000 meters per second. This produces a thrust of 106,000 newtons.

    The Penn State ICAN-II spacecraft was to have an ACMF engine, a delta-V capacity of 100,000 m/s, and a dry mass of 345 metric tons. The delta-V and exhaust velocity implied a mass ratio of 2.05. The dry mass and the mass ratio implied that the silicon carbide propellant shell has a mass of 362 metric tons. The wet mass and the thrust implied an acceleration of 0.15 m/s2 or about 0.015g. It can boost to a velocity of 25 km/sec in about three days. At 0.8 kilograms propellant ablated per fuel pellet, it would require about 453,000 pellets to ablat the entire propellant shell.

    It carries 65 nanograms of antiprotons in the storage ring. At about 7×1014 antiprotons per nanogram, and 1×1011 antiprotons needed to ignite one fuel pellet, that's enough to ignite about 453,000 fuel pellets.

    The system is very similar to Positron Ablative.

    H-B inertial catalzyed fusion
    H-B cat inertial
    Exhaust Velocity156,960 m/s
    Specific Impulse16,000 s
    Thrust4,700 N
    Thrust Power0.4 GW
    Mass Flow0.03 kg/s
    Total Engine Mass65,089 kg
    T/W7.00e-03
    Frozen Flow eff.86%
    Thermal eff.85%
    Total eff.73%
    FuelHydrogen-Boron
    Fusion
    ReactorAntimatter Catalyzed
    RemassGraphite
    Remass AccelThermal Accel:
    Reaction Heat
    Thrust DirectorAblative Nozzle
    Specific Power176 kg/MW

    The fusion of hydrogen and boron 11 is a clean reaction, releasing only 300 keV alpha particles, which can be magnetically directed. However, the H-B fusion will not proceed at temperatures less than 300 keV unless catalyzed using exotic particles.

    One possibility: replace the electrons in H-B atoms with stable massive leptons such as magnetic monopoles or fractionally-charged particles (the existence of these is hypothetical). The resulting exotic atoms can fuse at “cold” temperatures, allowing the exotic catalysts to be recycled.

    A second possibility is to use antiproton-catalyzed microfission to initiate the H-B fusion. If a hundred billion antiprotons at 1.2 MeV in a 2 nsec pulse are shot at a target of three grams of HB: 235U in a 9:1 molar ratio, the uranium microfission initiates H-B and releases 20 GJ of energy. Operating at a fifth of a hertz, hydrogen and boron 11 reacting at a rate of 145 mg/shot produces 2000 MWth. A shell of 200g of lead about the target thermalizes the plasma from 35 keV average to 1 keV, low enough that this radiation can be optimally transferred to thrust using a magnetic or ablative nozzle at 73% efficiency. The ejected mass per shot is 2.4 kg. The exotic catalysts are recycled. Catalyzed fusion enjoys an excellent thermal efficiency (86%) and thus a good thrust/weight ratio (3.2 milli-g), making it one of the best engines in the game. The specific impulse ranges between 8 and 16 ksec, depending whether spin-polarized free radicals are used as the hydrogen fuel.

    “Antiproton-Catalyzed Microfission/Fusion Propulsion Systems for Exploration of the Outer Solar System and Beyond”, G. Gaidos, et al., Pennsylvania State University, 1998.

    (I used the ICAN-II spacecraft design, modified from cat D-T to cat H-B fuel, and scaled way down from 1 Hz to 0.2 Hz, and 302 GW to 2 GW.)

    From High Frontier by Philip Eklund

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