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
    Direct Fusion Drive
    FUSION-ENABLED PLUTO ORBITER
    Mass Schedule
    ItemmassTotal mass
    Enginesx21,357 kg2,714 kg
    Radiatorsx266.75 kg133.5 kg
    Magnetic Nozzlesx271.43 kg142.86 kg
    D2 tanksx13,432 kg3,432 kg
    He3 Tankx10.22 kg0.22 kg
    Insulating shellx1200 kg200 kg
    Optical trussx210 kg20 kg
    Gimbalsx23.75 kg7.5 kg
    Laser comnx22 kg4 kg
    Orbiter Payloadx1270 kg270 kg
    Landerx1230 kg230 kg
    TOTAL7,154 kg
    Engine
    TypeDirect Fusion Drive
    Num Enginesx2
    Thrust5 N
    Total Thrust10 N
    Isp10,000 sec
    Exhaust Vel98,100 m/s
    Power1 MW
    Total Power2 MW
    Num Radiatorsx2
    Radiator Area50 m2
    Radiator Cap.840 kW
    PLASMA PHYSICS TRADING CARD
    Thrust16 N
    Specific Impulse12,500 s
    Exhaust Velocity122,600 m/s
    Thrust Power2 MW
    Radius0.3 m

    This is currently the front-runner for something that can actually be made into a real working fusion drive. The specific impulse is fantastic, but predictably the thrust is measured in hummingbird-powers. Regardless of the low thrust, it can deliver a metric ton of payload to Pluto in 3.75 years flat, instead of chemical rocket New Horizon's pathetic 30 kilograms taking freaking nine years.

    Even better is the fact that it can run bi-modal: switching from generating thrust into generating electrical power. This comes in real handy if the spacecraft is traveling further than the orbit of Mars from Sol, solar power becomes pretty worthless in the outer solar system .

    It is a magnetic-confined fusion design, also a afterburner engine, so you can shift gears: increasing thrust by lowering specific impulse.

    It also plans to use the practically aneuronic (almost no deadly neutron radiation) D-3He fusion fuel so the ship does not need a massive neutron-radiation shield, which would savagely cut into the allowed payload mass.

    Understand that D-3He is only "practically" aneuronic because some of the deuterium stubbornly refuses to fuse with 3He as it should but instead unhelpfully fuses with other deuterium in the fuel and thus creates neutron radiation. Worse: the D+D reaction produces tritium, and if the tritium accumulates it can fuse with more deuterium and create even more neutron radiation. The Direct Fusion Drive deals with this by selective 3He heating, and by doing its darnedest to flush any tritium created out the exhaust stream ASAP. This does not totally eliminate the neutron radiation but any reduction is a win.

    The drawback is the reaction is harder to ignite, and Helium-3 is scarce stuff (at least on Terra). The report suggest trying to scrape together the scraps of Helium-3 found naturally in helium-rich natural gas wells. Currently most commercial Helium-3 comes from the decay of tritium triggers in nuclear warheads. Tritium can be produced by bombarding lithium-6 with neutrons, then tritium has a half-life of 12.3 years, decaying into Helium-3. Forget about mining Luna for Helium-3, it isn't concentrated enough to be economical. The best extraterrestrial source is the atmosphere of Saturn, it exists in Jupiter's atmo but the gravity is so great it is hard for the harvest ships to escape.

    To deal with the fact that the D-3He fusion reaction is harder to ignite, the engines uses a innovative way of altering the fields. This raises the plasma temperature high enough to kindle the reaction.

    The Bremsstrahlung and synchrotron radiation emitted from the plasma heat up the engine components. The coolant which prevents the engine from melting is sent through a Brayton heat engine to run an electrical power generator. The coolant is then sent to heat radiators. The power is used to energize the electromagnetic coils, the radio-frequency plasma heater, and any other power needs the spacecraft has.

    DIRECT FUSION DRIVE

    Direct Fusion Drive (DFD) is a conceptual low radioactivity, nuclear-fusion engine designed to produce both thrust and electric power for interplanetary spacecraft. The concept is based on the Princeton field-reversed configuration reactor invented in 2002 by Samuel A. Cohen, and is being modeled and experimentally tested at Princeton Plasma Physics Laboratory, a US Department of Energy facility, and modeled and evaluated by Princeton Satellite Systems. As of 2018, the concept has moved on to Phase II to further advance the design.

    Principle

    The Direct Fusion Drive (DFD) is a conceptual fusion-powered spacecraft engine, named for its ability to produce thrust from fusion without going through an intermediary electricity-generating step. The DFD uses a novel magnetic confinement and heating system, fueled with a mixture of helium-3 (He-3) and deuterium (D), to produce a high specific power, variable thrust and specific impulse, and a low-radiation spacecraft propulsion system. Fusion happens when atomic nuclei, comprising one species in a hot (100 keV or 1,120,000,00 K) plasma, a collection of electrically charged particles that includes electrons and ions, join (or fuse) together, releasing enormous amounts of energy. In the DFD system, the plasma is confined in a torus-like magnetic field inside of a linear solenoidal coil and is heated by a rotating magnetic field to fusion temperatures. Bremsstrahlung and synchrotron radiation emitted from the plasma are captured and converted to electricity for communications, spacecraft station-keeping, and maintaining the plasma's temperature. This design uses a specially shaped radio waves (RF) "antenna" to heat the plasma. The design also includes a rechargeable battery or a deuterium-oxygen auxiliary power unit to startup or restart DFD.

    The captured radiated energy heats to 1,500 K (1,230 °C; 2,240 °F) a He-Xe fluid that flows outside the plasma in a boron-containing structure. That energy is put through a closed-loop Brayton cycle generator to transform it into electricity for use in energizing the coils, powering the RF heater, charging the battery, communications, and station-keeping functions. Adding propellant to the edge plasma flow results in a variable thrust and specific impulse (in other words it can shift gears) when channeled and accelerated through a magnetic nozzle; this flow of momentum past the nozzle is predominantly carried by the ions as they expand through the magnetic nozzle and beyond, and thus, function as an ion thruster.

    Development

    The construction of the experimental research device and most of its early operations were funded by the US Department of Energy. The recent studies —Phase I and Phase II— are funded by the NASA Institute for Advanced Concepts (NIAC) program. A series of articles on the concept were published between 2001 and 2008; the first experimental results were reported in 2007. Numerous studies of spacecraft missions (Phase I) were published, beginning in 2012. In 2017 the team reported that "Studies of electron heating with this method have surpassed theoretical predictions, and experiments to measure ion heating in the second-generation machine are ongoing." As of 2018, the concept has moved on to Phase II to further advance the design. The full-size unit would measure approximately 2 m in diameter and 10 m long.

    Stephanie Thomas is vice president of Princeton Satellite Systems and also the Principal Investigator for the Direct Fusion Drive.

    Projected performance

    Analyses predict that the Direct Fusion Drive would produce between 5-10 Newtons thrust per each MW of generated fusion power, with a specific impulse (Isp) of about 10,000 seconds and 200 kW available as electrical power. Approximately 35% of the fusion power goes to thrust, 30% to electric power, 25% lost to heat, and 10% is recirculated for the RF heating.

    Modeling shows that this technology can potentially propel a spacecraft with a mass of about 1,000 kg (2,200 lb) to Pluto in 4 years. Since DFD provides power as well as propulsion in one integrated device, it would also provide as much as 2 MW of power to the payloads upon arrival, expanding options for instrument selection, laser/optical communications, and even transfer up to 50 kW of power from the orbiter to the lander through a laser beam operating at 1080 nm wavelength.

    The designers think that this technology can radically expand the science capability of planetary missions. This dual power/propulsion technology has been suggested to be used on a Pluto orbiter and lander mission, a well as integration on the Orion spacecraft to transport a crewed mission to Mars in a relatively short time (4 months instead of 9 with current technology).

    From the Wikipedia entry for DIRECT FUSION DRIVE
    DIRECT FUSION DRIVE ROCKET

    I serve on the External Council of NIAC, NASA's Innovative Advanced Concepts program, an organization that funds and encourages innovative ideas that are applicable to the US space program. NIAC had a meeting this June in Washington, DC, and there I heard a presentation describing an innovation that I've awaited for many years: the promise of a rocket that is propelled by the energy of nuclear fusion. Chemical rockets, the workhorses of our present space program, produce too little energy per kilogram of fuel and have exhaust velocities and specific impulse values that are too small. Elaborate and very expensive aerospace engineering efforts are necessary to get around the inadequacies of chemical rockets. The high energies and high exhaust velocities provided by fusion for space propulsion are exciting prospects. In particular, fusion rockets should have specific impulse values (how much push you get per mass of fuel) that are 10 to 100 times larger than those of chemical rockets. Amazingly, there is now a line of development that may make fusion rockets possible. To begin this discussion, I want to review a few basic ideas about nuclear fusion.


    The energy source that heats most stars is the nuclear fusion of hydrogen. For our Sun, it is a multi-step process involving the strong and weak interactions that starts with four protons (symbol p, the nucleus of a hydrogen atom) and finishes with the production of helium-4 (4He, a mass-4 helium nucleus containing two neutrons and two protons), along with some neutrinos, positrons, and gamma rays. In the deep interior of the Sun the temperature and pressure are high enough to fuse two protons to deuterium (d, mass-2 hydrogen nucleus containing one neutron and one proton), to fuse deuterium and a proton to helium-3 (3He, mass-3 helium nucleus containing one neutron and two protons), and to fuse two helium-3 nuclei to one helium-4 (4He, two protons and two neutrons) plus two free protons. This is the so-called p-p fusion chain that dominates fusion processes in all stars having the mass of our Sun or smaller.

    Fusion machines on Earth like the large and expensive ITER tokomak machine being developed in France must operate at lower temperatures and pressures than those in a star and must attempt to produce usable energy from controlled fusion using a simpler single-step process that fuses deuterium and tritium (t, mass-3 hydrogen nucleus containing two neutrons and one proton) into a 4He and a neutron (reaction: d+t4He+n). Much of the energy from this process is given to the neutron with a kinetic energy of 14.1 million electron volts (14.1 MeV). This neutron steals valuable energy and presents hazards for both radiation-sensitive materials and for human operators. Usually the fast neutrons must be moderated with massive shielding and captured in a lithium blanket to produce additional energy. The break-even temperature, the temperature to which the d+t plasma (ionized atoms) must be heated in order to produce more fusion energy than was required to create it, is 13.6 thousand electron volts (13.6 keV). Fusion machines are designed to contain such plasmas in a strong magnetic field while the plasma is heated, fusion occurs, and energy extracted.

    The problem with applying such fusion-machine designs to fusion-driven space propulsion is that they are typically very large and expensive, they have not yet produced any useful fusion energy, they have no obvious exhaust ejection path for propulsion, and they would produce large quantities of 14.1 MeV neutrons in close proximity to payloads and crew, with their neutrons removing energy needed for propulsion and requiring many tons of shielding material. It is apparent that d+t fusion, while possibly useful for power applications on Earth, is inappropriate for space applications. Clearly, a different approach is needed.


    Such a new approach may be the direct fusion drive rocket (DFDR) design of the Princeton Plasma Physics Laboratory, which has provided the basis for a new NIAC Phase I grant to Stephanie Thomas of Princeton Satellite Systems. At the NIAC meeting I attended, she discussed a mission to Pluto using a DFDR drive. The DFDR geometry is a cylinder that uses the so-called "field-reversed configuration". This means that the loading of the plasma in the system employs a trick. A plasma is initially created within a magnetic field from pinch coils at the two ends of a cylindrical polycarbonate vacuum vessel. This field is aligned in along the axis of the cylinder and causes the ions to orbit around the lines of magnetic flux, preventing them from moving away from the axis of the cylinder and sustaining the field. Then the current in the pinch coils is abruptly reversed, applying a new external magnetic field in the opposite direction. This abrupt change compresses and heats the plasma and creates a layered and increased magnetic field, with flux lines in the inner region in one direction and those in the outer region in the opposite direction. The outer magnetic field lines attempt to expand outward but are confined within the cylinder by a set of passive warm-superconducting "flux conserver" pancake coils spaced along the length of the cylinder. These coils develop induced currents of thousands of amperes when field lines attempt to cross them, keeping the magnetic flux lines within the cylinder. The trapped ions execute figure-8 orbits at the boundary between the inner and outer fields.

    The DFDR is designed to fuse deuterium and helium-3 to form a proton and a helium-4 nucleus (reaction: d+3Hep+4He), liberating 18.3 MeV of usable charged-particle kinetic energy in each fusion reaction. Note that neutrons are not produced in this primary reaction. However, because deuterium is present in the plasma, the fusion of two deuterium nuclei to tritium and a proton or to helium-3 and a neutron with a kinetic energy of 2.45 MeV (reactions: d+dt+p or d+d3He+n) are both secondary reactions that will also occur in the heated plasma. Further, if tritium from the first reaction is allowed to accumulate, one could again face the problem of dealing with 14.1 MeV neutrons from d+t fusion. Fortunately, the DFDR design includes mechanisms for suppressing d+d reactions by selective 3He heating and for moving tritium from the plasma into the exhaust stream as it is produced.

    We note, however, that 3He is an expensive fuel, mainly a small byproduct derived from helium-rich natural gas wells. Its use in fusion requires a considerably higher plasma temperature for fusion. While the break-even temperature for d+t fusion is 13.6 keV, the break-even temperature for d+3He is 58 keV, more than three times higher. Thus, an effective method for heating the plasma to this high temperature is a key element of the DFDR design.

    This heating is accomplished by applying to the plasma an "odd-parity rotating magnetic field" produced by four rectangular figure-eight shaped antenna coils surrounding the cylinder above, below, and on the sides. The drive currents in the four antenna coils are sequenced so that the resulting magnetic field is always perpendicular to the cylinder axis and rotates at a drive frequency in the MHz region. The "odd parity" description means that the front and rear parts of the antenna coils have oppositely circulating currents and produce magnetic field that point in opposite directions. This drive field oscillates near the cyclotron resonance frequency of 3He and therefore selectively transfers more heat to 3He ions than to d ions. In particular, 3He ions are heated to about 100 keV while d ions are heated to only 50 keV. This differential heating enhances 3He+d fusion with respect to d+d fusion by a large factor, minimizing the production of neutrons and tritium.

    The use of the rotating magnetic field brings another advantage: following fusion ignition of the plasma, the same antennas can be used to directly extract electric power from the plasma ions through induction. The result is a fusion rocket that also directly generates its own electric power, a very significant advantage for space missions that venture far from the Sun, where solar panels are not efficient.


    As illustrations of the utility of the DFDR, Princeton Satellite Systems has designed and described in some detail a spectrum of space missions that might use the fusion rocket technology. These include:

    1. the transport of the James Webb Space Telescope from low-earth orbit to the desired Lagrange-2 halo orbit by using a 1 megawatt (1 MW) DFSR
    2. a Pluto Orbiter/Lander sample-return mission, the subject of the NIAC grant mentioned above, using a 2 MW DFDR (x2 DFDR, each with 5 N and 1 MW)
    3. the deflection of an Apophis-type asteroid away from an Earth-collision orbit using a reusable "space tug" with a 5 MW DFDR engine
    4. a manned mission to Mars with a 46 day one-way travel time using a cluster of eight DFDRs generating power totaling 160 MW and delivering 2,000 newtons of thrust (x8 DFDR, each with 250 N and 20 MW)
    All of these missions would be cheaper and faster than similar missions using chemical rockets. Clearly a mature DFDR technology would bring a "game changing" renaissance to our space program.


    Therefore, the questions are: how soon will the research on fusion rockets be completed, and when can we begin to use them? The present incarnation of this technology, the PRFC-2, is only a prototype unit that has demonstrated ion heating to a few kV with a 15 KW rotating magnetic field for a duration of 100 ms. The system is reported to be behaving as predicted by theoretical modeling and shows good confinement time and no unanticipated instabilities. The warm-superconductor flux conserver coils are behaving as expected and can sustain induced currents of up to 3,100 amperes.

    However, there is a long way to go from this test configuration to a usable fusion rocket. To achieve fusion temperatures, the rotating magnetic field drive must deliver around 200 KW. The detailed design of the magnetic nozzle that shapes and directs the fusion products in the exhaust is a work in progress. The expectations are that the work will ultimately result in fusion engines capable of producing power of 1 to 20 megawatts, thrusts of 5 to 250 newtons, and specific impulses of 5,000 to 50,000 seconds.

    The timeline provided by Princeton Satellite Systems and the Princeton Plasma Physics Laboratory shows the planned PFRC-3 test unit demonstrating fusion around 2019, the PFRC-4 unit demonstrating operational thrust and energy production on the ground around 2024, the first robotic space mission being operational in about 2030, and a Mars Orbital Mission around 2038. This is probably an optimistic schedule, and it critically depends on whether the Department of Energy and NASA will provide funding that supports these developments.

    All I can say is that we really need fusion rocket technology, the DFDR is the most promising fusion rocket design I have seen, and I hope the timeline can be maintained.


    References:

    Modular Aneutronic Fusion Engine,IAC-12,C4,7-C3.5,10
    http://w3.pppl.gov/ppst/docs/razin2012iac.pdf

    Direct Fusion Drive Rocket for Asteroid Deflection, J. B. Mueller, et al.
    http://yosefrazin.weebly.com/uploads/1/5/7/7/15770718/iepc-2013-296.pdf

    Direct Fusion Drive for a Human Mars Orbital Mission, M. Paluszek, et al.,
    http://bp.pppl.gov/pub_report/2014/PPPL-5064.pdf

    Fusion-Enabled Pluto Orbiter and Lander
    https://www.nasa.gov/feature/fusion-enabled-pluto-orbiter-and-lander

    From THE DIRECT FUSION DRIVE ROCKET by John G. Cramer (2016)
    DFD SOLAR SYSTEM ROCKET

    I. INTRODUCTION

         At any rate there is no doubt that to become a real spacefaring civilization we must develop rocket engines based on nuclear fusion. The idea to use fusion power for spacecraft propulsion has a long history. For the fusion propulsion there are two alternatives:similar to NTP and fusion NEP. In the last 20 years many studies have been devoted to the development of fusion nuclear power in general — mostly for general power generation — and specifically of fusion nuclear rockets. Fusion NEP requires the development of lightweight fusion reactors, which is something that today appears to be a diffcult achievement. Moreover, also here the point is again just the specific mass of the generator α, and many years will pass before fusion generator will have a better value of α than fission generators — apart from the fact that today no fusion generator, even with a very high α, is available. In fusion NEP, the lower is the value of α, the higher is the optimum value of the specific impulse, so even when a lightweight generator will be available, much work will be required also for improving the electric thruster.

         The revolutionary Direct Fusion Drive (DFD) is a nuclear fusion engine and its concept is based on the Princeton field-reversed configuration reactor, which has the ability to produce thrust from fusion without going through an intermediary electricity-generating step. The engine development is related to the ongoing fusion research at Princeton Plasma Physics Laboratory. The DFD uses a novel magnetic confinement and heating system, fueled with a mixture of isotopes of helium and hydrogen nuclei, to produce a high specific power, variable thrust and specific impulse, and a low-radiation spacecraft propulsion system. The simplest type of fusion drive is using small uncontrolled thermonuclear explosions to push forward the spacecraft, as was planned in the Orion Project, but even if a continuous, controlled reaction is used, DFD seems to be much easier to realize and D — 3He direct fusion thrusters seem to be the thrusters which will allow to colonize, in the medium term, the solar system.

         While most of the studies related to DFD deal with missions to the outer solar system or the near interstellar space, the aim of the present paper is studying in some detail fast human missions to Mars and to the Asteroid Belt. The result is that nuclear fusion propulsion is the enabling technology to start the colonization of the solar system and the creation of a solar system economy.


    II. THE THRUSTER

         The experimental study of the D-3He plasma led to the proposal of a new kind the fusion-based thruster — the Direct Fusion Drive (DFD), which has field-reversed configuration (FRC) reactor for an original plasma-formation. The FRC employs a linear solenoidal magnetic-coil array for plasma confinement and operates at higher plasma pressures. One should note that several FRCs have achieved stable plasmas.

         The DFD employs the radiofrequency technique called rotating magnetic field (RMF) to form and heat plasma. An important figure-of-merit for fusion reactors is β, the ratio of the plasma pressure to the magnetic energy density. The innovative radiofrequency RMF method, which heats particles and allows the size of the FRC to be relatively small was suggested in Ref. [23].

         In Refs. [10, 12, 15, 24] was considered a compact, anuetronic fusion engine, which enables more challenging exploration missions in the solar system and beyond. The DFD concept is result of the Princeton Field-Reversed Configuration Reactors which employ heating method invented by S. Cohen. The Scrape-off Layer (SOL) of the DFD is quite different than that of any other fusion device. The energy is deposited in the SOL directly from the D-3He fusion products via a non-local process and is predominantly transmitted to the electrons via fast-ion drag. The random thermal energy in the SOL electrons is transferred to the cool SOL ions through a double layer at the nozzle and via expansion downstream, thus being converted into directed flow of a propellant fluid.

         The heat transport into SOL is described by Fick's law, by the local flux-surface-normal gradient in pressure. In Refs. [10, 26] is used a fluid model for the SOL between the gas box with the propellant and the nozzle and dependencies of the thrust and specific impulse on gas input flow for powers of 0.25 to 7 MW transferred to the SOL are studied. The calculations are performed using UEDGE fluid-code for simulations. Results of these simulations for the propellant gas input 0.08 g/s yields to the data given in Table I.

    TABLE I
    DFD propulsion parameters
    based on UEDGE Model spacecraft
    Total Fusion Power, MW11:52
    Specific Impulse, Is, s10,00012,00012,500
    Thrust, T, N81011
    Fusion Effciency0.17 — 0.46
    Specific Power, kW/kg0.75 — 1.25

         The nuclear fuel for such a thruster is D—3He and the propellant fluid is atomic or molecular deuterium, which is heated by the fusion products and then expanded into a magnetic nozzle, generating an exhaust velocity and thrust. Adding propellant to this flow results in a variable thrust, variable specific impulse exhaust through a magnetic nozzle. The thrust of the DFD depends on the input gas flow and varies from about 4 N for the power 0.25 MW to 60 N, when the power is 7 MW. The results of simulations show that when the gas input flow increases from 0.08 to 0.7 g/s the thrust increases from 4 N to 60 N. For the specific impulse the preferable gas feed for the power 0.25 MW to 7 MW is 0.08 — 0.3 g/s.

         Approximately 35% of the fusion power goes to the thrust, 30% to electric power, station keeping and communication, 25% lost to heat, and 10% is recirculated for the radio frequency heating. The current estimated DFD specific powers are between 0.3 and 1.5 kW/kg. One could considered as a conservative estimate the power to thrust effciency, about 0.3 — 0.5.

         A full-sized D-3He fusion reactor is perfectly suited to use as a rocket engine for two reasons:

    1. the configuration results in a radical reduction of neutron production compared to other D-3He approaches
    2. the reactor features an axial flow of cool plasma to absorb the energy of the fusion products.

    In other words, the cool plasma flows around the fusion region, absorbs energy from the fusion products, and then is accelerated by a magnetic nozzle. The ratio of the total mass of fuel and propellant to the mass of 3He is about 670 and to get a specific power 0.18 kW/kg the small amount of 3He is needed — about 0.53 kg. The most Helium-3 used in industry today is produced from the radioactive decay of tritium.

         A spacecraft driven by a fusion thruster was studied at the turn of the century by NASA: its goal was to perform a human mission to Jupiter or Saturn as described in the Movie 2001, a Space Odyssey. The spacecraft was aptly named Discovery II. The main characteristics of the thruster (in the version for the Saturn mission) which were obtained in that study were: specific impulse Is = 47,205 s and specific mass of the propulsion system α = 0.00016 kg/W and are listed in Table II.

         These values are very favorable indeed. DFD, with a specific impulse in the range of 10,000 to 20,000 seconds and a specific power about 1 kW/kg, is suitable for almost any interplanetary mission. In NASA solicitation for rapid, deep space propulsion, four candidate missions were identified: Mars, Jupiter, Pluto, and 125 AU for an interstellar precursor mission. In Ref. [35] has sized a DFD engine for each candidate mission. The main characteristics of the spacecraft are reported in Table I. A more recent study for a DFD driven spacecraft is reported in Ref. [10]. Although showing a small spacecraft aimed at the focal line of the gravitational lens of the Sun and an interstellar probe aimed at Alpha Centauri, the basic values there reported for a 2 MW fusion rocket can be considered as a conservative estimate for a larger unit aimed to power an interplanetary piloted spacecraft.

    TABLE II
    SpacecraftDiscovery IIDFD [10]
    Specific Impulse Is, s47,20523,000
    Specific Mass engine α, kg/W0.0001160.0018

    III. EARTH — MARS MISSION

    A. Ideal Variable Ejection Operations

         In our consideration of the Earth — Mars mission we use the parameters for the DFD thruster given in Table II. As it was shown by the authors in a previous paper [36], a thruster with such a high specific impulse and low specific mass must operate in a continuous thrust mode. A first study of an Earth-Mars transfer was performed assuming that it can operate in an optimal (unlimited) Variable Ejection Velocity (VEV) conditions. The study was performed using the IRMA 7.1 computer code with the following data: launch opportunity: 2037; specific mass α = 1:25 kg/kW; overall effciency η = 0:56; tankage factor ktank = 0:10; height of circular starting LEO: 600 km; height of circular arrival LMO: 300 km. The optimal trajectory for a 120 days Earth-Mars journey starts 66.6 days before opposition, spends 8.4 days spiraling about Earth, 105.8 days in interplanetary space and finally 8.4 days spiraling about Mars to reach the final LMO. The mass breakdown and the jet power are reported in Table III, second column. Notice that the ratio between the installed power and the vehicle mass is of the order of magnitude of that of a modern small car, showing that traveling fast in the solar system does not require enormous amounts of power!

         The optimum specific impulse is shown in Fig. 1. The specific impulse ranges between 1,790 s at start and 60,250 s at midcourse, which is 60 days after starting.

    B. Limited Variable Ejection Velocity operations

         The minimum and the maximum values of the specific impulse are certainly beyond the possibilities of the thruster, so the computation was repeated limiting the specific impulse between 9,900 and 12,000 s. In this case the optimal strategy is increasing the duration of the planetocentric phases (the specific impulse is higher than the optimal one in these phases, and keeping their duration at the optimal value of the unlimited case would result in an unacceptable increase of the jet power) and introducing a coast arc at the interplanetary mid course, introducing a bang-bang regulation of the thruster.

         The orbit-to-orbit bacon plot is reported in Fig. 2: at equal transfer time the payload mass fraction is slightly lower and thus to maintain the same payload fraction a slightly longer travel time has to be accepted.

         A slightly longer transfer time, tt = 123 days, is chosen. The trajectory starts 71.9 days before opposition. The mass breakdown and the jet power are reported in Table III, third column. The trajectory is shown in Fig. 3, while the time histories of the acceleration, the ejection velocity, the thrust and the power of the jet are shown in Fig. 4

         The limitation of the minimum exhaust velocity reduces the propellant consumption but causes an increase of the installed power and thus of the mass of the thruster. The overall result is a decrease of the payload mass at equal total journey time.

    TABLE III: Timing and mass breakdown of the missions studied in the present paper.
    DestinationMarsPsyche
    TypeUnlimitedLimited fastLimited cargo
    td (days)66.671.9189.9120
    tt (days)120123350250
    t1 (days)8.420.694.527.6
    t2 (days)105.896.0219.2222.3
    t3 (days)5.86.436.30.1
    (ml + ms)/mi0.2540.2580.7150.241
    mp/mi0.5250.3190.1780.416
    mt/mi0.1690.3910.0890.169
    mtank/mi0.0520.03190.0180.042
    Pjet/mi (W/kg)75.62175.3540.09134.60

    C. Slow cargo spacecraft

         A slow cargo ship able to carry to Mars large payloads in an inexpensive way can also be built with this technology. Assuming a travel time of almost one year (namely 350 days) and starting from Earth orbit about 190 days before the opposition, the results reported in in Table III, fourth column are obtained. The payload and structures mass fraction is quite high, above 70% (namely 0.715), which means that using a single superheavy launcher able to carry 130 t in LEO, a cargo of about 93 t (minus the structural mass) can be carried into LMO.

         Also the power of the jet is quite small, of about 40 W/kg (referred to the IMLEO).


    IV. MISSION TO 16 PSYCHE ASTEROID

         Asteroid 16 Psyche, which belongs to the asteroid belt, is a metal asteroid extremely rich in nickel and iron, but also in gold. NASA plans a mission to survey this asteroid which should be launched in August of 2022, and arrive at the asteroid in early 2026, following a Mars gravity assist in 2023. The asteroid has a mass of 1.7×1019 kg and an average diameter of 226 km.

         Using the DFD thruster here described a mission to the same asteroid can be performed in a quite short time: for instance, using the launch opportunity of 2037 (the opposition is on March 4, 2037) and starting 120 days before the opposition, a mission lasting only 220 days can be performed. This figure must be compared with the roughly 3.5 years of the mentioned NASA proposal, based on chemical propulsion and gravity assist. The mass breakdown and the jet power are reported in Table III, last column.

         The payload and structure fraction is quite high (0.241) and the travel time is low enough to imagine even a human mission to a metal asteroid of the main belt like 16 Psyche — since the planetocentric part of the trajectory lasts almost one month, a human mission in which the astronauts reach the spacecraft at the exit from the earth sphere of influence would last about 225 days, roughly like most of the human Mars missions presently planned.


    V. CONCLUSIONS

         From the study here performed it is clear that the development of a nuclear fusion rocket engine based on the D-3He technology will allow to travel in the solar system with an ease never before attained, opening almost 'science fiction' possibilities to humankind.

         One way travels to Mars in slightly more than 100 days become possible and also journeys to the asteroid belt in about 250 days After the return to Earth orbit the spacecraft can be refitted and refurbished to make another travel in the following launch opportunity: a sort of commuting Earth-Mars service aimed at the colonization of the red planet. A spacecraft able to carry 30 t in 120 days or 85 t in 350 days to Mars may be launched from the Earth surface with a single superheavy-lift launcher (slightly bigger than the Saturn 5 or the Energia). A cargo ship able to carry to LMO the propellant required for the return journey and much cargo is also possible.

         However, the performance of such devices is still hypothetical and the value of its specific mass here assumed is conservative also taking in mind that this technology has very ample margins for improvements — as an alternative to chemical propulsion which has already reached the limits of this technology. If a lower value of the specific mass (a higher value of the specific impulse) will prove to be feasible, even faster interplanetary spacecraft could become possible.

         The spacecraft described in the present paper still require much research and development, but it is possible that they become feasible in less than two or three decades (the launch opportunity here studied is that of 2037, — 17 years from now), which is a fairly favorable one for Mars, while, on the contrary is not a very good one for 16 Psyche however with such powerful spacecraft the difference between a 'good' and a 'bad' launch opportunity is smaller than when using chemical propulsion.

         If a DFD could be made available in time for the first human Mars missions — as the launch opportunity here chosen implicitly implies —, the latter would become much easier, safer and affordable than what is today thought. These results show that the development of this technology should be given a high priority by space agencies and public and private research centers.

         Today chemical propulsion technologies are available to make a Mars mission possible and the foun- dation of fusion propulsion is already being built. However, it could be a fusion-powered spacecraft that ferries us to Mars in foreseeable future. We should believe that by mid-21st century, trips to Mars may become as routine as trips to the International Space Station today due to achievements in developments of fusion-powered thrusters.


    VI. REFERENCES

    (ed note: see original document)


    From Achieving the required mobility in the solar system through Direct Fusion Drive
    by Giancarlo Genta and Roman Ya. Kezerashvili (2020)
    Flow-Stabilized Z-Pinch
    Flow-Stabilized Z-Pinch
    Sample Thrusters
    ParamD-He3
    fuel
    p-B11
    fuel
    Pinch Length10 m50 m
    Temp80 keV100 keV
    Current5 MA10 MA
    Input Power1.8×1012W8.4×1012W
    Fusion Power3.3×1012W9.9×1012W
    Mass Flow0.095 kg/s0.53 kg/s
    Exhaust Velocity3.5×106 m/s1.3×106 m/s
    Specific Impulse356,800 sec132,500 sec
    Thrust3.3×105 N6.8×105 N

    This is from Advanced Space Propulsion Based on the Flow-Stabilized Z-Pinch Fusion Concept (2006) and Sustained neutron production from a sheared-flow stabilized Z-pinch (2019)

    I'm not sure I believe these numbers, they are getting close to being a torchship. Not quite, the Saturn V first stage puts out a hundred times more thrust. Having said that, the Robert Werka FFRE engine has a comparable exhaust velocity of 5.2×106 m/s but its thrust is a pathetic 43 Newtons. Not kilo-Newtons, just Newtons. The Flow-Stabilized Z-Pinch cranks out 7,700 times as much thrust.

    Remember: zeta-pinch or z-pinch works by taking a stream of plasma and sending a bolt of electricity down the center axis. The Lorentz force crushes the plasma toward the center axis. If the plasma is made of fusion fuel and the crush is sufficiently strong, the fuel undergoes nuclear fusion. If the reaction chamber is a linear tube (instead of a torus as is sometimes used), you just have to have one end open and capped with a magnetic nozzle to make a fusion rocket engine.

    The trouble is that the plasma is wildly unstable, with several gross disruption modes. Blasted thing squirms at high velocity like an angry snake being stepped on. Specifically it writhes so fast that only miniscule fraction of the fuel gets a chance to undergo fusion. Once the plasma stream bends enough to hit the chamber walls the electricity shorts out, the electrical current is no longer down the plasma axis, and the Lorentz force vanishes. No more fusion.

    But in 2006 researchers at the University of Washington figured out how to stabilize the plasma stream using what is known in fluid dynamics as sheared axial flow. And in 2019 other researchers at UWash working with sheared flow managed to stablize a z-pinch reaction for five thousand times longer (16 μs) than an unstablized z-pinch. A neutron signature of nuclear fusion was detected for 5 μs, which was also five thousand times longer than an unstablized z-pinch can manage.


    Flow-Stabilized Z-Pinch Fusion Space Thruster

    To utilize sheared axial flow stabilization, you need some flow. Since most rocket engines make the propellant flow as their basic operating principle, sheared axial flow fits in like a hand in a glove. The plasma flow undergoes nuclear fusion, releasing far more energy than any mere chemical reaction can manage. All you need to do is make the far end of the reaction chamber open to act as a rocket nozzle.

    Since no external magnetic fields are required to confine the plasma, massive magnetic coils can be dispensed with. Which is a good thing, those heavy coils really cut into the payload mass. Z-pinch fusion rockets are typically much lower in mass than conventional magnetic-confinement fusion engines, which vastly improves their specific power rating.

    In the diagram above, fusion fuel is injected at left at velocity V. Electrical current leaves inner electrode, travels through the axis of the fuel flow, and leaves fuel at flared end of outer electrode (nozzle at right side). The axial current in fuel creates the Lorentz force (mag field) which pinches the fuel flow. The pinch causes the fuel to undergo thermonuclear fusion. This accelerates the fusion reaction products to velocity Ve (which is a heck of a lot faster than a chemical reaction can do). The products exit the nozzle, creating thrust.

    The outer electrode exit end is flared. This is to give the fusion reaction products a chance to cool down from star-core-hot temperatures. Otherwise the heat would vaporize the electrode and void the rocket engine's warranty.

    A small amount of the hot fusion products are bleed off the other end of the engine. They enter the direct energy converter, creating electrical power. This harvesting of energy is common with many fusion propulsion designs, since fusion engines tend to be power hogs. Some kind of alternate electrical power is used as a "pilot light" to start things off.

    In the Sample Thruster table, the power needed for the axial current is listed under "Input Power".

    The electrical power can be used in the axial current, to supply power to the spacecraft's habitat module, and/or to energize a magnetic nozzle. Such a nozzle can improve the conversion of fusing product thermal power into thrust.

    As with most fusion engines cold propellant can be injected in order to shift gears (raise the thrust at the cost of lowering the exhaust velocity/specific impulse).

    The Sample Thruster table shows two thrusters. Both were optimized for the fusion fuels they utilize. The equations used can be found in the first report, they are rather involved.

    Magnetio Inertial Confinement

    Magnetio Inertial Fusion is in the Pulse section.

    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.

    Breeder Fusion Engine

    This is from Maximizing Specific Energy By Breeding Deuterium (2019)

    Deuterium-Deuterium fusion is sort of the red-headed stepchild of fusion reactions. All the other reactions are easier to ignite (with the exception of hydrogen-boron) and produce more energy.

    In the following, "MeV" stand for Mega Electron-Volt. 1 MeV equals 1,000,000 electron-volts. Nuclear physicists use MeV a lot because it is a convenient size.

    Back in the 1970's researchers were taking a second look at D-D fusion. When you fuse two deuterons together, there are two fusion chains it can follow. One produces energy (4.0 MeV) plus one tritium nuclei and one hydrogen nuclei. The second chain produces energy (3.3 MeV) plus one helium-3 nuclei and one neutron. Hey, waitaminute! If you have some spare deuterium, the reaction products have the makings for the Deuterium-Tritium reaction and the Deuterium-Helium-3 reaction.

    So you fuse some deuterium, then send the reaction products into a second chamber with more deuterium and fuse that. Three deuterons are consumed. The end result is 21.6 MeV of energy; plus one Helium-4 nuclei (an alpha particle), one hydrogen nuclei, and one neutron. This is called the Catalyzed D-D fuel cycle and it is much better than the ordinary D-D reaction.


    In the paper, the author noted that the catalyzed reaction is still wasting energy on producing deadly neutrons. The neutrons produce zero thrust, and can damage the engine (and crew) three different ways. What if the hydrogen and neutrons (hydrogen from either the reaction products or extra carried on-board) were used to breed the hydrogen into more deuterium?

    All you have to do is surround the reaction chamber with a blanket of liquid hydrogen (inside a hollow-walled shell), let the neutron transmute hydrogen atoms into deuterium atoms, then skim out the deuterium (using the Girdler Sulfide process). The fresh deuterium can be sent back into the reaction chamber. The new fuel cycle is two deuterons are consumed. The end result is 23.8 MeV of energy, plus one Helium-4 nuclei. The paper calls this the Catalyzed D-D+D fuel cycle.

    Fusion Specific Energies
    Fuel CycleSpecific
    Energy
    Specific
    Momentum
    Catalyzed D-D+D
    breed reaction hydrogen
    6.0 MeV/AMUOpt 1: 11.3% c
    Opt 2: 4.4% c
    Opt 3: 7.2% c
    Catalyzed D-D+D
    breed carried hydrogen
    6.0 MeV/AMUOpt 4: 6.1% c
    Catalyzed D-D+D
    breed scooped hydrogen
    6.0 MeV/AMUOpt 5: 7.6% c
    Opt 6: 8.9% c
    D-3He3.7 MeV/AMU7.1% c
    Catalyzed D-D3.6 MeV/AMUOpt 0: 5.6% c
    D-T3.5 MeV/AMU
    D-T w/ T breeding2.8 MeV/AMU
    D-D0.9 MeV/AMU
    p-B-110.7 MeV/AMU

    The above table compares the specific energies of various fusion reaction cycles. That is, how much energy are they getting out of each atom? 1 AMU is more or less the mass of a hydrogen ion, MeV is how nuclear physicists like to measure nuclear energy.

    • p-B-11 is boron fusion, the only reason it's on the list is because the reaction produces no deadly neutrons. Specific energy wise it is the bottom of the list
    • D-D is the red-headed stepchild, barely above boron fusion in specific energy
    • D-T is next best specific energy. The only reason D-T w/ T breeding is on the list is because tritium rapidly decays in the fuel tanks and has to be restored
    • Catalyzed D-D makes the former red-headed stepchild even better than D-T in specific energy
    • D-3He was specific energy top-dog of the reasonable fusion engine fuels, the main problem is it's hard to manufacture and as far as we know is only found naturally in worthwhile amounts within gas giant atmospheres.
    • Catalyzed D-D+D turns Catalyzed D-D into the new specific energy top dog.

    The report is quick to note that the specific energy of a reaction is only one of many criteria to be considered when designing an engine.


    Engine Designs

    The report notes that "specific energy" is the mass of the fuel divided by the energy released. "Specific momentum" is the momentum of the exhausted particles divided by the mass of the input particles, so it is close to what we call the "exhaust velocity".

    The point is that a high specific momentum is important for pure fusion engines, while a high specific energy is important for afterburner fusion engines.

    Without deuterium breeding, the D-3He looks like it has a great specific energy and great specific momentum. And since all the reaction products are charged particles, they can be efficiently redirected to provide thrust. With Catalyzed D-D+D things are not so clear-cut. Some analysis is needed.


    OPTION 0: First they looked at the old-fashioned Catalyzed D-D fuel cycle, the one without the "+D" and no deuterium breeding. The full fuel cycle is:

    6 2H ⇒ 4He (3.5 MeV) + 1H (3.02 MeV) + 1n (14.1 MeV) + 4He (3.6 MeV) + 1H (14.7 MeV) + 1n (2.45 MeV) + 1.83 MeV

    • 1H = hydrogen
    • 2H = deuterium
    • 3H = tritium
    • 3He = helium-3
    • 4He = ordinary helium
    • 1n = neutron

    The kinetic energy of each particle is in parenthesis, and the energy carred by intermediate products which remain on-board are in the last term (1.83 MeV).

    This shows that fully 38% of the total energy is wastfully stolen by neutrons and cannot be used for thrust. Well, actually you can place a hemispherical neutron absorber shield ahead of the fusion reaction chamber. This will allow about 1/4 of the neutron energy to be used as thrust. This means only 28.5% of the total energy is wasted by neutrons.

    In addition, the energy in the tritium and helium-3 ions is wasted, because they have to be halted and sent to the secondary reaction chamber for further fusion. That wastes another 4% of the total energy.

    Bottom line is that Catalyzed D-D fuel cycle has a specific momentum of 5.6% c.


    OPTION 1: Adding the full coverage hydrogen blanket converts this into the Catalyzed D-D+D fuel cycle, the one with the "+D" and with deuterium breeding. The theoretical maximum is a specific momentum of 11.3% c. In practice it will be almost impossible to take all the 23.8 MeV of reaction energy and transfer it into accelerating the helium-4 ions. Especially since so much of the energy is in the form of rapidly moving neutrons.


    OPTION 2: With reaction hydrogen retained in order to breed more deuterium, the fuel cycle is:

    4 2H ⇒ 4He (3.5 MeV) + 4He (3.6 MeV) + 40.5 MeV

    Even assuming that the helium-4 is exhausted perfectally, the specific momentum is only 4.4% c. This is because the hydrogen produced in the fusion reaction has lots of momentum, all of which is lost when the hydrogen is halted and fed into the breeding blanket.


    OPTION 3: The fact remains that all Catalyzed D-D+D fuel cycles have 6.0 MeV/AMU, which is a heck of a lot. Compared to the others, this is tremendous amount of energy. Yes, braking to a halt the hydrogen loses about 20 MeV of momentum, but the braking process can convert the momentum into electricity. This can be used in an ion acceleration stage at the exhaust nozzle to add more speed to the helium-4 ions.

    IF the efficiency of transfering the 18 MeV to the helium-4 had an overall efficiency of just 30%, the 20 MeV would become about 6 MeV of acceleration. That would boost the helium-4 ions from 3.5 MeV to 9.5 MeV, resulting in a specific momentum of 7.2% c.


    OPTION 4: If you are not going to use an ion acceleration stage, the better option is to not halt the hydrogen reaction product. Let it contribute to the thrust in the exhaust. The drawback is the spacecraft will have to carry a tank of extra hydrogen for the breeding blanket.

    With reaction hydrogen jettisoned in exhaust, and extra hydrogen carried to breed deuterium:

    4 2H + 21H ⇒ 4He (3.5 MeV) + 1H (3.02 MeV) + 4He (3.6 MeV) + 1H (14.7 MeV) + 22.8 MeV

    This will give a specific momentum of 6.1% c. Better than standard Catalyzed D-D, but not as good as D-3He.


    OPTION 5: For some extreme speculation, use Option 4 but instead of carrying an onboard tank of hydrogen, give it a Bussard Ramscoop. That will let it scoop hydrogen out of the interstellar medium. This will raise the specific momentum from 6.1% to 7.6% c.

    The good news is that 22.8 MeV of on-board energy can energize a good-sized ramscoop. Which is a relief since such scoops are power hogs. Also Ramjets were thought to only be useful with impossible-to-do proton-proton fusion. But a Catalyzed D-D+D can make do with much easier D-D fusion.

    The bad news is that Bussards have some problems. Ramjets have a minimum speed to be effective at scooping, somewhere between 1% to 6% c. And the drag of the scoop will give the ship a terminal velocity equal to the exhaust velocity, which kind of negates the advantage of avoiding an on-baord hydrogen tank. On the other hand, this will work marvelously during the deceleration phase. There the drag will be to your advantage.


    OPTION 6: If you really want to go all-out, take the ramscooping Option 5, but take some of the energy away from the scoop and use it for an ion accelerator stage. Again with an overall efficiency of 30% you could boost the specific momentum up to 8.9% c.

    Nuclear Magnetic Spin Alignment

    This is an unobtainium 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

    Matter Beam's Analysis

    THE EXPANSE'S EPSTEIN DRIVE

          We aim to take a fictional propulsion technology from The Expanse, and apply the appropriate science to explain its features in a realistic manner.

         This also applies to other SciFi settings that want a similar engine for their own spacecraft. The Epstein Drive

         Title art is from here.

         Central to the setting of The Expanse is a very powerful fusion-powered engine that allows spacecraft to rocket from one end of the Solar System to the other quickly and cheaply.

         It reduces interplanetary trips to days or weeks, allows small shuttles to land and take off from large planets multiple times and accelerate at multiple g’s for extended amounts of time.

         Such a propulsion system is known as a ‘torch drive’: huge thrust, incredible exhaust velocity and immense power inside a small package.

         Fusion energy can certainly provide these capabilities. Using fuels like Deuterium provides over 90 TeraJoules of energy per kilogram consumed. Proton fusion, the sort which powers our Sun, could release 644 TJ/kg if we could ever get it to work.

         The Epstein Drive (art Gautam Singh) is described in The Expanse as a breakthrough in fusion propulsion technology. A short story provides some details. A small spaceship equipped with this engine could reach 5% of the speed of light in 37 hours, averaging over 11g’s of acceleration. A magnetic bottle is mentioned. Since we don’t know the mass of the vehicle or what percentage of it was propellant, we can’t work many useful details.

         The main book series and the TV show focus on the adventures of the Rocinante and its crew. We know that it uses laser-ignited fusion reactions and water as propellant. Again, we don’t have a mass or propellant fraction, so we cannot get definitive performance figures. However, we have detailed images of its interior and exterior. Note that there are no radiator fins or any heat management system visible.

         The cross-section also reveals that there is very little room for propellant. Despite this, it can accelerate at over 12g’s and has reached velocities of 1800km/s while averaging 5g. Presuming that it can slow down again and jet off to another destination, this implies a total deltaV on the order of 4000km/s, which is 1.33% of the speed of light.

         Official figures for the masses of spacecraft from The Expanse do exist. In collaboration with the TV show’s production team, SpaceDock created a series of videos featuring ships such as the Donnager-class Battleship for which a mass of 250,000 tons is provided.

         Using the battleship’s dimensions, we obtain an average density of about 20 to 40 kg/m^3. For comparison, the ISS has a density of 458 kg/m^3. We will use this average density for now, but you can read the Scaling section below to understand how different mass assumptions for the Rocinante don't 'break' our workings so far. 

         Applying the battleship density to the Rocinante's size gives us a mass of about 130 to 260 tons. It is likely to change a lot depending on what the ship is loaded with, seeing as it is almost entirely made up of empty volumes. We’ll use a 250 tons figure for an empty Rocinante and add propellant to it as needed.

         Let’s put all these numbers together.

         The Epstein drive technology allows for >250 ton spacecraft to accelerate for several hours at 5g with bursts of up to 12g, achieving a deltaV of 4000km/s, while not having any radiators and a tiny propellant fraction.

         Can we design a realistic engine that can meet these requirements?

    The Heat Problem

         The biggest problem we face is heat.

         No engine is perfectly efficient. They generate waste heat. Some sources of waste heat are physically unavoidable, however performant the machinery becomes.

         Fusion reactions result in three types of energy: charged kinetic, neutron kinetic and electromagnetic.

         Charged kinetic energy is the energy of the charged particles released from a fusion reaction. For a proton-Boron reaction, it is the energy of the charged Helium ions (alpha particles) that come zipping out at 4.5% of the speed of light.

         We want as much of the fusion reaction to end up in this form. Charged particles can be redirected out of a nozzle with magnetic fields, which produces thrust, or slowed down in a magnetohydrodynamic generator to produce electricity. With superconducting magnets, the process of handling and using charged kinetic energy can be made extremely efficient and generate practically no heat.

         Neutron kinetic energy is undesirable. It comes in the form of neutrons. For deuterium-tritium fusion, this represents 80% of the fusion output. We cannot handle these particles remotely as they have no charge, so we must use physical means. Neutron shields are the solution; the downside is that by absorbing neutrons they convert their all of their energy into heat. This is a problem because materials have maximum temperatures and we cannot really use radiator fins to remove the heat being absorbed.

         Electromagnetic radiation is another unavoidable source of heat. Mirrors can reflect a lot of infrared, visual and even ultraviolet wavelengths. However, fusion reactions happen at such a high temperature that the majority of the electromagnetic radiation is in the form of X-rays. These very short wavelengths cannot be reflected by any material, and so they must also be absorbed.

         With this information, we can add the following requirements:

    • We must maximize energy being released as charged particles.
    • We must minimize heat from neutron kinetic and electromagnetic energy.

         Thankfully, there is a fusion reaction that meets these requirements.

    Diagram from here

         Helium-3 and Deuterium react to form charged Helium-4 and proton particles. Some neutrons are released by Deuterium-Deuterium side reactions, but by optimizing the reaction temperature, this can be reduced to 4% of the total output. An excess of Helium-3 compared to Deuterium helps reduce the portion of energy wasted as neutrons down to 1%. Another 16% of the fusion energy becomes X-rays. Other ‘cleaner’ source of fusion energy exists, using fuels such as Boron, but they cannot be ignited using a laser.

         An optimized Deuterium and Helium-3 reaction therefore releases 1 Watt of undesirable energy (which becomes waste heat if absorbed) for every 4 Watts of useful energy.

         If this reaction takes place inside a spaceship, then all of the undesirable energy must be turned into heat. However, if it is done outside the spaceship, then we can get away with only absorbing a fraction of them. It's the idea behind nuclear pulsed propulsion. 

         How else do we reduce the potential heat a spaceship has to absorb?

         Distance.

         A fusion reaction produces a sphere of very hot plasma emitting neutrons and X-rays in all directions. A spaceship sitting near the reaction would eclipse most of these directions and end up absorbing up to half of all this undesirable output.

         If the fusion reaction takes place further away, less of the undesirable output reaches the spaceship and more of it escapes into space.

         It is therefore a good design choice to place the fusion reaction as far away as possible. However, we are limited by magnetic field strength.

         The useful portion of the fusion output, which is the kinetic energy of the charged particles, is handled by magnetic fields to turn it into thrust. Magnetic fields quickly lose strength with distance. In fact, any magnetic field is 8 times weaker if distance is merely doubled. 10 times further away means a field a 1000 times weaker. If we place the fusion reaction too far away from the source of these magnetic fields, then the useful fusion products cannot be converted into thrust.

         We could calculate exactly how far the fusion reaction could take place from the spaceship while still being handled by magnetic fields, but whether you use magnetic beta (magnetic pressure vs plasma pressure) or the ion gyroradius (turning radius for fusion products inside a magnetic field), it is clear that kilometres are possible with less than 1 Tesla. For a setting with the Expanse’s implied technology level, generating such field strengths is easy.

         What does this all mean for a fusion engine?

         If we can generate a magnetic field strong enough to deflect fusion particles at a considerable distance, then we can convert a large fraction of the fusion output into thrust while only a small fraction of harmful energies reaches the spaceship.

         The Rocinante is about 12 meters wide. If we describe it as a square, it has a cross-section of about 144m^2. A fusion reaction taking place 20 meters away from the spaceship would have spread its undesirable energies (neutrons and X-rays) over a spherical surface area of 5027m^2 by the time they reach the Rocinante. This means that 144/5027= 2.86% of the fusion reaction’s energy is actually intercepted by the spaceship.

         Increase this distance to 200 meters and now only 0.0286% of the fusion reaction’s harmful output reaches the spaceship. A much more powerful fusion output is possible.

         Finally, we need a heatshield.

    NASA heatshield materials test.

         Despite only a portion of the fusion output being released as neutrons and X-rays, and a small fraction of even that becoming radiation that actually reaches the spaceship, it can be enough to melt the ship.

         We therefore need a final barrier between the fusion reaction and the rest of the spaceship. A heatshield is the solution.

         This heatshield needs to enter into a state where it balances incoming and outgoing energy. With no active cooling available, no heatsinks or external fins, the heatshield has to become its own radiator.

         The Stefan-Boltzmann law says that a surface can reach the state described above at its equilibrium temperature. It can be assumed that emissivity is high enough to not matter (over 0.9).

         Equilibrium temperature = (Incoming heat intensity/ (5.67e-8))^0.25

    Equilibrium temperature is in Kelvin.
    The heat intensity is in Watts per square meter (or W/m^2)

         Using this equation, we can work out that an object sitting under direct sunlight in space (at 1 AU from the Sun, so receiving 1361 W/m^2) would have an equilibrium temperature of 393 Kelvin.

         A concentrating mirror focusing sunlight to 1000x intensity (to 1.36 MW/m^2) would heat up an object to the point where radiates heat away at a temperature of 2213K.

         For a fusion-powered spaceship, you want this temperature to be as high as possible. Higher temperatures means that the incoming heat intensity can be greater, which in turn means that the spaceship can shield itself from more powerful fusion outputs.

         Tungsten, for example, can happily reach a temperature of 3200K and survive a beating from 5.95MW/m^2.

         Graphite can handle 3800K before it starts being eroded very quickly. That’s equivalent to 11.8MW/m^2.

         Tantalum Hafnium Carbide is the current record holder at 4150K. Keep it below its melting temperature at 4000K, and we would see it absorb 14.5MW/m^2. Scientists have also simulated materials which could reach over 4400K before they melt.

         This heatshield needs to rest on good insulation so that it doesn’t conduct heat into the spaceship. A design similar to the Parker Solar Probe’s heatshield mounting can be used. Low thermal conductivity mountings and low emissivity foil can reduce heat transfer to a trickle.

    Proposed design

         Let’s talk specifics.

         We will describe now a fusion-powered rocket engine design that can perform most similarly to the Expanse’s Epstein Drive as shown on the Rocinante.

    VISTA

         It is based on this refinement to the VISTA fusion propulsion design. Like the VISTA design, a laser is used to ignite a fusion fuel pellet at a certain distance from the ship and a magnetic coil redirects the fusion products into thrust. The rear face of the spaceship takes the full brunt of the unwanted energies and re-emits them as blackbody thermal radiation.

         The refinement consists of a shaped fusion charge that can be ignited by laser slamming a portion of the fusion fuel at high velocity into a collapsing sphere, raising temperatures and pressures up to ignition levels.

         Instead of the fusion products being released in all directions, a jet of plasma is directed straight at the spaceship. This increases thrust efficiency up to 75%, as the paper cites.

    Somewhat similar magnetic nozzle configuration from this MICF design

         Meanwhile, the X-rays and neutrons escape the plasma in all directions.

         The Epstein Drive is assumed to be a version of this. Instead of a spherical firing squad of lasers (as can be found in the NIF facility) that requires lasers to be redirected sideways with mirrors, a single laser is used for ignition. It is less effective but it means we can dispense with mirrors hanging in space. 

         We will also be using Deuterium and Helium-3 fuels instead of Deuterium and Tritium. They are harder to ignite, but give much more useful energy (79% comes out as charged particles). By adjusting the fusion temperature and ratio of Helium-3 to Deuterium, we can increase this output to become 83% useful while neutrons fall to 1% of the output and X-rays represent 16%.

         Also, using powerful magnetic coils, we will be igniting the fusion pellets at a much greater distance from the physical structures of the engine. We can take the 'nozzle' to actually be a mounting for the magnetic coil and everything with a line of sight to the fusion reaction to be covered in a heatshield. More importantly, the engine will be much, much smaller than the 120m diameter of the VISTA design.

         The Rocinante has a cross-section area of 144m^2. Its heatshield will be a black metal carbide that can reach an equilbirium temperature of 4000K. It is separated from the hull with insulating brackets that massively reduce the heat being conducted to the 300K interior.

         The heatshield needs to be thick enough to fully absorb X-rays and neutrons from the fusion reaction (it might be supplemented by boron carbide in cooler <3000K sections).

         At 4000K, the heatshield can handle 14.5MW/m^2. The rear of the Rocinante can therefore absorb 2.09GW of heat.

         The magnetic field acts on a fusion reaction 300m away from the hull. It acts like a spring; it requires no energy input to absorb the kinetic energy of the charged fusion reaction products and transmit it to the spaceship. Using figures from the cited paper, thrust efficiency is 75%.

         Thanks to this arrangement, only 0.0127% of the unwanted energies from the fusion reaction are intercepted and absorbed as waste heat by the heatshield.

         Some of the heat can be converted into electricity and used to power the laser igniting the fusion reactions. The generator can be of the superconducting magnetohydrodynamic type, and the laser could be cryogenically cooled. This makes them both extremely efficient. The electrical power that needs to be generated to run the laser can be very small if the fusion gain is extreme (small ignition, big fusion output).

         Putting these percentages so far together, 0.00216% of the fusion reaction energy ends up as heat in the heatshield.

         Using that percentage, it is now evident that we have a very large ‘multiplier’ to play with. For every watt that the heatshield can survive, 46,300 watts of fusion output can be produced.

         A heatshield absorbing 2.09 GW of heat means that its Epstein drive can have an output of 96.8 TW. About 2.2kg of fuel is consumed per second.

         83% of that fusion power is in the form of useful charged particles, and the magnetic field turns 75% of those into thrust. So, 41.5% of the fusion power becomes thrust power; which is 60.25 TW.

         The effective exhaust velocity of a Deuterium-Helium3 reaction can be as high as 8.9% of the speed of light. This assumes 100% burnup of the fusion fuel. Because we are using an excess of Helium-3, this might be reduced to 6.3% of the speed of light.

         With this exhaust velocity, we get a thrust of 6.37 MegaNewtons.

         An empty 250 ton Rocinante would accelerate at 2.6g with this thrust.

         We know it can accelerate harder than that but it cannot handle any more fusion power. So, it must increase its thrust by injecting water alongside fuel into its exhaust.

         There is a linear relationship between exhaust velocity and thrust at the same power level, but a square relationship between thrust and mass flow.

         Halving the exhaust velocity doubles the thrust but quadruples the mass flow rate. The Rocinante can have a ‘cruise’ mode where only fuel is consumed to maximize exhaust velocity, and a ‘boost’ mode where more and more water can be added to the exhaust to increase thrust.

         It is useful to know this, as we must now work out just how much fuel (Deuterium and Helium-3) and extra propellant (water) it needs.

         1800km/s is done in the ‘boost’ mode, and then 2200km/s in the ‘cruise’ mode, for a total of 4000km/s. How much fuel and propellant does it need?

         As with any rocket equation calculation, we need to work backwards.

         Mass ratio = e^(DeltaV/Exhaust Velocity)

         An exhaust velocity of 6.3% of the speed of light and a deltaV requirement of 2200km/s means a mass ratio of 1.123.

         The 250 ton Rocinante needs to first be filled with 30.75 tons of fusion fuel. A 1:2 mix of Deuterium (205kg/m^3) and Helium-3 (59kg/m^3; it won't freeze) has an average density of 107.6kg/m^3, so this amount of fuel occupies 285m^3. It represents about 4.9% of the spaceship’s 12x12x40 m internal volume.  

         And now the ‘boost’ mode. 5g of acceleration while the spaceships gets lighter as propellant is being expended means that thrust decreases and exhaust velocity increases gradually over the course of the engine burn. The propellant load can to be solved iteratively... on a spreadsheet.

         Using 0.25 ton steps for water loaded onto the Rocinante, it can be worked out that an initial mass of 352 tons is required. This represents an additional 57 tons of water and 17.25 tons of fuel.

         The full load is therefore 57 tons of water in 57m^3, and 48 tons of fusion fuel in 446m^3. Together, they fill up 8.7% of the Rocinante’s internal volume.

         The thrust level during the acceleration to 1800km/s varies between 13.77MN and 17.27MN. It takes just over 10 hours to use up all the water.

         Boosting to 12g would require that this thrust be increased further, between 33.05MN and 41.44MN. However, it could only be sustained for 106 minutes, until 751km/s is reached.

    Official art by Ryan Dening

         In ‘cruise’ mode and with no water loaded, the Rocinante would have 3320km/s of deltaV and can cross the distance between Earth and Saturn in 10 to 12 days at any time of the year.

         At 12g, it can sprint out to a distance of 21.2 thousand kilometres in about 10 minutes, and 0.76 million kilometres in an hour.

    Scaling

         This proposed design can be easily scaled to adjust for different figures for mass, acceleration and deltaV.

         The variable will be the ignition point distance from the spaceship and therefore the magnetic field strength of the coils in the 'nozzle'. A stronger field allows for fusion products to be redirected from further away, so that an even smaller portion of the harmful energies are intercepted.

         If we assumed a ten times greater density for the Rocinante, for example, we would have an empty mass of 2500 tons. To adjust for this while maintaining the same performance, we would simply state that the fusion reaction is ignited 10^0.5: 3.16 times further away, or 948m. The 'multiplier' mentioned earlier jumps from 46,300 to 461,300, just over 10 times better than before. In other words, the fusion output can be increased 10 times and all the performance falls back in line with what was calculated so far.

    Consequences

         Beyond what we’ve seen on the show or read from the books, there could be some interesting consequences to having this sort of design.

         Visually, for example, the rear end of spaceships would glow white hot. They cannot come close to each other while under full power, as then they’d expose each other’s flanks to intense heat from the fusion reactions.

         You might have noticed from a previous diagram that a portion of the fusion plasma travels all the way up the magnetic fields without being redirected. This could be the reason why we see 'gas' in the 'nozzle'; it is simply the leaking plasma hitting a physical structure and being compression heated up to visible temperatures. 

         A failure of the magnetic fields would immediately subject the heatshield to 5x its expected heat intensity. This would quickly raise the temperature by a factor 2.23, so it would turn from solid to explosively expanding gas. Not exactly a ‘failure of the magnetic bottle’, but a similarly devastating result.

         On the other hand, the magnetic field passively provides shielding against most of the radiation that can affect space travellers. If it is strong enough to repel fusion protons, then it could easily deal with solar wind protons and other charged particles, as found in the radiation belts around Earth or Jupiter. This could be a reason why we don’t see thick blankets of radiation shielding all around the hull.

         Our proposed engine design is pulsed in nature. We want smooth acceleration, so we want as many small pulses in such quick succession that the spaceship feels a near-continuous push. This can be achieved with as few as 10 pulses per second, or hundreds if possible.

         However, even at 10 pulses per second, you need to shoot your fusion fuel from the fuel stores to the ignition point 300 meters away at a velocity of 3km/s. This can be accomplished by a railgun, and it is incidentally a good fraction of the projectile velocities used in combat.

         Could the Belters in the Expanse simple have pointed their fuel injection railguns in the opposite direction to equip themselves with their first weapons?

         Similarly, an intense laser is needed to ignite the fuel quickly enough to achieve an extreme fusion gain. Doing so from 300m away requires a short wavelength and a focusing mirror… which are also the components needed to weaponize a laser. If a laser can blast a fuel hard enough to cause it to ignite, then it could do the same to pieces of enemy spaceships, and all that is needed to extend the range is a bigger mirror. This implication can be countered by having an extreme fusion gain ratio — i.e., a 10,000,000 fold ratio between the energy input of a laser ignition system to the fusion output. That means a 100TW reaction can be ignited by just a 10MW laser, which is far less likely to be weaponized.

         There is also a claim made where the Rocinante’s fuel reserves are ‘enough for 30 years’. This cannot mean propulsion. Even at a paltry 0.1g of acceleration in ‘cruise’ mode, the Rocinante can consume all of its fuel in just 40 days. Add in a lot of drifting through space without acceleration, and we’re still looking at perhaps a year of propulsion. It is much more likely that this claim refers to running the spaceship; keeping the lights on, the life support running and the computers working. That sort of electrical demand is easily met by the energy content of fusion fuels.

         Finally, keep in mind that the propulsion technology described here is not specific to the setting of the Expanse. It respects physics and you can introduce it to any setting where real physics apply. In other words, it is a ready-made and scalable solution for having rapid travel around the Solar System without much worry about propellant, radiators, radiation shielding and other such problems!

    From THE EXPANSE'S EPSTEIN DRIVE by Matter Beam (2019)

    Pulse

    These are propulsion systems where the thrust is not delivered as a constant burn, but instead in a series of intermittent pulses.

    Note that most pulse propulsion systems can "throttle" their effective thrust by varying the pulse rate from 0 to max.

    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.


    DIRTY LITTLE SECRET

    The dirty 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 enviromentalists 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.

    • LIFT-OFF: Orion is great! Can boost huge amounts of payload into orbit. Alas, nobody is going to allow hundreds of nuclear bombs to be detonated in Terra's atmosphere.
    • ORBIT-TO-ORBIT: Orion is run-of-the-mill average. There are other propulsion systems with much better exhaust velocities.
    • LANDING: DO NOT TRY! This will destroy the spacecraft, since you will be flying into the fireball of your nuclear detonations.

    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.


    PULSE UNIT DETAILS

    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.

    Tungsten has an atomic number (Z) of 74. When the tungsten plate is vaporized, the resulting plasma jet has a relatively low velocity. 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.


    PROPELLANT

    A short digression:

    When a nuclear device explodes, 90% of the bomb energy appears as electromagnetic radiation (80% soft X-rays and 10% gamma rays). So in airless space, a nuclear weapon destroys its target by x-rays.

    However, things are different inside Terra's atmosphere, or other planet's atmo. Atmospheres are typically opaque to x-rays (as Larry Niven put it: "so much for Superman's x-ray vision"). Which means the flux of x-rays are rapidly absobed, converting room-temperature air into a raging fireball with a temperature of roughly 100,000,000° Celsius. This is called blast. The end result is that nukes detonated inside an atmosphere are much more efficient at causing widespread destruction than nukes detonated in space.

    What does this mean? Orion pulse units designed to be used inside a planet's atmosphere can get away with using much smaller kiloton yield explosion sizes than units used in the vacuum of space. The atmosphere can also act as extra propellant.

    In the early Project Orion designs each charge was to accelerate the spacecraft by about 12 m/s. So in space a 4,000 ton spacecraft would use 5 kiloton charges, and a 10,000 ton spacecraft would use 15 kiloton charges. But during blast-off inside Terra's atmosphere, they could use 0.15 kt and 0.35 kt respectively. Quite a saving on plutonium.

    In the reports they only calculated the atmospheric effects for Terra's atmosphere. Because there are very few nearby planets and moons with atmospheres that are safe for space explorers to visit. You can see the different yield sizes in the Pulse Unit Table.


    PLUTONIUM

    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.


    NEWTONS

    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.

    For details about spacecraft using Orion propulsion, go here.


    COST

    How much do each pulse unit cost? GA-5009 vol III "Nuclear Pulse Space Vehicle Study" had this to say:

    PULSE UNIT COST

          Propellant costs fo,r nuclear-propelled vehicles are typically a larger fwaction of the total direct operating cost (DOC) than are propellants for chemically propelled vehicles. Nuclear-pulse propellants provide no exception to this statement, especially for the smaller (10-m) vehicles of this study (propulsion module with 10 meter diameter pusher plate). For exploration missions using the 10-m propulsion module, the nuclear-pulse-propellant costs accounted for some 25 to 30 percent of the DOG; for orbit-launched lunar systems, the propellant accounted for 12 to 15 percent. The percentages would have been considerably higher if the DOG were not dominated by the cost of the chemical ELV, which typically accounts for some 60 to 65 percent on exploration missions and 70 to 80 percent on orbit-launched lunar missions (see Vol. II, Sec. 4, "Mission Cost Indications").

         The nuclear-pulse-propellant costs for this study, however, are considered conservative, as has been previously stated. They are based on the use of currently well-understood nuclear-explosive-device technology and thus they do not reflect any potential developments in explosive devices intended particularly for propulsion. The propellant costs used in this study do, on the other hand, reflect a considerable amount of cost reduction due to "learning. " The costs of concern here are propellant costs for the first operational vehicles, which will follow the production and use of some thousands of pulse units during development and qualification of the propulsion systems. (Current development planning estimates indicate 6,000 to 7,000 pulse units will be used, mostly in the flight qualification phase.)

         The costs per pulse unit used for this study, with a breakdown displaying the major cost components, are shown in Fig. 8.3. Cost-breakdown bars are shown for pulse units defined for propulsion modules of various effective thrusts, which cover a wide range of module sizes. It will be noted that there is very little difference in the pulse-unit costs for the first three different thrusts, and there is no difference in fissionable-material costs for these three cases. It will also be noted that the smallest cost bar represents the pulse unit for the 10-m propulsion module (FE = 3.5×106 N) and that the second-to-smallest bar is nearly large enough to represent the pulse unit for the 20-m module (FE = 16×106 N).

         There is no difference in the cost or amount of fissionable material shown for the smaller pulse units represented (for propulsion modules up to thrusts of some 28×106 N). The range of yields required of the nuclear devices (less than 1 KT to approximately 15 KT), assuming current technology devices are used, reportedly do not change the amount of fissionable material required. The amount of fissionable materials used for the three lower-cost pulse units was the cost equivalent of 2.9 kg of plutonium. The plutonium cost used was $18,000/kg (in 1963 dollars).

         For the three lower-cost pulse units shown, and again using current nuclear-device designs, it is possible to use less fissionable material and produce lower-cost pulse units, but at an increase in the nuclear-device mass. In this manner the amount and cost of the fissionable material can be reduced to the amount indicated by the dotted line shown in the three cost bars. The resulting increased mass of the pulse unit, however, causes a reduction in Isp such that the change was found uneconomical from a systems viewpoint; thus, the higher cost, but higher Isp, data were used exclusively in this study.

         The least-understood cost component in the pulse-unit breakdown is that for the nuclear-device fabrication. The implosion system of the device is understood to be complex and to require close tolerances. Its trigger and circuitry obviously need to be highly reliable. A $10,000 (1963 dollars) per unit allowance was made for fabrication, after considering, as previously mentioned, a prior production of some thousands of units during the propulsion-system development.

         The remaining cost is largely for fabrication of the pulse unit, exclusive of its nuclear device and the fissionable material therein. The materials used in the pulse unit, relative to the fissionable material at least, are relatively common and inexpensive. They were costed at from $2 to $12/kg (1963 dollars) for nonfabricated materials. Modest quantities of material were required in all but the larger pulse units, which use large masses of propellant (i.e., the slab of tungsten) and channel filler, which, in turn, cause a significant cost increment.

         The mass of the pulse units increases rapidly with increasing thrust (although somewhat less than linearly with thrust as reflected by the increasing Isp) , whereas the pulse-unit cost, as shown in Fig. 8.3, increases only slightly, and hence results in a rapidly decreasing propellant cost per kilogram of over-all propellant with increasing thrust, as shown in Fig. 8.4. The solid curve shows the nominal nuclear-pulse-propellant costs used in this study. These costs per kilogram include the mass and cost of all material expended to attain the desired impulse: coolants, ejection gases, antiablation oil, etc., as well as the pulse units. The curve then represents total propellant cost (in the vehicle-system sense) and the cost values are properly applied directly to the expended propellant mass from "rocket" mass-ratio equations. The cost values are in 1963 dollars, as are the other cost data of this study.

         The lower dotted curve of Fig. 8.4 shows the propellant unit cost currently predicted to result from a redesign of the nuclear device for propulsion purposes. It indicates a factor of 4 cost reduction for the thrust of the 10-m propulsion module and a 2.8 factor for thrusts of the 20-m module. The upper dotted curve reflects a factor of 2 cost increase over the nominal curve (presumed to be a conservative estimate of possible error in that direction). The area between the dotted curves represents a rather large area of uncertainty. The system-cost sensitivity to propellant-cost differences of this magnitude are shown in Sec. 5 of Vol. II.


    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. Nuclear detonations in space are basically a flash of x-rays, which can be shielded against. But detonations in an atmosphere means the x-rays are absorbed by the air and transformed into a nuclear fireball and a blast wave of death.

    This doesn't matter when boosting from the surface into orbit. The Orion spacecraft is accelerating, moving away from the fireball. But when landing on a planet with an atmosphere, the Orion spacecraft is decelerating, moving INTO the fireball. Kind of like a moth flying into a blast furnace.

    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. 

    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

    Orion Thrust and Isp

    For what it is worth, designs that I have seen in technical reports have specific impulses ranging from 3,354 seconds to 12,000 seconds (exhaust velocity 32,900 m/s to 12,000 m/s).

    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

    Bottom line: you can vary the Orion's thrust by varying the delay between detonations. The shorter the delay, the higher the effective thrust. Of course there is a lower limit on the delay, you have to wait for the first explosion to dissipate before initiating the second. Throwing a second pulse unit into an active nuclear explosion is just asking for a disaster.


    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 these two pages. But be prepared for some heavy math.

    ORION EFFECTIVE ISP

    SUMMARY

         There are three principal factors that control the effective specific impulse: (1) the mean propellant velocity, (2) the fraction of total propellant flow fc, which intercepts the pusher of the vehicle, and (3) a mass loss factor fm, which accounts for other mass necessarily ablated from the pusher plate of the vehicle, but which has been assumed herein to contribute little impulse to the vehicle in doing so.

         Based on the model used, the following conclusions were drawn:

    1. There is an optimum pulse energy for a given system (i. e., a given pusher diameter, and opacity of ablated pusher material) to yield a maximum specific impulse.
    2. Increasing the mean propellant velocity does not necessarily result in an increased effective specific impulse for a given system.
    3. Mean opacities of 103 square meters per kilogram or above appear necessary to approach the achievement of maximum effective specific impulses.
    4. Increasing the vehicle size (i. e., increasing pusher diameter) leads to higher values of fc but lower values of fm. The resulting effective specific impulse tends to increase if the pulse energy is kept at the optimum value.

    BASIC NUCLEAR PULSE PROPULSION CONCEPT

         A schematic diagram showing the use of externally exploded pulse units to propel a space vehicle is shown in sketch (a). A pulse unit containing fusionable material plus propellant mass is ejected into position behind the vehicle and the pulse energy triggered. The propellant mass expands. A fraction of the propellant intercepts the pusher plate of the vehicle and transfers momentum and heat to the vehicle. The heat flux causes some ablation of the pusher surface. A succession of such pulses is continued until the desired total impulse for the mission is obtained.

         In the usual chemical or electric rocket case, all the propellant mass ejected from the vehicle contributes its momentum to the vehicle; thus, the effective specific impulse (the impulse per unit weight flow) is a function only of the mean propellant velocity:

    (All symbols are defined in the appendix. )

         As is apparent in sketch (a), not all the mass ejected from the vehicle in the nuclear pulse case is effective in contributing impulse to the vehicle. For the pulse case, the effective specific impulse is

    where

    is the total impulse intercepted by the pusher. The weight of material (other than the propellant) which is lost from the vehicle per pulse and which is assumed to contribute no effective momentum to the vehicle is represented by Wa. In the analysis herein, the only such material considered is material ablated from the pusher plate. The mass loss factor is defined as

    The effective specific impulse for the pulse system can thus be expressed as

    where

         To evaluate the specific impulse for this type of system, then, one has to look at the mean propellant velocity v that the system can tolerate, the effectiveness with which the mass of the pulse can be collimated so as to intercept the pusher plate of the vehicle, and the unavoidable mass losses in the system, particularly those lost through interaction of the high velocity propellant with the pusher surface.

         The analysis that follows considers the characteristics of the expanding propellant to derive conditions affecting the interaction between the propellant and pusher surface. The principal interactions affecting the performance limitation of the system are the rate of heat transfer leading to pusher ablation, stress limits on the pusher plate material, and pulse unit design as reflected in the maximum amount of collimation that is attainable.

    SELF-SIMILAR EXPANSION

         The propellant mass will be at a high temperature and pressure condition immediately following the pulse energy release. As this material expands into the vacuum of space, some recombinations of ionized and dissociated products will occur. Eventually, through expansion, the density drops to the point where interparticle collisions are relatively unimportant, and the material continues to expand in what is called a "self-similar" manner. The characteristic relation of this type of expansion for the case herein is

    In the treatment herein, it is assumed that all the energy absorbed by the propellant mass appears finally as kinetic energy with a Maxwellian distribution about the mean velocity v:

         Also, it is assumed that the condition for collisionless expansion is reached in a relatively short distance, compared to the dimensions of the system, so that the expansion products are effectively emitting from a point source.

         The density at any location and time is given by

    From equation (8), then, the other properties readily follow:

    Mass flow rate per unit area:

    Pressure:

    Energy flow rate per unit area:

         If equation (6) is used, the various property relations obtained are as follows:


         Some plots of equations (12) to (15) are shown in figure 1 for a particular Ep/r3 value. The time scales are nondimensional in this figure, the reference time being tr = r/v. One can note, then, that the time at which the maxima in the various parameters occur (tm) is a direct function of the separation distance r. Also, the total time of pulse interaction is of the order of three times tm, so that pulse interaction time also varies directly with separation distance. This fact has a bearing on the heat-transfer effects as will be seen later.

         Consider the arrival of propellant from a pulse onto a plane normal to the main flow direction (sketch (b)). The mass flux at point (z, β) normal to the plane is

    and the pressure on the plane at that point is


    Typical radial variations of pressure and density are shown in figure 2. The impulse per unit area on the plane at (z, β) in the z-direction is

    The total impulse in the z-direction from flux within a given cone angle θ is

    But the fraction of the total mass flow which is included within a given cone angle θ is

    for isotropic distribution. Thus, considering only the propellant interception factor, the effective specific impulse of a system using a circular pusher plate to intercept the mass flow within a cone angle θ is

         If a pulse unit is designed to direct a disproportionate fraction of the total mass into a given cone angle, the flow is still assumed uniformly distributed within the cone. The parameter C (hereafter referred to as a collimation factor) is defined as the ratio of the enhanced total mass in the cone to the amount in the cone if the distribution were isotropic. It can be expressed as

    With this assumption of the flow distribution, the relations developed for the isotropic distribution may be used for collimated flow cases by replacing the propellant mass term Mp with the product C Mp .

         If the case with collimated flow is now assumed, the relation for total impulse (eq. (19)) is put in terms of pulse energy and C:

    The pressure is highest at the center of the plate (β = 0):

    At β = 0, the maximum pressure at any time is

         The effect of two factors (equivalent energy of the pulse and attainable collimation factor) involved in the design of pulse units on the attainable propellant interception factor fc can be seen by the following development. Combining equations (21)and (23) yields

    In all subsequent relations where a specific value of maximum pressure is used, a value of pm = 6.9×108 newtons per square meter (equivalent to about 100 000 psi) is used. This value represents a reasonable upper limit to the allowable yield stress of materials that might be used for the pusher. If this value is used, equation (25) becomes


         The pusher diameter required to intercept the flux in a given cone angle θ is obtained from the geometric relation (shown in sketch (c)).

    Combining equations (26) to (28) yields the relation


    With the assumption that all the propellant mass has the mean velocity v, the upper limit to fc is 0.5 in order to satisfy the momentum balance requirement. Equation (29), with the upper limit restriction of 0.5 for fc, is shown plotted in figure 3 for four values of total pulse energy, Ep = 4.18×109, 4.18×1010, 4.18×1011, 4.18×1012 joules (1, 10, 100, and 1000 ton equivalents). (For reference, 1 gram of deuterium-tritium (DT) mixture fully reacted is equivalent to about 3.344×1011joules (80 tons TNT). ) The interrelation among vehicle size (as reflected by pusher diameter), pulse energy size (Ep) and pulse unit design (as reflected by the collimation factor C) is evident.

    When the separation distance is maintained at the smallest value permitted by pressure limitations (the conditions imposed for fig. 3), one can note that there is a large improvement in the propellant interception factor fc for (1) better collimation of the propellant, (2) smaller energy pulse value for the same degree of collimation, and (3) larger size vehicles (i. e., larger pusher diameters).

    PROPELLANT-PUSHER INTERACTION

         When the flux of propellant arrives at the pusher plate, the initial, high velocity particles cause some sputtering. Some penetration into the material of the pusher also occurs. The effect of this initial bombardment is small compared to the eventual ablation caused by the arrival of the remainder of the pulse mass. The propellant that arrives is assumed to just lose its kinetic energy and form a hydrodynamic stagnation layer. The temperature of this stagnation layer is calculated by assuming that it reaches equilibrium through blackbody radiation back to the vacuum of space.

         Thus, when the energy flow rate relation (15) is used, the equilibrium can be expressed as

    or


         A plot of this relation is shown in figure 4. Stagnation temperatures up to the 20- electron-volt range are typical.

         The formation of this high temperature layer causes the temperature of a pusher surface to rise quickly to the ablation level. The ablated gas then forms a protective layer and slows down subsequent ablation rates.

         At the temperature levels of the stagnation layer of gas, heat transfer to the pusher is mainly by radiation. Therefore, a surface material whose ablated products have a high absorptance for radiation in the frequency range characteristic of the temperature of the stagnation layer would be a distinct advantage in limiting ablation amounts. This situation is similar to that encountered in the gas-core nuclear rocket.

         In order to estimate the magnitude of the heat-transfer problem, the model of the interaction process shown in sketch (d) was assumed. The ablated vapor layer and the high-temperature layer from stagnating propellant were assumed to remain unmixed. The flow of heat through the ablated vapor layer was then looked at as a combined process of radiation and conduction. It is assumed that the ablated vapor, of necessity, will be of material which has a high absorptance for radiant energy at the temperature of the stagnation layer. The one-dimensional equation describing the transfer of heat in an optically thick radiative-conductive medium with no heat source terms is

    where aR is the adsorptance of vapor layer layer.

         Numerical solutions to equation (32) may be obtained by assuming a boundary temperature history at x = 0 (given by the stagnation temperature relation (31)) and with the temperature gradient approaching zero as x becomes large. Typical temperature profiles for these solutions are shown in figure 5. The rate of advance of the temperature "front" into the ablated vapor medium is also obtained.

         The inflection point of the temperature-distance relation occurs at about the temperature level for which equal rates of heat transfer occur by both radiation and conduction modes, This condition is given approximately by

    This relation becomes

    when substituting for σ and expressing temperature in electron volt units. The temperature level of the major portion of the ablated medium is below this inflection point temperature. This observation is noted here because of its relation to the properties of the ablated layer.

         The assumption that most of the radiant energy from the stagnation layer is absorbed in a relatively small thickness of the ablated vapor leads to the temperature profiles noted in figure 5, that is, a relatively steep temperature front that propagates through the medium. The similarity here to the gas-core rocket profiles is noted. In the gas-core case, seeded gas is fed toward the advancing temperature front at such a rate as to maintain the steep temperature profile away from the wall of the rocket chamber. In the pusher case herein, ablated material is fed into the vapor state at a rate governed by the amount of heat that reaches the wall and the amount of energy required to vaporize plate material and raise it to the temperature level of the ablated medium.

         In the following calculation of the amount of pusher ablation, it is assumed that heat transfer to the surface by radiation (though only a small fraction of the total radiant energy available) is still the major mode of energy transfer. The incremental heat transfer per unit area, then, is

    The increment of mass ablated per unit area is

         Equations (35) and (36) were solved numerically for energy input using equation (30) when no ablated layer (x = 0) was present at t = 0 and when any decrease in x(t) resulting from propagation of the temperature front into the ablated medium was neglected. The calculated ablation amounts will thus be lower than actual because of this latter assumption.

    Typical total ablation per unit area values are shown in figure 6. These were calculated using a value of 5×107 joules per kilogram for Ha.

    The total ablation amount, however, is not especially sensitive to Ha as shown in figure 7. A factor of 10 change in Ha causes only a 15 to 20 percent change in the total ablation amount under the conditions of these calculations.

    Figure 8 shows the range of energy absorption that goes into just ionization and thermal energy of the species for two metal vapors, iron (Fe) and uranium (U). Sublimation energy is, of course, also included in Ha.

         The effect of separation distance on ablation rates is shown infigure 9 by a comparison of curves. As the separation distance is increased, the energy arrival rate (per unit area) decreases. However, the total interaction time increases. The net effect (fig. 9) of increasing the separation distance to four times the minimum separation distance (eq. (28)) was to decrease the total ablation by only about 32 percent at Ep = 4.18×1012 joules (1000 tons) and 38 percent at Ep = 4.18×109 joules (1 ton).

         The ablation calculations shown up to this point have been for conditions at the center of the pusher (β = 0). Away from the center (β > 0), the ablation decreases as shown in figure 10. The same countering influence of the two factors, energy intensity and interaction time, are present in the radial variation as in the separation distance variation (fig. 9). For Ep = 4.18×109 joules (1 ton), a 17 percent decrease in the ablation rate was calculated at 45° off the axis.

         Of special interest now is a calculation of the mass loss factor fm. Since the only such loss considered herein is that by means of ablation from the pusher surface, fm is given by equation (4).

         A cylindrical pusher plate of diameter d (sketch (e)) is now considered. The ratio of total ablation per pulse to propellant mass for the pusher plate of diameter d is

    The energy arrival rate at (z, β) for a pulse with collimation factor C is

    Now, let tz = z/v . Then tr = tz sec β and, using equation (16),

    At this point the calculations are restricted to values of z corresponding to the maximum pressure limitation (eq. (27)). When equation (27) is used, equation (39) becomes

    Equation (37) is transformed to

    by using the previous relations and putting the pulse energy in terms of Ep.

         The inner integral (with respect to t/tz) was solved numerically under the same assumptions as used in solving equations (35) and (36). The resulting values of the mass loss factor fm for several combinatims of variables are shown in figure 11. The curves stop at the limiting diameter where the propellant interception factor is 0.5.

         The larger the pusher diameter, the smaller is the factor fm, other factors being constant. More pusher area is exposed to ablating conditions, while pulse mass Mp remains constant. The mass ablation loss factor is lower for smaller energy pulses for the same size pusher plate. This is because the separation distance zm is lower for lower energy pulses, and the pusher intercepts a greater fraction of the total energy flux from the pulse.

         The absorption coefficient aR has a marked effect on the mass loss factor since, as was noted before (fig. 6), the total ablation amount is nearly inversely proportional to aR for the conditions of these calculations.

    SPECIFIC IMPULSE

         A simplified model of the overall processes involved in the external nuclear pulse propulsion scheme has been assumed. Only the features of the propulsion system that affect the overall or effective specific impulse have been considered. The propellant flow from the pulse energy source has been assumed to occur self-similarly from a point source. A collimation factor has been used to account for the concentration of more propellant into smaller flow cone angles than would occur simply from isotropic expansion. The hydrodynamic stagnation layer temperature is determined by the balance between incoming kinetic energy and blackbody radiation back to space. Ablation of pusher surface material occurs by radiant heat transfer from the stagnation temperature through the ablated layer. A mean opacity for the ablated layer material is assumed.

         Using this model, two principal factors determining the effective specific impulse were calculated: the propellant loss factor fc (eq. (29) and fig. 3), and the mass loss factor fm (eq. (4) and fig. 11). These two factors are combined to yield the ratio


    Some typical plots of relation (42) are shown in figure 12 for a collimation factor of 3 and aR value of 102 square meters per kilogram. It is apparent in this figure that the optimum specific impulse for smaller pusher diameters is attained with the small pulse energies. Under the conditions of figure 12 there is little or no improvement in effective specific impulse in going to higher mean propellant velocities at the smaller pulse energy levels.

    APPENDIX - SYMBOLS

    VARYING ORION THRUST
          Dear Mr. Taylor
         I am making a Project Orion mod for Kerbal Space Program.
         Some people have expressed a desire to vary the thrust of the propulsion system. From my reading of the 1960's era documents, they proposed doing this by altering the frequency of the detonations.
         This means the impulse imparted to the spacecraft per detonation is constant, but by increasing the time, the effective acceleration is reduced.
         But the ship will still get kicked by the full impulse.
         Somebody mentioned that in Larry Niven and Jerry Pournelle's novel FOOTFALL, the orion drive vessel would vary the impulse per bomb by varying the standoff distance between the bomb detonation point and the bottom of the pusher plate.
         If you have the time, I'd like your thoughts on the feasibility of that idea.
         Offhand I'd say that by increasing the standoff distance, you decrease the amount of the propellant and/or bomb blast that actually strikes the pusher plate. This would lower the impulse per bomb.
         Decreasing the standoff distance would have no effect on the amount of blast striking the pusher plate, it would all hit the plate, but just in a more concentrated area of the plate. Which would probably severely damage the plate.
         Footfall also mentions using a form of thrust vectoring by detonating the bombs off-center. This strikes me as a very bad idea. The impulse would then not be delivered co-axially with the shock absorber shafts, probably doing severe damage.

    — Winchell Chung


         From what I remember, the yield of the bombs would vary during launch from 0.1 kt at low altitude to 5-15 kt above the atmosphere I don't recall if that actually alters the thrust or not, because the extra mass swept up by the air will make a big difference. But certainly that would be one way to do it in a vacuum.

         For a carefully controlled launch, that's one thing. You'd just pre-arrange the bombs so that they're ejected in the right order. As for selecting bombs of the appropriate yield on the fly, I don't know. It seems like adding a lot of complicated moving equipment which will have to work perfectly otherwise all is lost (unless you have a Star-Trek like ability to control the yield of individual bombs electronically, on demand). But maybe that isn't so much extra crazy compared to the rest of the project.

         Altering the detonation frequency will work during a launch phase — longer intervals will mean more deceleration due to gravity. I can't see that makes any difference in an orbital environment though.

         Increasing the standoff distance seems like the best approach to me. In an orbital environment I can't immediately see any problems with this. But I don't think it works as a catch-all solution : above the atmosphere, you absolutely need the higher yield bombs to deliver a useful specific impulse. At low altitudes, you really aren't going to want to detonate a 5kt nuke anywhere nearby. A more powerful gas gun could shoot them to greater distances to lower the damage, but we're still talking about something that's effectively a WMD pointed the wrong way.

         I agree that decreasing the standoff distance doesn't help beyond the point where the pusher plate is able to absorb the majority of the plasma. The caveat is how directional the nukes are, which of course we can't know precisely. There was the Medusa concept of using a sail to catch more of the plasma, and I think the ship in Footfall had a curved plate. But it sounded to me that getting quite a tight beam wasn't that much of a problem.

         Perhaps one solution to allow variable thrust in all environments is to have two different avaiable yields for the pulse units. In vaccum, you have to use the high yield devices. For atmosphere, choose a lower yield but something that's higher than the nominal 0.1 kt that you could get away with in the denset part of the atmosphere. Compensate by varying the standoff distance and detonation interval, so that you avoid delivering the maximum impulse at ground level (which would be too high to withstand). Gradually lower the distance and reduce the interval until you're delivering the maximum impulse, then switch to the higher yield devices (if necessary, starting those with a higher than optimum standoff distance and detonation interval too). I don't have any numbers to say if this is plausible or not though.

         I also agree that off-center detonations reek of suicide. Given the massive accelerations (something like 1000g on the pusher plate) I can't see how this wouldn't end badly (I don't know for certain though, I never even tried the math on this one). I prefer the Mythbusters solution of "strap rockets onto everything" and rotating the ship in between detonations.

    (ed note: Aldo Spadoni had some thoughts about the Footfall's ship's off-center detonations)

    by Rhys Taylor (2013)

    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.

    Annoyingly this is real hard to do because the freaking magnetic pole keeps wandering around.

    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. As Jeff Zugale says: "Pretty sure that’s a rounding error when using nukes to launch 5000 tons." So this is a case of 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.

    Weaponized Orion

    Excalibur

    Lasers have long been the death-ray of choice for scifi authors, ever since they were invented in 1960.

    With lasers, the shorter the wavelength of the beam, the more damage it does to the target. So there was a push among laser weapon designers to make the laser wavelength as short as possible.

    Which is where the designers ran into a brick wall.

    You see, the "lasing medium" has to be "pumped" (i.e., energized) by flooding it with a wavelength a bit shorter than the desired beam wavelength. What's the shortest wavelength? The gamma-ray band of wavelengths. That's a little extreme, so they were willing to settle for using x-rays. So all the designers had to do was flood their lasing medium with x-rays in the short wave part of the x-ray band, and they could theoretically produce a laser beam composed of medium-wave x-rays.

    One problem: there ain't no convenient source of huge amounts of x-rays.

    The only convenient sources produced pathetic trickles of x-rays. Certainly not enough to make a weapons-grade laser beam.

    In the 1970s, a certain George Chapline Jr. was working for Edward Teller in Teller's "O-Group" at the Lawrence Livermore National Laboratory. Chapline was trying to figure out how to make an x-ray laser and was pounding his head against the wall. He was frustrated enough that he was willing to use an inconvenient source of large amounts of x-rays. But where to find them?

    Then he heard about an underground nuclear weapons test in Nevada. Used to test the effect of blasts of x-rays on ICBMs. Because nuclear explosions produce huge amounts of x-rays.

    Thus was born Project Excalibur. In orbit, arrange a number of sacrificial x-ray lasers around a nuclear warhead. Each takes aim at a different Soviet ICBM heading for an American city, then you detonate the nuke. Sure the blast vaporizes the x-ray lasers, but in the fraction of a section between the pumping with x-rays and the arrival of the blast, the x-ray lasers emit a beam that goes through the ICBMs like a white-hot knife throught butter. You can read about all the nitty-gritty details here.


    Now for a change of venue. Some time before 1985 noted science fiction authors Larry Niven and Dr. Jerry Pournelle were working on their masterpiece alien invasion novel Footfall. They needed a superweapon for the climactic final battle in the novel.

    Dr. Pournelle had some expertise in this area. In his earlier years he worked in operations research at Boeing, and had invented an amusing orbital bombardment weapon called Project Thor aka "Rods from God." You may have heard of it.

    In the novel, invading aliens conquer Terra. Us terrans can throw off the alien rule if we can somehow destroy the alien bussard ramjet starship. The only way to do it is to boost what amounts to a battleship into orbit. Quickly, or the aliens will Thor it to death. And the battleship will have to be quick and dirty, there is no time for a long drawn-out develoment period.

    Which means Project Orion. It is about as quick and as dirty as they come, but it can boost outrageous amounts of mass into orbit at high acceleration. And you don't have to spend decades trying to whittle down the mass of all the battleship components because The Crazy Nastyass Orion Just Doesn't Care.

    The protagonists in the novel don't have a lot of time, so they cannot afford to waste it on making nice efficient Orion pulse units that send 80% of the blast in a narrow cone. Instead they are just going to use off-the-shelf nuclear warheads that waste blast power in all directions.

    About this time Dr. Pournelle's eyes narrowed as he remembered Project Excalibur.

    The nukes are wasting x-rays in all directions. Why not use some of them to energize some Excalibur x-ray lasers on the side?

    Understand that this trick probably won't work with optimized Orion pulse units. They probably won't leak enough x-rays to the side for thirsty Excalibur units.

    NUKEDAR

    RADAR is an acronym for RAdio Detection And Ranging. Powerful pulses of radio band electromagnetic energy are sent out, when they hit objects the reflected radio waves detected and displayed on a screen.

    LiDAR is doing the same thing with laser pulses instead of radio pulses. Since laser light typically has a shorter wavelength than radio, the resolution is finer. Meaning you can see more of the fine detail of the object you are detecting.

    The thought occurs that Orion nuclear pulse units also emit powerful pulses of electromagnetic energy. These can be used to detect objects, such as enemy warships.

    Nuclear detonations are typically 80% soft X-rays, 10% gamma-rays, and 10% neutrons. The neutrons are probably worthless for detection since they tend to be absorbed. The x-rays and gamma-rays are more useful, or their energy can be absorbed by clouds of specific gases to change their frequency to more useful wavelengths.

    I have no idea if this would be more useful than a conventional radar or not, but in theory the shorter wavelengths will have a finer resolution. And it might have a vastly superior range compared to conventional radar. For science fiction author purposes, it sure sound impressive as all get-out.

    Note that optimized Orion pulse charges are designed so most of the energy is aimed at the ship's pusher plate. For nukedar purposes, slots may be cut in the radiation case to allow beams of x-rays to escape to be used as detection rays. If you don't give a damn about efficiency, just use a larger inefficient nuclear pulse unit with no radiation case at all. Some of the x-rays will drive the tungsten propellant into the pusher plate, the rest will make a nukedar pulse.

    Also note that the pusher plate will cast a "shadow" in the detection pulse. Meaning that it cannot see any hostile ships which are "ahead" of the Orion. Naturally if the hostile ship also uses Orion drive, you will probably be aware of its general location already. Series of nuclear explosions are a dead giveaway.

    But a more precise detection by nukedar or radar will be needed for a useful weapon targeting solution. Meaning just because you can see the enemy ship is no guarantee you can hit it with your weapons.

    Casaba Howitzer

    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.

    This is gone into in far more detail here.

    SNAK

    SNAK is a concept designed by a knowledgable person who goes by the internet handle "Kerr". SNAK is an acronym for Shaped Nuclear (Charge) Accelerated Kinetic (Vehicle)

    SNAKs are meant to augment a casaba howitzer round.

    A casaba howitzer does large amounts of damage, but due to poor collimation the effective range will be under a thousand kilometers or so. Imagine a cartridge in a firearm that was missing the bullet part. When fired, the burning gunpowder would make a jet of hot gas that would be dangerous to a person for a couple of inches past the firearm muzzle. But further than a few feet the hot gas will dissipate to the point where it will just make a person's ears ring but otherwise do no harm.

    Placing a bullet in the cartridge changes things. Now when fired, the firearm can kill you at a range a couple of thousand of meters.

    So a SNAK is a "bullet" for a casaba howitzer. The damage it inflicts will be the same regardless of range because the bullet is not expanding or otherwise dissipating. The range limit become more a question of how accurately you can target the enemy spacecraft.


    Kerr says the SNAK uses a composite sail made out of a high shear-strength material mixed with a high-temperature superconducting film. The size is determined by the mechanical stress the sail is subject to. The mass will be smaller than the casba howitzer's plasma jet so the SNAK velocity will be higher.

    The SNAK will work like an explosively formed penetrator, meaning it will initially be a wide sail but the casaba explosion will collapse the SNAK sail into a deadly dart shape. The geometry of the SNAK is determined by the requirement that it stays whole and parallel to the casaba plume accelerating it. The idea is to include a slight asymmetry in the sail such that the center has enough momentum to fold into more of a dart shape without damaging it.

    Kerr says a SNAK can readily achieve over 50% conversion efficiency. Meaning the SNAK dart will inflict a bit more than half the casaba's destructive force. The reduction in damage is a small price to pay for the vast increase in weapons range.

    Warning, the equations below are good as long as the SNAK velocity is below 0.6 c (180,000,000 m/s or 180,000 km/s)

    r = cubeRoot((m * b)2 / (M * ρ * π * x))

    SNAKvel = (b * (1 - e(-h*m/M))) / 103

    SNAKη = ((1 - e(-h*m/M))2 M) / m

    where:
    r = radius of SNAK
    SNAKvel = final SNAK velocity (km/s)
    SNAKη = efficiency of SNAK, ratio between energy of SNAK and energy of casaba = 0.81
    m = casaba beam plasma mass (kg) = 1
    b = casaba beam plasma velocity (m/s) = 1,000,000
    M = SNAK mass (kg) = 1.8
    ρ = average shear stress strength of SNAK material (pascals) = 1,000,000
    π = pi = 3.14159…
    x = casaba beam length to diameter ratio = Beamlength / Beamdiameter = sqrt(casaba propellant plate diameter) / sqrt(casaba propellant plate height)
    e = base of the natural logarithm = 2.71828…
    h = reflection parameter. h=2 means all plasma is caught and thrown back. h=1 is comparable to traditional EFP. = 2

    Atomic Manhole Cover

    This is one of those urban legends, but it does have a grain of truth. Science fiction authors will find it an interesting concept. Especially if the plot has an urgent need for a quick-and-dirty way to get assets into space.

    OPERATION PLUMBBOB

    Propulsion of steel plate cap

    During the Pascal-B nuclear test, a 900-kilogram (2,000 lb) steel plate cap (a piece of armor plate) was blasted off the top of a test shaft at a speed of more than 66 km/s (41 mi/s; 240,000 km/h; 150,000 mph). Before the test, experimental designer Robert Brownlee had estimated that the nuclear explosion, combined with the specific design of the shaft, would accelerate the plate to approximately six times Earth's escape velocity.

    The plate was never found, and Dr. Brownlee believes that the plate left the atmosphere, however it may have been vaporized by compression heating of the atmosphere due to its high speed.

    The calculated velocity was sufficiently interesting that the crew trained a high-speed camera on the plate, which unfortunately only appeared in one frame, but this nevertheless gave a very high lower bound for its speed. After the event, Dr. Brownlee described the best estimate of the cover's speed from the photographic evidence as "going like a bat out of hell!"

    From the Wikipedia entry for OPERATION PLUMBBOB
    OPERATION PLUMBBOB
    Test:Pascal-B
    Time:22:35:00.00 27 August 1957 (GMT)
    Location:NTS, Area U3d
    Test Height and Type:-500 feet, open shaft
    Yield:Often listed as "slight", actual yield 300 tons (predicted 1-2 lb)
    Device Description:64.6 lb; 11.75x15 inches; plutonium pit; PBX 9401 and 9404 explosives

    Pascal-B is an interesting footnote to the history of nuclear testing, and surprisingly - spaceflight.

    The Pascal-B (originally named Galileo-B) was a near duplicate of the Pascal-A shot. It was another one-point criticality safety test, of the same basic primary stage design. Like Pascal-A it was fired in an open (unstemmed) shaft. One significant difference was that it had a concrete plug, similar to the concrete collimator used in Pacscal-A, but this time it was placed just above the device at the bottom of the shaft.

    The close proximity of this plug to the bomb had an unanticipated side effect.

    The Thunderwell Story

    The February/March 1992 issue of Air & Space magazine, published by the Smithsonian, contained an article about nuclear rocket propulsion:

    Overachiever
    "Every kid who has put a firecracker under a tin can understands the principle of using high explosives to loft an object into space. What was novel to scientists at Los Alamos [the atomic laboratory in New Mexico] was the idea of using an atomic bomb as propellant. That strategy was the serendipitous result of an experiment that had gone somewhat awry.
    "Project Thunderwell was the inspiration of astrophysicist Bob Brownlee, who in the summer of 1957 was faced with the problem of containing underground an explosion, expected to be equivalent to a few hundred tons of dynamite. Brownlee put the bomb at the bottom of a 500-foot vertical tunnel in the Nevada desert, sealing the opening with a four-inch thick steel plate weighing several hundred pounds. He knew the lid would be blown off; he didn't know exactly how fast. High-speed cameras caught the giant manhole cover as it began its unscheduled flight into history. Based upon his calculations and the evidence from the cameras, Brownlee estimated that the steel plate was traveling at a velocity six times that needed to escape Earth's gravity when it soared into the flawless blue Nevada sky. 'We never found it. It was gone,' Brownlee says, a touch of awe in his voice almost 35 years later.
    "The following October the Soviet Union launched Sputnik, billed as the first man-made object in Earth orbit. Brownlee has never publicly challenged the Soviet's claim. But he has his doubts."

    Although the shaft test goes unnamed in the article, only two shaft shots were fired before Sputnik was launched on 4 October 1957 - Pascal-A and Pascal-B. The nighttime Pascal-A shot could not have been the shot involved, since notably absent from the accounts of Pascal-A are the dazzlingly brilliant fireball streaking into the heavens that such an object would produce. Also Pascal-B was the only one of the two that was fired in summer as the article describes. This conclusion was confirmed to this author by Dr. Robert Brownlee, who has written expressly for this website his own account of this event.

    Objects can only be propelled to very high velocities by a nuclear explosion if they are located close to the burst point. Once a nuclear fireball has grown to a radius that is similar in size to the radius of a quantity of high explosive of similar yield, its energy density is about the same and very high velocities would not be produced. This radius for a 300 ton explosion is 3.5 meters.

    The steel plate at the top of the shaft was over 150 m from the nuclear device, much too far for it to be propelled to extreme velocity directly by the explosion. The feature of Pascal-B that made this possible was the placement of the collimator close to the device. The mass of the collimator cylinder was at least 2 tonnes (if solid) and would have been vaporized by the explosion, turning it into a mass of superheated gas that expanded and accelerated up the shaft, turning it into a giant gun. It was the hypersonic expanding column of vaporized concrete striking the cover plate that propelled it off the shaft at high velocity.

    To illustrate the physics, and estimate how fast it might have been going, consider that if the collimator absorbed a substantial part of the explosion energy (say a third of it, or 100 tons) it would have been heated to temperatures far higher than any conventional explosive (by a factor of 50 with the previous assumption).

    The maximum velocity achieved by an expanding gas is determined by the equation:

    
         u = 2c/(gamma - 1)
    
    
    where u is the final velocity, c is the speed of sound in the gas, and gamma is the specific heat ratio of the gas. If we further assume that the thermodynamic properties of vaporized concrete are similar to the hot combustion gases of high explosives, then the speed of sound in the vaporized collimator would be about 7 km/sec (the square root of 50 times the value of c for an explosive combustion gases, which is 1 km/sec). For molecular gases gamma is usually in the range of 1.1 to 1.5, for explosives it is 1.25. Thus we get:
    
         u = 2*7 km/sec / (1.25 - 1) = 56 km/sec
    
    
    This is about five times Earth's 11.2 km/sec escape velocity, quite close to the figure of six times arrived at by Dr. Brownlee in his detailed computations.

    But the assumption that it might have escaped from Earth is implausible (Dr. Brownlee's discretion in making a priority claim is well advised). Leaving aside whether such an extremely hypersonic unaerodynamic object could even survive passage through the lower atmosphere, it appears impossible for it to retain much of its initial velocity while passing through the atmosphere. A ground launched hypersonic projectile has the same problem with maintaining its velocity that an incoming meteor has. According to the American Meteor Society Fireball and Meteor FAQ meteors weighing less than 8 tonnes retain none of their cosmic velocity when passing through the atmosphere, they simply end up as a falling rock. Only objects weighing many times this mass retain a significant fraction of their velocity.

    The fact that the projectile was not found of course is no proof of a successful space launch. The cylinder and cover plate of Pascal-A was also not found, even though no hypersonic projectile was involved. Even speeds typical of ordinary artillery shells can send an object many kilometers, beyond the area of any reasonable search effort.

    Also, apparently the project name "Thunderwell" refers to a proposed project that was never carried out. Carl Feynman, by email, related the following account:

    In the mid-80s I heard of a "Project Thunderwell" from someone who had been employed at Livermore. In about 1991, I asked Dr. Lowell Wood about it, who was (and presumably still is) a prominent weapon physicist at Livermore. He told me that it was a project, never actually constructed, to launch a spacecraft on a column of nuclear-heated steam. The idea was that a deep shaft would be dug in the earth and filled with water. A spacecraft would be placed atop this shaft, and a nuclear explosive would be detonated at the bottom.

    BEAT SPUTNIK INTO SPACE?

    How a nuke blast lid may have beaten Soviets by months

    As any space enthusiast knows, beachball-sized Sputnik was the first manmade object to orbit the Earth after it was launched by the Soviets in October 1957. But it's possible the US managed to put an object into space a few months before that.

    In 1956, astrophysicist Dr Robert Brownlee was asked by his boss at the Los Alamos National Laboratory in New Mexico to figure out a way to test nuclear weapons underground. The scientists working on Operation Plumbbob were concerned about the amount of radiation spewed out by the nukes during tests above the surface, so Dr Brownlee started experimenting with the idea of blowing up small a-bombs below the surface.

    "Most of the radiation generated in a blast has a half life of about four hours," Dr Brownlee, 91, of Loveland, Colorado, told The Register. "We figured you could keep everything in but for a few per cent by going underground. But Mother Nature can outwit you in a great variety of ways."

    In July 1957, for an experiment codenamed Pascal A, the team drilled a borehole 500ft deep for what was to become the world's first underground nuclear test. Unfortunately, the bomb yield was much greater than anticipated – 50,000 times greater, apparently. Fire shot hundreds of feet into the air from the mouth of the uncapped shaft, in what Dr Brownlee described as "the world's finest Roman candle."

    Let's try again

    The next month, in a test codenamed Pascal B, the team wanted to experiment with reducing the air pressure in the explosives chamber to see how that affected the explosion and radiation spread. A four-inch-thick concrete and metal cap weighing at least half a ton was placed over a 400ft-deep borehole after the bomb was installed below. The lid was then welded shut to seal in the equipment.

    Before the experiment, Dr Brownlee had calculated the force that would be exerted on the cap, and knew that it would pop off from the pressure of the detonation. As a result, the team installed a high-speed camera to see exactly what happened to the plug.

    The camera was set up to record one frame every millisecond. When the nuke blew, the lid was caught in the first frame and then disappeared from view. Judging from the yield and the pressure, Dr Brownlee estimated that it left the ground at more than 60 kilometres per second, or more than five times the escape velocity of our planet. It may not have made it that far, though – in fact the boffin, who retired in 1992, believes it never made it into space, but the legend of Pascal B lives on.

    "I have no idea what happened to the cap, but I always assumed that it was probably vaporized before it went into space. It is conceivable that it made it," he told us.

    "Many years later, when I was in Baikonur, the subject of Russia being the first to launch something into space came up. I did not raise my hand to add to the discussion, though I thought about doing so."

    Did a twisted chunk of American hardware make it into space before the Soviets? We'll never know, but this was just one of the weird and wonderful experiences Dr Brownlee has had in a lifetime's nuclear research.

    GOING LIKE A BAT

    (ed note: in 2009 the Starship Modeler website had their eighteenth online plastic modeling contest: To The Moon. One of the entries in the diorama category was titled "Going Like a Bat!")

    1957 - The year that humans put objects into space. Everyone knows about Sputnik, which was launched on October 4, 1957. But, what about the event on August 27, 1957? A mine shaft hole cover plate that was four inches thick and four feet across. It weighed 1984 pounds (900 kilograms) and was launched with a plutonium fission bomb?

    Yep. That is to say, up to a specific point, it is very real. Yes, it honestly happened. But, after a specific point during the event, it's all conjecture . . . for now.

    Here is the history part:

    • Test Series: Operation Plumbob
    • Test name: Pascal-B
    • Time: 22:35:00.00 27 August 1957 (GMT)
    • Location: NTS, Area U3d
    • Test Height and Type: 500 feet underground, open shaft
    • Yield: Often listed as "slight," actual yield 300 tons
    • Device Description: 64.6 lb; 11.75 x 15 inches; plutonium pit; PBX 9401 and 9404 explosives

    Dr. Robert R. Brownlee's own words from his website: “Incidentally, the Pascal B test, and those immediately following, had a 4-foot-diameter pipe. The cap welded to the top of Pascal B was four inches thick, so was of appreciable mass from a 'man-handling' point of view. For Pascal B, my calculations were designed to calculate the time and specifics of the shock wave as it reached the cap. I used yields both expected and exaggerated in my calculations, but significant ones.

    When I described my results to Bill Ogle, the conversation went something like this:"

    Ogle: “What time does the shock arrive at the top of the pipe?”
    RRB: “Thirty one milliseconds.”
    Ogle: “And what happens?”
    RRB: “The shock reflects back down the hole, but the pressures and temperatures are such that the welded cap is bound to come off the hole.”
    Ogle: “How fast does it go?”
    RRB: “My calculations are irrelevant on this point. They are only valid in speaking of the shock reflection.”
    Ogle: “How fast did it go?”
    RRB: “Those numbers are meaningless. I have only a vacuum above the cap. No air, no gravity, no real material strengths in the iron cap. Effectively, the cap is just loose, traveling through meaningless space.”
    Ogle: “And how fast is it going?” [This last question was more of a shout. Bill liked to have a direct answer to each one of his questions.]
    RRB: “Six times the escape velocity from the earth.”

    “Bill was quite delighted with the answer, for he had never before heard a velocity given in terms of the escape velocity from the earth! There was much laughter, and the legend was now born, for Bill loved to report to anybody who cared to listen about Brownlee's units of velocity. He says the cap would escape the earth. (But of course we did not believe that would ever happen.)

    The next obvious decision was made. We'll put a high-speed movie camera looking at the cap, and see if we can measure the departure velocity.

    In the event, the cap appeared above the hole in one frame only, so there was no direct velocity measurement. A lower limit could be calculated by considering the time between frames (and I don't remember what that was), but my summary of the situation was that when last seen, it was 'going like a bat!!'

    As usual, the facts never can catch up with the legend, so I am occasionally credited with launching a 'man-hole cover' into space, and I am also vilified for being so stupid as not to understand masses and aerodynamics, etc., etc., and border on being a criminal for making such a claim.”

    Now for the fiction . . .

    Given the current contest on Starship Modeler, I personally think it's humorous to assume that the cover plate was not vaporized and to go ahead and plop it onto the lunar surface.

    With the “estimated” six-times-escape-velocity speed (and the nonaerodynamic nature of the cover plate), I decided I could reasonably tweak the story of the cover plate to ensure that it made it to the moon. But then the question becomes, where?

    August 25 1957, was a new moon, making August 27 a waxing crescent moon. Is there a (relatively) simple template formula to calculate this sort of a flight path? Well, when in doubt ask the nearest expert, so I did!

    Winchell Chung (Nyrath) kindly offered me some thoughts when I requested his assistance. “Now, if it has six-times-earth-escape velocity, it also has two-times-solar-escape velocity, so it has enough speed to go anywhere in the galaxy. It certainly has enough to go to the moon.

    Now, the moon always keeps the same face to the earth (more or less), even if all of it is not always visible. So even if it is a waxing crescent, the entire near side of the moon is facing the earth.

    Unfortunately, there is no simple way of calculating if the cover plate even hit the moon, much less where on the moon. Chances are it missed the moon, but if you want it to hit, you could pretty much pick any spot you wanted.”

    So, it was now fairly reasonable for me to assume that the cover plate survived its blast off through the earth's atmosphere and made it to the moon. For a lunar surface, I used Wilco Model's excellent base for their kit of the Luna. This was primed and then painted Krylon Ultra Flat Black. This was allowed to dry and then coated with a thin layer of Bob Ross White Gesso. I rinsed the brush clean, and then I used the still very damp brush to go back over the entire surface of the base. This had the effect of thinning the white gesso, which gave it a dirty white, almost gentle gray look much like the lunar surface.

    The actual steel cover plate was a bit harder. I really wanted to use the Wilco base, so, the model of the cover plate had to be small. I settled on metal “snap” grommets as a likely candidate. With the help of my needle-nosed pliers, I was able to successfully mangle a grommet into the proper shape. With the help of pinpoint drops (micro drops) of Tamiya Clear Red, Clear Green, and Clear Blue, I was able to simulate the colors that are often found on heated metals. And, a careful spritz of more Krylon Ultra Flat Black helped too!

    So, to close, I need to point out that the cover plate has never been found and was most likely destroyed or went past the moon. But, nobody knows what really happened to it. So why couldn't it be on the moon?


    Alas, Maximilian Crichton discovered that the man hole cover probably could not have made it to the moon. Another nice scifi idea bites the dust.

    Maximilian Crichton: I did some research regarding that Pascal B diorama speculation, unfortunately if you look up a sky view on 27 August 1957 from the coordinates of the test sight at the relevant time, the Moon was actually on the horizon, so it's rather unlikely that it would actually have hit the Moon, if it survived passing through the atmosphere at that velocity.

    From GOING LIKE A BAT! by Joe Brown (2009)

    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.

    Medusa Sail Deceleration

         The program allows for the application of a Medusa Sail deceleration mechanism, using the theory as developed by Solem [14, 15, 16]. This involves a large sail canopy, connected by various spinnaker and servo-winches, to the main vehicle. Pellets or units are detonated inside the sail area, imparting a pressure force and thereby thrust in the opposite direction of motion. The working assumption in the current model is to use a high-strength polymer (e.g. polyethylene) which has a material density of around 990 kg/m3. The user also specifies the sail material Young's modulus of elasticity, tensile strength of the spinnaker material, which for the high-strength polymer are given values of 220 GNm2 and 5 GNm2 respectively. The distance to the detonation point from the spacecraft is also specified, as well as the time between detonations.

         The Specific impulse (Isp) of the Medusa Sail is given by:

         Where g is the acceleration due to gravity, Ap is the projected area of the canopy, r is the detonation distance from the spacecraft, E is the energy release per detonation, mb is the mass of an individual unit. This can then be multiplied by acceleration due to gravity to get the exhaust velocity vex:

         The impulsive pressure (P) delivered by each detonation is given by:

         Where t is the approximate debris expansion time per detonation.

         The average thrust (T) is given by:

         Where δt is the time between detonations.

         The approximate radius of the canopy debris cloud per detonation (rd) is given by:

         Where Eparticle is the approximate energy of the explosion per detonation, leading to the emitted particles.

         The mass of the sail canopy (mc) is given by:

         Where σmax is the tensile strength of sail material, Y is the Young's Modulus of elasticity, ρs is the density of sail material

    (ed note: for purposes of the study they looked at Ap=7.85e7 m2, r=1,000 m, mb=25 kg, E=100 GJ to 100,000 GJ, σmax=5 GNm2, Y=220 GNm2, and ρs=990 kg/m3)

    MEDUSA SAIL DECELERATION:
    =============================================
    Medusa Exhaust Velocity (km/s): 1,042
    Medusa Specific Impulse (s): 106,220
    Total Medusa Unit Mass (tonnes): 750
    Radius of Gas Debris expansion from single unit (km): 20
    Maximum Conservative Spinnaker Mass (tonnes): 4
    Impulsive Pressure (N/m2): 2.48057942E-04
    Average Thrust (kN): 26,042
    Single Unit Mass (kg): 25
    Number Units: 30
    Wet (incl.Medusa) Mass (tonnes): 1,038.40002
    dry (incl.Medusa) Mass (tonnes): 1,033.65002
    Medusa delta V (km/s): 4.7759
    Pre-Medusa delta V (km/s): 36,985.7578      12.3371210
    Final effected velocity (km/s): 36,980.9805
    Percentage Medusa dv Reduction: 1.29167121E-02

         [14] Solem, J.C, The Moon and the Medusa: Use of Lunar Assets in Nuclear-Pulse-Propelled Space Travel, JBIS, 53, pp.362-370, 2000.
         [15] Solem, J.C, Nuclear Explosive Propulsion for Interplanetary Travel: Extension of the Medusa Concept for Higher Specific Impulse, JBIS, 47, pp.229-238, 1994.
         [16] Solem, J.C, Medusa: Nuclear Explosive Propulsion for Interplanetary Travel, JBIS, 46, pp.21-26, 1993.

    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
    D-T FUSION INERTIAL

    ENZMANN: There has been a twenty-year world-wide effort to tame the elusive geni of fusion (an apt analogy because during that time the primary line of research was directed toward trapping a plasma within a strong magnetic “bottle” until enough of it could “fuse” to release more energy than the containment process used). It was twenty years marked by dogged perseverance, brilliant theoretical insight, and agonizing frustration as physicists practically had to invent a whole new branch of Physics, something with the unpronounceable title — “Magnetohydrodynamics.”

    The essence of the problem was simple. For each new technical innovation devised to contain the plasma long enough for fusion to occur, the plasma devised three new techniques to escape. It was somewhat like trying to trap an angry anaconda with rubber bands.

    Into this dismal arena (for prospects of controlled fusion seemed to be beyond the end of the century, until recently), a new idea was injected. Quite simply, it asked, “Is there anything in the rules of this exotic game which insists that fusion has to be a continuous process? Suppose, instead of pursuing the exceedingly difficult road of containing the plasma indefinitely, with fusion energy trickling out, we examine an alternative technique of compressing the plasma intermittently. If we do this sequentially and often enough, the effect will be identical to a steady trickle of fusion power such as we have been laboriously pursuing with other techniques. The secret here is that all we have to do is hit that plasma hard enough, from all sides, and plain old inertia will do the rest. The result will be a fusion power plant somewhat similar to an internal combustion engine where it is the average power of the eight sequential explosions in the cylinders which moves the car. Of course, there is one problem: what are we going to hit the plasma with in the first place?”

    It was at this point that another technical breakthrough came to the rescue. Enter the LASER. It was suggested that intense light from a large laser, a source of precisely controllable electro-magnetic radiation, could be directed via suitable optics into a very small volume Of space. If, as the laser was fired, a tiny pellet of fuseable material (in this case, frozen deuterium-tritium) were dropped precisely into that tiny volume, the following would happen:

    The focused electro-magnetic radiation would exert a pressure on the pellet. Focused to such a small volume and arriving in such quantity, the prqssure would be enormous. But more important, the frozen deuterium (heavy isotopes of hydrogen, the most abundant element in the Universe) would absorb this energy at its surface which would, of course, be violently heated. It was Dr. John Nuckolls (of the Lawrence Radiation Laboratory, attached to the Univ. of Calif.) who predicted what would happen.

    If the laser pulse is actually two pulses—a smaller pulse of energy followed immediately by the main blast—then the outside of the pellet will absorb the first pulse, vaporize, and thus surround the pellet with a sort of atmosphere. The main pulse of intense laser light, upon arriving, will then further heat this “atmosphere,” causing it to expand rapidly in all directions. At this stage, out tiny pellet of frozen deuterium resembles very much a tiny synthetic star with a superheated atmosphere blowing off explosively in all directions. Now, Newton enters the picture, for the reaction pressure to this explosive departure of the shell of gas surrounding the pellet drives shockwaves from all sides into the tiny, icy heart of this miniature “star.” These crushing pressures actually compress the center of the pellet into the densities and temperatures found within the centers of stars like our sun, a million miles across! Yet the star created in the center of the vacuum chamber is only barely visible to the naked eye, a few tenths of a millimeter in diameter.

    At such densities and pressures the deuterium-tritium mixture fuses, the nuclei colliding and transmuting themselves into helium in a violent analogue of processes that take millions of years to complete in “normal-sized stars” such as our sun. The liberated fusion energy blasts apart the heart of this newly created “star,” sending the reactants in all directions at appreciable fractions of the speed of light. The tiny star explodes, ending its brief existence—as do many of the real stars a trillion times as large—as a supernova. Total time from creation to the death of this artificial star is less than a millionth of a second.

    If this process were accomplished successfully, the released energy would be greater than that required to fire the laser, maintain the vacuum, and keep the fuel frozen in precisely deliverable pellet quantities. Repetition of the entire sequence at rates ranging from once per second to a hundred times per second would provide for the “average” flow of energy envisioned previously.

    There is enough deuterium on Earth alone to provide essentially unlimited energy for the remaining lifetime of the sun. This is readily agreed upon by a wide spectrum of energy and environmental experts. However, what some may have apparently failed to consider, is that there are stores of deuterium within the rest of the solar system which dwarf our terrestrial supply (which would come primarily from seawater.) One of the moons of Jupiter, Callisto, for instance, which Pioneer 10 has revealed to have a density of only 1.65, seems to be a satellite with a 3,000 mile diameter, composed essentially of ice! In that ice, there is a vast supply of deuterium waiting to be mined. Little thought is necessary to realize that with fusion, which gives us the solar system through fusion rockets, we will discover enormous quantities of fuel beyond the “meager” quantity presently on Earth. No, energy is decidedly not a problem of the future.

    It naturally occurred to an awful lot of people at about the same time that if you aim a high-power laser through magnifying glass at a deuterium pellet, fusion will be in hand . Those same people were shortly seen rapidly retreating behind their office doors, biting their thumbs with a vacant look, pounding their heads against the nearest convenient hard object, or just standing staring down at their shoelaces. Word quickly spread (bad news may exceed light speed under certain circumstances) that what you achieved when you aimed a high-power laser at a deuterium pellet through a magnifying glass or any other lens system, was not a fusion reaction, but a mad scramble ofwhite-coated laboratory personnel for the cover of the near desks, benches, closets, and lavotories as the precision optics promptly exploded in about a million high temperature fragments, thus wiping out both the experiment and initial high hopes for fusion from lasers.

    The problem, of course, was discontinuities in the glass. At the energy densities emitted by the lasers in question, the slightest imperfection (and even the finest optical glass is not perfect) absorbs enough energy to flash instantly into vapor, shattering the lens. These lasers had been used in an M.I.T. project designed to blast tunnels through solid granite! They had shattered cobblestones into screaming shards of high velocity shrapnel and had punched through inch-thick destroyer plate. The power in these beams exceeds that of the sun by factors approaching the millions. No lens system could have the perfect transparency necessary to withstand even the shortest pulse of these hellish systems, not even for the billionths (10-9) or trillionths (10-12) of a second it would take to produce the deuterium “star.” Fusion, ignited by the “match” of the laser, seemed impossible to achieve for the very reasons which had first made it so attractive. How do you set off a reaction with a match you cannot hold?

    If the problem of the lens could be surmounted, Man would succeed in an incredible quest—bringing the stars, essentially, to Earth, harnessing their unlimited potential to solve Man’s most threatening problems for all time. But to succeed, the problem of the lens had to have its solution. The answer, as with all answers in the Universe to fundamental problems, was the picture of elegant simplicity: instead of attempting to focus the laser with a lens, use a mirror! With a suitable mirror system, the ravening power of one, ten, or a hundred laser systems could be spread out across a reflecting surface so that the power density per unit of area was well below the level required even to significantly raise the temperature of the mirror. Then, with appropriate geometry, this dilute radiation could be brought to a needlepoint focus on the deuterium target. Result: FUSION. Simple. Elegant. Practical.

    I like to think the first solution was the result of our work in Northeast Cryonics, but that isn’t quite correct. Perhaps, however, ours, I feel, is one of the least expensive and most elegant solutions. One of our designs, in fact, can be seen in Freff s illustration for this article.

    The secret of fusion-by-laser lies in discovering the correct geometry for the mirror system, a geometry which will first dilute the radiation from lasers of incredible power, lasers which are now being constructed or are within sight of our present state-of-the-art. With those two tools, creation in a fusion reactor of actual “stars” identical in every respect to those we see spangling the night sky will become a reality. And a new Age will have begun for mankind. That is the scientific breakthrough now only instants away by the standards of the cosmic clock.

    Examine carefully, if you will, the diagram I alluded to previously. You will notice that laser energy enters from two regions, is combined by appropriate optical flats, then flashes down into a conical mirror protected from destructive heating through a process identical to the reason we get cold in the winter and hot in the summer—grazing incidence of incoming energy. The ring of laser energy (since, of course, this system is three-dimensional) is reflected all along the mirror length, as you can see, and is brought to a tiny pinpoint focus of searing power at the precise special point where it will impact a pellet of deuterium mixture.

    Now, note very carefully. The end of this arrangement of optics, lasers, and hyperbolic mirror is open to space! And what is a container, closed on three sides, in which a high-temperature gas is expanding? Obviously, a rocket.

    This is why we shall have fusion torchships before we have fusion reactors lighting cities. You have to proceed through the stage of rocket development to get to power reactors.

    Spaceflight, up to now, has consisted of assembling a very large quantity of fuel and oxidizer in a metal tube, together with an engine to burn it in, and a very small payload (relatively speaking). The object: to burn said propellants as soon as possible, thus accelerating fuel, tank, engine and payload away from the earth as rapidly as possible. Once having released the payload from the final stage, you are in for the Long Wait.

    Since you have used most of the energy contained in the fuel you burned just to climb to the top of Earth’s gravitational “hill,” there isn’t much left to give you a healthy push on your way to Mars, the Moon, Venus or Jupiter. There you are, coasting along at a few thousand miles per hour, with millions of miles to cover. Worse, you are not traveling in a straight line, but a curving path which will add literally hundreds of millions of miles to the trip. This is the classic, coasting interplanetary journey portrayed by everyone from Asimov to Zelazny.

    Therefore, later—much later—varying from about a hundred days for a “quick” trip to Venus to almost two years to Jupiter (or six years to Saturn), you arrive. By which time most people will have forgotten you’re out there, except for that dedicated gang back at Mission Control.

    That is the picture of spaceflight held by 99.99 percent of those who take the trouble to think seriously about the subject at all.

    The days of such absurdities are essentially over. Alas, the 145-day flights to Venus and the 240-day missions to Mars (with its exciting layover of a Martian year, waiting for Earth to be in correct position for the return coasting flight) are not going to happen. Technology and time have caught up, even with Arthur Clarke (at least in the solar system) (alas, that turned out not to be the case).

    This is the way it will happen: A torchship will leave earth orbit, accelerating on a series of explosions produced by the events previously described. Fusion, with millions of times the energy of chemical reactions, and much higher coupling of this energy to the exhaust, results in a rocket engine and total ship performance which is nothing less than sensational, compared to the previous scenario. The ship accelerates away from Earth at (let us say, for the purpose of making a point), one “gravity”—an acceleration equivalent to that experienced on the surface of Earth where all objects fall at the same rate, 32 ft/sec2

    To those of us in the ship, everything will appear as it does on Earth, unless we look out the windows. Something dropped in the cabin will apparently “fall” to the floor at the same rate as it would on Earth, although actually it is the floor which is accelerating up to meet the object. No difference. Our “weight,” synthetic as it is and produced only by the thrust of our fusion engine, will be just as useful when it comes to sitting in chairs, or walking, or drinking liquids as actual gravitational weight is on Earth.

    After about half an hour of this, we may begin to wonder if there isn’t something rather strange about the performance of our vehicle. After all, we know that “normal” rockets such as those used in Apollo never burned for longer than about 12 minutes, and in that time consumed literally thousands of tons of fuel! This ship, about as massive as a jumbo jet (200 tons) has, according to our fuel gauge, consumed only 1800 pounds of deuterium—less than a ton! And we are still accelerating.

    After about two hours of this novel experience, enjoying normal earth weight, carpeted lounges, the pleasant attentions of stewards who bring drinks we can consume in the normal manner, we walk down to the observation area where we see a magnificent panorama of space. Imagine the shock as we realize that we are halfway between Earth and the moon—120,000 miles away from Earth and still accelerating, still consuming fuel. At this point we discover something else. The heavens are slowly turning around; the earth which was behind us is now in front, and the moon which was before us has taken up a position aft (to borrow a nautical phrase). It becomes apparent to us almost at once that the two celestial objects have not changed positions at all. Our 200-ton ship has rotated 180 degrees (Heinlein calls this a "skew flip", The Expanse calls it a "flip-and-burn"). Our fusion “torch” engine, which only moments before was accelerating us to higher and higher velocities, is continuing to thrust, but its effect is now to kill our enormous velocity. Inside, of course, nothing changes. Acceleration, deceleration, it’s all the same within the ship where the floor still presses reassuringly against our feet with normal Earth weight.

    Glancing at the system read-outs positioned so conveniently near the view-glass, we are incredulous at our measured velocity indicator. It must be in error! We are moving, it says, at 63 kilometers per second, relative to Earth. We remember Apollo, when the Command Module crawled across this point at a mere .6 kilometers per second—one hundredth our velocity—not in two hours, but over two days! Two hours more and the Captain slides us neatly into a breathtaking orbit of the moon. Under its gravitational field, weightless for the first time during the flight (the drive is turned off), we take 45 minutes to swing around the Farside and head home. Earth before us once again, the torch is lit, normal gravity resumes, and we accelerate away from Luna. It has taken us less time to span the almost half million miles between these two worlds than it took, in 1974, to fly across the United States in a vehicle of comparable size. It has taken far less fuel (a total of about 15 tons of deuterium-tritium) than a 747 burned flying cross-country (about 70 tons of kerosene) and at vastly higher peak velocities—227,000 km/hr, compared to a 747’s 960 km/hr. We have made the trip totally contained in an essentially terrestrial environment with all the “comforts of home.”

    Similar journeys, to any planet in the solar system, under identical environmental conditions (simulated Earth gravity through continuous acceleration /deceleration; conventional meals served on real plates; and beverages served in cups or glasses) will be commonplace within 15 years. No point in the solar system will be further from any other point, at one “G” acceleration, than 5 weeks’ travel time, the length of a relaxing terrestrial cruise. The ships, of course, will resemble ocean liners far more than they will terrestrial aircraft

    From TORCHSHIPS NOW! by Robert D. Enzmann and Richard C. Hoagland (1974)
    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
    Specific Impulse50,000 s to 100,000 s
    Gear Shift Isp5,000 s to max
    Specific Power10 kW/kg to 100 kW/kg

    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.


    The proposed solution is to combine magnetic confinement and inertial confinement.

    This is called Magneto Inertial Fusion (MIF) or Magnetized Target Fusion (MTF). For some researchers there are subtle differences between what mechanism the two terms describe, for other researchers the two terms are interchangeable. I'm going to use the terms as synonyms because the subtle differences are too subtle for my tired brain to distinguish.

    A blob of fusion fuel is converted into plasma. It is captured in a field reversed configuration. This means the plasma is shaped into a spinning torus, much like a smoke ring. If a smoke ring had a temperature of hundreds of thousands of degrees. The smoke ring is stablized by a magnetic field, that is, it is held by magnetic confinement.

    The point is the smoke ring of plasma is self-stable, once its internal magnetic field is established the ring does not need external electromagnets to prevent it from dissipating like a fart in a windstorm. What the external electromagnets does do is constrain the ring to travel down the axis of the engine. The smoke rings magnetic field is reversed with respect to the external magnets, so it is repelled by them (that's why it is called field reversed configuration). The repulsion prevents the smoke ring from collding with the engine walls.

    The smoke ring travels down the axis until it enters the reaction chamber.

    In the chamber, the smoke ring of fusion fuel is brutally crushed by a "liner", causing fusion. In standard inertial confinement fusion the fusion pellet is crushed by a circular (actually spherical) firing squad of laser beams or particle beams. But here the fuel is crushed by a liner made of matter. The liner is crushed by a magnetic field, but a much weaker field than is required by magnetic confinement fusion. Which is generated by electromagnetic coils which are much lower in mass than the ones used in MC fusion.

    In some designs the liner is a ring of metal foil. In others the liner is a circular firing squad of plasma jets.

    And in others, they do not bother with the FRC smoke ring of fusion fuel. Instead, the circular firing squad of plasma jets first fires a tiny jet of fusion fuel, immediately followed by a longer jet of plasma to use as a liner.


    What advantages does this Rube-Goldberg contraption give us?

    Trying to compress fusion fuel with immaterial laser beams is inefficient. Try hammering a nail using the beam of light from your flashlight if you don't believe me. Using a liner made of metal is vastly more efficient, which is why we pound nails using hammers made of matter. This makes MIF better than inertial confinement fusion. Attempting to compress using immaterial magnetic field is worse, all the problems of laser beams plus plasma instabilities on top of that. This makes MIF better than magnetic confinement fusion. In other words: Problem 1 solved.

    Since the fusion fuel is being crushed by the liner, pretty much all of the exploding fusion energy released is going to be absorbed by the liner. For "liner" read "propellant." So unlike inertial confinement and magnetic confinement engines, the MIF will be very efficient at transfering the fusion energy into the propellant where it should be. Problem 2 solved.

    And the more of the fusion energy intercepted by the liner/propellant, the less damaging blast hitting the reaction chamber walls and the less deadly radiation inflicted on the crew. Problem 3 solved.

    In addition, the lack of gigantic magnetic coils and batteries of laser beams means the MIF engines have much lower mass than magnetic confinement and inertial confinement engines.

    Thio MTF

    Thio Magnetized Target Fusion
    Fusion Yield per pulse<1 GJ
    Fusion Gain70
    Specific Impulse77,000 sec
    Exhaust Velocity760,000 m/s
    Engine Mass41,000 kg
    Pulse Rate 40 Hz
    Jet Power25 GW
    Thrust66,000 N
    Specific Power α605 kW/kg
    Specific Thrust1.5 N/kg
    Pulse Rate 200 Hz
    Jet Power128 GW
    Thrust340,000 N
    Specific Power α1,141 kW/kg
    Specific Thrust3 N/kg

    This is from High-Energy Space Propulsion based on Magnetized Target Fusion (1999)

    This is a Magneto Inertial Fusion concept where the liner is jets of plasma.

    They calculate that the hydrogen liner plasma is capable of converting more than 97% of the otherwise wasted neutron flux into charged particle energy available for thrust. Which is fantastic since otherwise 38% of the fusion energy is wasted. This also allows the heavy radiation shielding to be reduced, since neutrons are very damaging to engines and deadly to the crew.

    Theoretically it is possible to operate a magnetic nozzle in such a manner that it would have a nozzle efficiency of 80% in converting the spherically radial momentum of the exploding fusion into axial rocket thrust AND also harvesting some of the energy as electrical power. This is done with a magnetic flux compression generator. As per standard operating procedure, this is used using the camera strobe principle, where energy is harvested from one pulse and used to ignite the following pulse.

    A plus rate of up to 200 Hz appears to be practical, given the simplicity of the electrical circuit.

    Unlike most inertial confinement fusion engine, the MTF does not require intricately machined and layered fuel pellets. Just a tank of deuterium fuel and you are good to go.

    The Thio MTF had a very low system mass and volume, high thrust and Isp, high fusion gain, relatively low thermal waste, and the aforementioned ability to convert 97% of the neutron flux into thrust.

    Just like the HOPE MTF a pair of opposed conical theta pinch guns fire the plasma smoke-rings which collide at the target location to created the FRC magnetized target plasma. This is imploded by a barage of 32 plasma accelerators, whose plasma jets merge to form a spherically converging plasma liner. The implosion heats the target plasma to thermonuclear fusion temperature, and it undergoes fusion.

    Now, also just like the HOPE MTF, the plasma liner jets are actually in two parts. Each jet starts as a small spurt of deuterium gas then becomes a long jet of ordinary hydrogen. So the spherical plasma liner has a thin inner layer of deuterium fusion fuel, and a think outer layer of hydrogen propellant.

    The thermonuclear explosion makes the plasma liner think it hit a brick wall. The inner deuterium layer of the plasma liner is compressed to extremely high density, and undergoes fusion. The fusion of the target plasma is just a spark, the fusion of the deuterium layer is the main event.

    The outer hydrogen layer is heated by the deuterium fusion, including 97% of the neutrons. This become the superheated propellant. The lower half of the propellant shoots out of the magnetic nozzle, creating thrust. The upper half of the propellant slams into the magnetic nozzle, is reflected downward, and also creates thrust. The magnetic nozzle is created out of magnetic lines of force generated by cryogenically cooled electromagnetic coils ("thrust coils").

    The thrust coils also contain the magnetic flux compression generator, which steals a bit of thrust energy and converts it into electricity. This is stored in the capacitor bank, and used in the next pulse.

    Also, like many pulse propulsion systems, a large shock absorber will be needed between the engine and the payload to prevent the spacecraft from being jolted to pieces. This smooths out the impulse.

    A system of heat radiators is used to dispose of waste heat; which comes mostly from the plasma guns, the electrical recharge system, and neutron heating.

    On top will be the customary anti-radiation shadow shield to protect the crew.

    HOPE (MTF)

    HOPE (MTF)
    EngineMagnetized
    Target
    Fusion
    FuelD-D
    Inner Liner (fuel)deuterium
    Outer Liner (propellant)hydrogen
    Specific Impulse70,485 s
    Exhaust
    Velocity
    691,460 m/s
    Thrust5,798 N
    Thrust Power2.038 GW
    Engine
    Waste Heat
    492.9 MW
    MTP Pulse Rate20 Hz
    Engine Mass121,333 kg
    Crew Radiation
    Dose
    <0.05 Sv/yr
    Thermal
    Mass Breakdown
    Propellant
    Cryocooler
    7,224
    Med-Temp Radiators22,340 kg
    Hi-Temp Radiators20,523 kg
    THERMAL TOTAL51,391 kg
    MTF Engine
    Mass Breakdown
    x49 Plasma Guns1,167 kg
    Capacitors3,502 kg
    x2 Theta Pinch350 kg
    Nozzle
    Structure
    20,576 kg
    Nozzle
    Neutron Shield
    12,551 kg
    Nozzle Coils35,000 kg
    Superconducting
    magnetic
    energy storage
    (SMES)
    3,000 kg
    Recharge Circuit1,664 kg
    Vehicle
    Neutron Shield
    (water tank)
    37,000 kg
    Power Cables2,000 kg
    ENGINE TOTAL116,021 kg

    This is from Conceptual Design of In-Space Vehicles for Human Exploration of the Outer Planets (2003).

    This is a Magneto Inertial Fusion concept where the liner is jets of plasma.

    For the rest of the ship, go here.

    Two theta (Θ) pinch guns fire magnetized blobs of easily ignitable D-T fusion fuel plasma on a collision course. They collide at the parabolic focus of the magnetic nozzle. The nozzle is a magnetic field formed by the thrust coils, because a nozzle made out of matter would be damaged by the fusion explosion.

    A split second behind the firing of the theta pinch guns, a battery of 48 plasma guns fire plasma jets targeted at the fusion fuel blob. These jets form a spherical "liner" around the fusion fuel.

    The jets are actually composed of two different plasmas. The inner bit is fusable deuterium fuel, the large outer part of the jet is hydrogen propellant.

    The liner collapses at about 750 kilometers per second and squeeze the fusion fuel like a nutcracker from hell. The fusion fuel ignites like a miniature H-bomb, which it is.

    The important points are that D-T fusion is easy to ignite (Lawson criterion of only one), but the reaction emits a relatively large amount of damaging neturons (79%) and uses expensive tritium. D-D fusion is much harder to ignite (Lawson criterion of 30), but the reaction only emits 38% neutrons and deuterium is very cheap. The idea is that the liner will ignite the tiny D-T fuel blob in the center, and the fusion explosion will be enough to ignite the huge amount of D-D fuel in the liner.

    The thermonuclear detonation drives the hydrogen propellant in the liner outwards, where it rebounds off the magnetic nozzle, producing thrust on the thrust coils, which produce thrust on the structural tapered spines, which produce thrust on the thrust frame of the spacecraft's spine.

    A large tank of water perched on top of the magnetic nozzle acts as an anti-radiation shadow shield, to protect the crew.

    As is standard operating procedure with many such pulse engines, some of the energy of the detonation is tapped and stored in capacitors. This energy is used to power the next pulse (for the plasma guns and to create the magnetic nozzle). Electrical current is induced in the coils as the plasma cloud expands. Each plasma gun has its own capacitor to store power for the next pulse. The energy for the magnetic nozzle is stored in something called a Superconducting magnetic energy storage (SMES) device, located just below the nuclear reactor.

    For the first pulse each of the capacitors and the SMES has to be slowly charged up by the nuclear reactor (since the poor little one-lung SP-100 can only crank out a pathetic 300 kilowatts). With subsequent pulses the capactors are recharged almost instantly, by the power of nuclear fusion.

    Slough FDR

    Slough Fusion Drive Rocket
    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

    Dr. John Slough and his associates have come up with a new type of magneto inertial fusion propulsion. You can find their published papers on the subject here (2012)

    This is a Magneto Inertial Fusion concept where the liner is a ring of metallic foil.

    In their design, 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.

    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 MIF

    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 (2013).

    This is a Magneto Inertial Fusion concept where the liner is 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.

    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

    Radioisotope Positron

    Radioisotope Positron Propulsion
    Positrons / pulse1.96×1011
    79Kr source area200 cm2
    (8 cm radius)
    Positron plus rate0.006Hz to 80kHz
    D fuel density1×1030/m3
    Ignition burn depth250 nm
    Specific Impulse3×105 sec
    Exhaust Velocity2,943,000 m/s
    Initial 79Kr1 μg
    Maximum 79Kr14 g
    79Kr enrichment0.99
    Accumulator lifetime100 sec
    Thrust efficiency0.65
    Thrust10nN to 0.2N
    Maximum engine power2.1 MW
    ΔV60,000 m/s
    Mass Ratio1.0 !!!

    This is from Radioisotope Positron Propulsion NIAC Phase I Report (2019)

    As with all non-torchship engines, this propulsion system suffers from the "can only increase the exhaust velocity at the expense of the thrust" problem. But this is one of the extreme cases. The exhaust velocity is a whopping 2,943,000 meters per second. Meanwhile the thrust is a totally minuscule 0.00000002 to 0.2 Newtons.

    Having said that, the delta-V is a jaw-dropping 60,000 meters per second WITH A MASS RATIO OF 1.0. With many other propulsion systems, rocket designers are happy if the spacecraft is only 75% propellant and 25% everything else. A spacecraft with Radioisotope Positron Propulsion is pretty much 100% rocket and payload, the propellant is only a few micrograms.

    Granted that a one metric ton space probe with such an engine will have an measly acceleration of 0.0001 meters per second (0.0125 snail-power), but you can't have everything. Be that as it may, the report compares their positron engine with an electric propulsion engine for a hypothetical capture/redirect of asteroid 2009BD and the positron engine kicks the electric engine to the curb.

    Theoretically you can use multiple engine arrays if you must have a higher thrust.


    The secret is positrons, i.e., antimatter electrons.

    Antimatter is the ultimate fuel, but trying to actually use the stuff has many practical problems. Manufacturing large amounts of antimatter is colossally expensive. And trying to safely contain that dangerous crap is like juggling live thermonuclear warheads during an earthquake.

    But the study authors realized that positrons occur naturally. Specifically there are several commonly available radioisotopes that emit positirons, such as sodium-22, cobalt-58, and krypton-79. By utilizing long-lived radioisotopes that emit positrons, one is storing the positrons safely inside the nuclei instead of trying to store them in a Penning Trap or something equally hazardous.

    Krypton-79 was selected as the fuel of choice. Each nuclei will eventually spit out a positron and decay into Bromine-79. It may be possible to convert the bromine into tetrabromomethane (CBr4) which can be utilized as a trapping or cooling gas. But the study did not look deeply into that.

    What's more, krypton-79 can be created during the mission (a "breeder" fuel cycle). The antiprotons will be used to catalyze deuterium-deuterium fusion, which creates lots of neutrons as a side-effect. These neutrons can be trapped by a layer of more-or-less stable krypton-78. The neutrons will transform krypton-78 into positron-emitting krypton-79. The 79Kr can be skimmed out and added to the fuel supply.

    The breeder layer of 78Kr will have to be pressurized to about 10 to 100 atmospheres, and be about one meter thick.


    Krypton-79 fuel gas will be frozen as a thin layer on a cryogenic surface. The positrons that escape will pass through a moderator to even out their energies. They then pass through the beam system. This transforms the continuously emitted positrons from a large area source into short pulses focused on a small spot size.

    The deuterium fuel is catalysed to form dense clusters. These are deposited on a moving tape substrate. The tape carries the deuterium clusters right into the small spot size of positrons. The annihilation of positrons with electrons create gamma rays. Each ray can kick a deuterium ion hard enough so it slams into another deuteron fast enough to undergo inertial confinement fusion. The charged particle fusion reaction products are ejected through a magnetic nozzle to create thrust. The neutron fusion reaction product are hopefully mostly captured by the krypton-78 blanket. The rest either escape into space or do terrible things to the spacecraft.

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