## Intro

These are spacecraft designs using fusion propulsion.

Many of these spacecraft have a table of parameters. You can find the meaning of many of them here. Numbers in black are from the documents. Numbers in yellow have been calculated by me using the document numbers, these might be incorrect.

## Asteroid Mining Crew Transport

Asteroid Mining Crew Transport | |
---|---|

ΔV | 51,000 m/s |

Exhaust Velocity | 100,000 m/s |

Specific Impulse | 10,000 s |

Propellant Mass Flow | 0.96 kg/s |

Thrust | 96,000 N |

Propulsion | D-D Fusion |

Propulsion Bus | 2,000,000 kg |

Propellant mass | 4,000,000 kg |

Payload Section 1250 person habitat +1250 persons (85,000 kg) + consumables + priority cargo (150,000 kg) | 4,000,000 kg |

Wet Mass | 10,000,000 kg |

Dry mass | 6,000,000 kg |

Mass Ratio | 1.67 |

Single Fusion powerplant | 6 GW |

Number powerplants | x2 |

Total power | 12 GW |

Thrust power | 4.8 GW |

Waste Heat | 2.8 GW |

Waste Neutrons | 4.4 GW |

Length | 480 m |

Diameter | 400 m |

Centrifuge radius | 150 m |

Radiator surface area | 19,200 m^{2} |

Passengers | 1,250 |

This little gem is from Aerospace Projects Review Blog. Scott Lowther discovered it in a 1981 Boeing report Controlled Ecological Life Support System: Transportation Analysis.

The spacecraft was a **fusion** powered rocket designed to transport miners to the asteroid belt. **1,250 miners per trip**. And a cargo of **150 metric tons**.

In case it is not clear, the nose of the ship is in the upper left corner, with the tanks on girders. The tail of the ship is in the lower right corner, with the engine.

In the first picture, note the fly-like object in the upper left corner. That looks as if it was supposed to be a 37 meter long Space Shuttle. The pods on the ends of the centrifuge arms may or may not be shuttle external tanks, 47 meters long and 9 meters in diameter.

This thing is freaking ginourmous.

I made a quick and dirty 3D model in Blender and scaled it to with the assumption that the fly in the corner is indeed a 37 meter Space Shuttle. Hard to do since the drawing of the "shuttle" is just a smudge. Reading the dimensions off my model it says the ship is roughly 480 meters long, has a diameter of 400 meters at the tips of the heat radiators, and the centrifuge has a 150 meter radius. Treet these numbers with grave suspicion, they could be off by an order of magnitude plus or minus.

The report Scott found only mentioned the ship in passing, he has filed a FOIA request for another report that might go into more details. I hope so, it would be nice to have some solid figures to work with instead of all this conjecture and assuming.

For the Terra-asteroid run, the vehicle would boost for 11 days, coast for 226 days and brake for 13 days to rendezvous. Adam Crowl calculates if the jet-power is 4.8 GW and the mass-ratio is 5/3 for a return to Earth mission, then an exhaust velocity of ~100 km/s and a total delta-vee of 51 km/s. That means a mass-flow rate of 0.96 kg/s.

There are absolutely huge heat radiators because the engine has to get rid of **2.8 freaking Gigawatts** of waste heat.

The heat radiators are triangular, so that they can stay inside the shadow cast by the anti-radiation shadow shield. This is for three reasons:

- parts of the radiator extending out of the shadow could scatter deadly radiation onto the passengers
- parts of the radiator extending out of the shadow will suffer neutron activation
- parts of the radiator extending out of the shadow will suffer neutron embrittlement.

Dr. Luke Campbell points out that the engine is going to need one heck of a shadow shield, because distance attenuation ain't gonna do diddly-squat. Not against 4.4 *gigawatts* of neutron radiation it isn't. At a measly distance of 480 meters the 4.4 GW of neutron radiation will still be strong enough to give everybody on board the ship a lethal dose of radiation in about 1/5 of a second.

(Doing my own calculation, assuming a person with a body mass of 68 kilograms, a cross section of 0.445 m^{2}, who is 480 meters away from 4.4 GW of neutrons, I figure that with no shadow shield they will be exposed to about 10 grays per second, or a LD35 lethal dose of 2 grays in 1/5 second)

He goes on to say that even with a perfect shadow shield enough neutron radiation would scatter around it if a heat radiator, another spacecraft, space station, or asteroid was outside of the shadow and close to the ship. This can be dangerous over the 12 or so days of continuous thrust (the 226 days between thrust events would probably allow any acute radiation injury to heal — but the chronic stuff will accumulate from different burns).

Dr. Campbell goes on to say that a good shadow shield would probably have an interaction length on the order of a few centimeters at the 2.2 MeV energy of D-D fusion, so a few meters of neutron shielding would reduce the dose by something like 40 orders of magnitude. By way of comparison, the shadow shield on an old NERVA nuclear rocket was only about 0.25 meters thick.

Assuming that the centrifuge arm is indeed 150 meters long, it can spin at a safe no-nausea 2.5 RPM and produce a full gravity of acceleration.

If those pods are indeed Space Shuttle external tanks, they will have an internal volume of a bit more than 2050 cubic meters (the sum of the LH_{2} and LOX tank). If all of that is passenger volume (meaning the consumables, cargo, life support systems, and everything else is at the ship's spine), then each of the 1,250 passengers will have about 14.8 m^{3} to call their own for the 8.3 month journey. This is less than the 17 m^{3} NASA figures the crew needs for missions longer than six months or so. On the other hand, NASA is talking about crew members, not passengers. They are not actually running the ship, so as long as they don't actually start foaming at the mouth and go berserk, 14.8 m^{3} is probably good enough. Spartan but managable.

Let's fly further into unsubstantiated fantasy, piling shaky assumptions upon shaky assumptions. Do not take these next figures seriously.

Assuming my hasty 3D model based on a crude sketch is anywhere near accurate, my modeling package says that one of the triangular radiators has a surface area of about 6,400 square meters (counting both sides). This means the entire radiator array has a total radiating surface area of about 19,200 square meters.

This has to cope with the 2.8 gigawatts of heat.

Say that the heat radiators are titanium-potassium heat pipes. These have a specific area heat of 150.22 kW_{th}/m^{2}, so to handle 2.8 GW it will take about 18,640 m^{2}. This is less than the model's radiator area of 19,200 m^{2} so we are in good shape.

Ti/K heat pipes have a specific area mass of 100.14 kg/m^{2} so 18,640 m^{2} worth would have a mass of 1,866,600 kg. This is less than the propulsion bus mass of 2,000,000 kg so we are in good shape.

This means the propulsion bus has 133,400 kg left for the engine and structure. Sounds reasonable to me. But again all of this is fantasy, done for amusement value.

In the data block, the figures in black are from the report, the yellow figures are deduced. Treat the yellow figures with some skepticism.

## Discovery II

Discovery II | |
---|---|

ΔV | 223,000 m/s |

Specific Power | 3.5 kW/kg (3,540 W/kg) |

Thrust Power | 3.1 gigaWatts |

Propulsion | Helium^{3}-DeuteriumFusion |

Specific Impulse | 35,435 s |

Exhaust Velocity | 347,000 m/s |

Wet Mass | 1,690,000 kg |

Dry Mass | 883,000 kg |

Mass Ratio | 1.9 |

Mass Flow | 0.080 kg/s |

Thrust | 18,000 newtons |

Initial Acceleration | 1.68 milli-g |

Payload | 172,000 kg |

Length | 240 m |

Diameter | 60 m wide |

This design for a fusion propulsion spacecraft is from the NASA report TM-2005-213559 by Craig H. Williams, Leonard A. Dudzinski, Stanley K. Borowski, and Albert J. Juhasz of the Glenn Research Center (2005). The goal was to produce a modern design for the spacecraft Discovery from the movie **2001 A Space Odyssey**. The report has all sorts of interesting details about where the movie spacecraft design was correct, and the spots where things were altered in the name of cinematography. The movie ship had no heat radiators, and the diameter of the centrifuge was too small. Arthur C. Clark was well aware of this, but was overruled by the movie people.

## Ehricke Fusion Ship

Ehricke Fusion | |
---|---|

Engine | Linear mirror |

Fusion beta | 0.8 to 0.9 |

Fuel | Deuterium Helium 3 |

Specific Impulse | 4,590 sec to 45,900 sec |

Exhaust Velocity | 45,000 m/s to 450,000 m/s |

Thrust | 4,450 N to 445 N |

Jet Power | 100 MW |

Engine Mass | 15,000 kg |

Propellant Mass | > 100,000 kg 255,000 kg |

Total Mass | 455,000 kg |

Mass Ratio | 2.3 |

Length | 92 m |

This is from "Solar Transportation" by Krafft Ehricke, collected in Space Age in Fiscal Year 2001, AAS Science and Technology series, Vol. 10 (1966).

The spacecraft was designed for missions in the 24,000 m/s to 37,000 m/s delta V range. It uses what the report calls a "controlled thermonuclear reactor" (CTR) using Deuterium/Helium 3 (D-3He) fuel (D 40%, 3He 60%). From the description it is a linear magnetic confinement engine. Note how cryogenic radiators are triangular to keep them inside the radiation free shadow cast by the shadow shield.

Note the Thrust Augmentor at the end of the engine. This allows the engine to shift gears, trading off trade thrust for exhaust velocity (specific impulse) and vice versa. It is used for similar reasons that one would downshift with an automobile. In the case of the rocket if it is currently deep in a gravity well, one can increase thrust so you can get out of the well quick and stop paying its per-second gravity tax. The cost is a lower exhaust velocity (which means bad gas mileage) but in this case it is worth it. The Thrust Augmentor shifts gears the standard way, injecting cold hydrogen propellant into the hot exhaust.

Thrust (newtons) | Exhaust velocity (m/s) | I_{sp}(sec) | mDot (kg/s) | accel (m/s) | accel (g) | Jet Power (megawatts) |
---|---|---|---|---|---|---|

34 | 5,886,000 | 600,000 | 5.83E-06 | 7.54E-05 | 7.68E-06 | 100 |

445 | 450,000 | 45,872 | 9.89E-04 | 9.78E-04 | 9.97E-05 | 100 |

890 | 225,000 | 22,900 | 3.96E-03 | 1.96E-03 | 1.99E-04 | 100 |

4,450 | 45,000 | 4,587 | 1.00E-01 | 9.89E-03 | 1.01E-03 | 100 |

Remember that the jet power is equal to the exhaust velocity times thrust, divided by two. When the drive changes gears the thrust and velocity change, but **the jet power stays the same** (100,000,000 watts or 100 megawatts). You can use this equation to calculate other values for thrust and exhaust velocity which are not on the table.

The values for acceleration assume a fully fueled spacecraft with a mass of 455,000 kg.

mDot is propellant mass flow in kg/sec, it is equal to thrust divided by exhaust velocity. Multiply mDot by the duration of the engine burn (in seconds) to calculate how much propellant was expended.

The report gave an example of shifting gears.

Say the spacecraft starts deep in Terra's gravity well in NEO (in a 1.5 hour orbit). If it used high gear (exhaust velocity 450,000 m/s) it would have a pathetic thrust of 445 Newtons, and would take forever to move out of NEO with a miniscule acceleration of 0.0000997 g. Instead it down-shifts to low gear (exhaust velocity 45,000 m/s) for a brawny thrust of 4,450 N. The relatively huge acceleration of 0.001 g will have the spacecraft out of the gravity well in 26.5 hours flat ("out of the well" defined as local parabolic velocity at 28 Earth radii distance). The drawback is it will burn 95 metric tons of propellant but you can't have everything (otherwise you'd have a mythical torchship in your hot little hands). At this point your ship is 95 tons lighter (new mass of 360,000 kg) so the instantaneous acceleration is up to 0.00127 g.

Since the ship is now basically in Sol's heliocentric gravitational field (0.0006 g) it can safely upshift into high gear fuel economy mode. Thrust of 890 N, exhaust velocity of 225,000 m/s. This will accelerate the spacecraft to solar parabolic velocity (42 km/s) in about 60 days, burning about 8 metric tons of propellant and moving the spacecraft a distance of 1.1 AU.

If you now set the engine to "idle" and just coast, you will cross the orbit of Mars in 60 days flat, and the orbit of Jupiter in 300 days. This is just for illustration, you will zip by both planets at 42 km/s. If you actually wanted to be captured into orbit you'd have to do a braking maneuver.

Given a requirement of 37,000 m/s delta V and heavy use of low gear (exhaust velocity 45,000 m/s) I calculate a mass ratio of about 2.3, if my slide rule isn't lying to me. The report didn't go into such details.

The spacecraft also has four of those adorable space taxis.

## Exacting Class Starfighter

Exacting Class Starfighter | |
---|---|

ΔV | 7,000,000 m/s (0.02c) |

Specific Power | 450 MW/kg (450,000,000 W/kg) |

Thrust power | 9 terawatts |

Propulsion | ICF Fusion |

Thrust | 3,000,000 newtons |

Exhaust velocity | 6,000,000 m/s |

Dry Mass | 20 metric tons |

Wet Mass | 40 to 65 metric tons depending upon fuel |

Length | 60 meters |

Width (Whipple shield) | 5 meters |

Width (Internal hull) | 4 meters |

Heat radiator width (deployed) | 30 meters |

Heat radiator width (collapsed) | 5 meters |

Power plant | 50 MW Brayton-cycle w/argon working fluid |

Armament | UV laser (3 turrets) Missiles Spinal coilgun (2) Exhaust plume |

This is a design by Artist Zach Hajj (a.k.a. Zerraspace), which I found astonishingly good. Personally I cannot find anything scientifically inaccurate with it. The artist mentioned that he used this website as a resource, and I'd say he did his homework.

The structural components of the spacecraft are composed of high-emissivity graffold (folded graphene) scaffolding. The skin is armored with low absorptivity + high emissivity alloy for anti-laser armor, and a Whipple shield to defend against kinetic attacks. For sensors it has frontal and rear IR batteries and several antennae incorporated into the skin.

## Firefly Starship

Firefly Starship 2013 design | |
---|---|

ΔV | 2.698×10^{7} m/s(0.09c) |

Wet Mass | 17,800 metric tons |

Dry Mass | 2,365 metric tons |

Mass Ratio | 7.526 |

Payload | 150 metric tons |

Propulsion | Z-Pinch DD Fusion |

Exhaust Velocity | 1.289×10^{7} m/s |

Thrust | 1.9×10^{6} N |

Acceleration | 0.11 m/s (0.01 g) |

Accel time | 4 years |

Coast time | 93 years |

Decel time | 1 years |

Firefly Starship 2014 design | |

ΔV | 2.998×10^{7} m/s(0.10c) |

Wet Mass | 45,000 metric tons |

Dry Mass | 3,000 metric tons |

Mass Ratio | 15.0 |

Payload | 150 metric tons |

Propulsion | Z-Pinch DD Fusion |

Specific Impulse | one million seconds |

Thrust | 855,000 N |

Acceleration | 0.019 m/s (0.002 g) |

Accel time | 25 years |

Coast time | 70 years |

Decel time | 5 years |

Length | ~1,0000 m |

Icarus Interstellar has a project to design a fusion-rocket based interstellar spacecraft. They call it "Firefly". The technical lead director is Robert Freeland.

Most of the other Icarus fusion designs use inertial confinement fusion. That's because IC fusion is easier to get halfway worthwhile power levels. Magnetic confinement fusion would be nicer but once you get enough nuclear fusion going to to be worthwhile, the magnetic bubble pops like a cheap balloon.

The drawback to IC fusion is that the confinement time is pathetic. The longer you confine the fusion reaction, the more of the fusion fuel actually burns and generates energy. But in IC fusion the first bit of fusion acts to blast the pellet apart, scattering the un-burnt fuel to the four winds.

Back in the olden days of fusion research, the darling was Z-Pinch fusion. You send a bolt of electricity (about 5 mega-amps) down the center of a long tube full of ionized plasma, creating magnetic field which compresses the plasma enough to ignite nuclear fusion. One of the big advantages with Z-Pinch was that the confinement time (and net energy output from the burn) can be increased by simply making the reaction chamber longer.

Unfortunatley, the disadvantage is that Z-Pinch fusion suffers from several hydrodynamic instabilities which disrupt the plasma. So researchers stopped working on it in.

But in 1998 Dr. Uri Shumlak discovered you could eliminate the instabilities if you made the plasma move at high velocities. Based on this work, Z-Pinch was selected for the Icarus design.

The Firefly's long thin tail is the Z-Pinch tube, frantically fusing and radiating x-rays like a supernova. So the starship was given its name for similar reasons as the one on the TV show: it is a flying thing whose tail lights up.

The spacecraft profile is long and skinny, for two reasons:

- Its cruise velocity is a substantial fraction of the speed of light (4.5c for the 2013 version). This make interstellar dust grains impact with about 9.1×10
^{-4}joules worth of damage, the equivalent of 46,000 cosmic ray photons. You want to reduce the ship's cross section as much as possible to minimize the number of grain impact events. - The longer the ship is, the farther the payload can be placed from the deadly radioactive Z-Pinch drive, taking advantage of distance shielding.

Many other starship designs use ^{3}He-D fusion, because all the reaction products are charged particles that can be easily shieldied. The drawback is that ^{3}He is rare, you'd have to harvest the atmosphere of Jupiter for twenty years in order to get enough.

Instead, Firefly uses D-D fusion, since deuterium can be easily found in common seawater. Of course then you have to deal with all the nasty neutrons and x-rays produced by that reaction. Firefly's approach is to forgo the use of massive radiation shields, and instead try to let as much of the radiation escape into space. The Z-Pinch core is almost totally open to space with only a triad of support rails connecting the aft electrode and magnetic nozzle to the rest of the vessel.

Even with that, the waste heat is going to be titanic. That's where the heat radiators come in. Notice how they are the bulk of the ship. Makes the thing look like a garantuan lawn-dart. The radiators use beryllium phase-change technology, and are positioned as close as possible to the heat loads on the tail.

A long conical shield forwards of the reactor core deflects x-rays away from the payload using shallow-angle effects. The electrodes, rails, and other structure near the core are constructed of zirconium carbide (which is capable of surviving the intensely radioactive environment.

The 2014 design had a total length of just under one kilometer, half of which is the fuel tanks. The forward part of the ship uses the old fuel tank in lieu of spine trick in an effort to save on ship mass.

A fission reactor provides secondary power.

*Firefly Starship, 2013 design*

*Firefly Starship, 2013 design*

*Firefly Starship, 2014 design*

*Firefly Starship being constructed in orbital drydock.*

Artwork by Michel Lamontagne? of Icarus Interstellar

## Gasdynamic Mirror

There are problems with attempting to confine ionized plasma in a reaction chamber long enough for most of it to undergo nuclear fusion. Either by trying to hold the frantically radiating piece of star-stuff in an impossibly strong magnetic chamber or by bending the chamber into a ring and letting the fusion stuff run around like stock cars on a racetrack. The fusion plasma fights you at every turn.

In the Gasdynamic Mirror propulsion system, they attempt to avoid that by making the reaction chamber a long and skinny tube, so the plasma just travels in a straight line until it is all burnt. The trouble is that the tube has to be *really* long. High exhaust velocity, remember?

**Gasdynamic Fusion Propulsion System for Space Exploration** by Terry Kammash and Myoung-Jae Lee (1995) has this useful table:

System 1 | System 2 | |||
---|---|---|---|---|

Parameter | R = 50 | R = 100 | R = 50 | R = 100 |

Rocket Length (m) | 31.75 | 15.87 | 213 | 107 |

Plasma density (cm^{-3}) | 1×10^{16} | 2×10^{15} | ||

Plasma temperature (keV) | 15 | 10 | ||

Magnetic field (T) | 11.28 | 4.12 | ||

Thrust (N) | 2.52×10^{4} | 3.36×10^{3} | ||

Total mass (Mg) | 1,611 | 1,589 | 400 | 295 |

Specific impulse (s) | 1.58×10^{5} | 1.29×10^{5} | ||

Specific power (kW/kg) | 24 | 11 | 11 | 14 |

τ_{RT} to Mars (days) | 106 | 105 | 143 | 124 |

Mg:mega-grams, another name for tonne or metric ton

R:plasma mirror ratio

τround-trip travel time_{RT}:

**Physics Basis For The Gasdynamic Mirror (GDM) Fusion Rocket** by T. Kammash and W. Emrich Jr. (1998) had a sample spacecraft:

Fuel | 50-50 detuterium-tritium |
---|---|

Specific impulse (s) | 1.27×10^{5} |

Exhaust velocity (m/s) | 1.25×10^{6} |

Specific power (kW/kg) | 13.4 |

Thrust (N) | 2.5×10^{3} |

Thrust power (MW) | 2.2×10^{3} |

Payload + structural mass (Mg) | 279.7 |

Engine mass (Mg) | 101 |

Dry mass (Mg) | 380.7 |

Wet mass (Mg) | 423 |

Propellant mass (Mg) | 42.3 |

Mass ratio | < 1.1 |

ΔV (m/s) | 119,000 |

Initial acceleration (m/s^{2}) | 0.0059 |

Mars round trip (days) | 170 |

β | 0.95 |

R | 100 |

Fuel density (cm^{-3}) | 10^{16} |

Temperature (keV) | 10 |

Plasma length ~spacecraft length (m) | 44 |

Plasma radius (cm) | 5 |

Mg:mega-grams, another name for tonne or metric ton

β:ratio of plasma pressure to vacuum magnetic field pressure (how efficient the magnetic field is in confining the plasma so it doesn't leak everywhere)

R:plasma mirror ratio

When Kammash and Emrich calculated round trip mission time to Mars they used a simplistic Brachistochrone trajectory *(accel to midpoint - flip - decel to destination)*, ignoring planet orbital motion and gravity. They chose what they considered to be appropriate values for the efficiencies and masses of the various components to obtain the engine and wet mass, but did not give a detailed breakdown in the report.

Propellant mass was a jaw-dropping less than 10% of wet mass (mass-ratio less than 1.1). Predictably the initial acceleration is a meager 0.0059 m/s^{2} *(about 0.74 snail-accelerations)*, but what did you expect, a torchship?

**Performance Optimization of the Gasdynamic Mirror Propulsion System** by T. Kammash and W. Emrich Jr. (1999) had a sample spacecraft (thrust, specific power, and spacecraft length are all about double the above design, wet mass is about triple):

Fuel | 50-50 detuterium-tritium |
---|---|

Specific impulse (s) | 1.422×10^{5} |

Exhaust velocity (m/s) | 1.395×10^{6} |

Specific power (kW/kg) | 133 |

Thrust (N) | 2.21×10^{4} |

Thrust power (MW) | 1.189×10^{4} |

Dry mass (Mg) | 1,500 |

Plasma length ~spacecraft length (m) | 72 |

Plasma diameter (cm) | 8 |

Vacuum β | 0.95 |

Plasma density (ion/cm^{3}) | 2.2×10^{16} |

Plasma temperature (keV) | 10 |

Gain factor (Q) | 2.35 |

Magnetic field at center (tesla) | 13.8 |

Magnetic field at mirror (tesla) | 15 |

Fusion power (MW) | 1.486×10^{4} |

Injector power (MW) | 5,064 |

Bremsstrahlung power (MW) | 317 |

Synchrotron power (MW) | 103 |

Neutron power (MW) | 1.189×10^{4} |

Neutron wall load (MW/m ^{2}) | 187 |

Magnets | 30 |
---|---|

Radiator | 1,077 |

Thermal Electric Converter | 55 |

Direct Electric Converter | 53 |

Neutral Beam Injector | 23 |

Fuel Cell/Capacitor System | 35 |

Tritium Breeding System | 10 |

Lithium Shield | 37 |

Magnet Cooling System | 19 |

Structure | 36 |

Habitat | 65 |

Mars Lander | 60 |

Total Dry Mass | 1,500 |

The fusion plasma is fueled and heated by neutral beam injectors. The injectors are powered from the nuclear fusion via a combination of direct *(harvesting charged particles)* and thermal *(harvesting thermal gradients)* energy converters. The direct electric conversion system has an assumed efficiency of 90%, the Brayton cycle thermal electric conversion system has an assumed efficiency of 30%, and the neutral beam injectors have an efficiency of 100%.

The charged particles from the fusion plasma will be split evenly between thrust and direct electric conversion.

The energy required to jump-start the engine will come from a capacitor bank charged by a set of fuel cells. The bank produces a 1,000 MW-sec pulse of electricity to start the fusion reaction. The capacitors have a charge storage density of 36 kJ/kg.

The fuel cells also provide station keeping power whien the fusion engine is shut down. When the fusion engine is started, some power is tapped to recharge the fuel cells.

The fusion engine has a radiation shield composed of liquid lithium. This is also part of the tritium breeder system.

The habitat module is a set of eight modified International Space Station modules, sized to proved long term accommodations for a crew of six. Storm cellar is a room with walls lined with foodstuffs, water, and waste products. The life support system is not fully closed, oxygen/carbon dioxide cycles are closed but foodstuffs are considered to be consumables.

Power budget for habitat module is 100 kW, which is a pitance compared to the megawatts demanded by the fusion engine. When the engine is shut down the 100 kW comes from the fuel cells.

The lander is a resuable launch vehicle having a vertical takeoff, vertical landing design. It includes a small in-situ fuel processing system powered by a nuclear reactor. Perhaps something like Zubrin's NIMF.

Shield is liquid lithium, also acts as a tritium breeder

*Artwork by Seth Pritchard. Click for larger image.*

## Hedrick Fusion Spacecraft

Hedrick Fusion Spacecraft | |
---|---|

Engine | Tandem mirror |

Fuel | Deuterium Helium 3 |

Thrust | 3,678 N to 37,500 N |

Specific Impulse | 10^{5} sec to200 sec |

Exhaust Velocity | 981,000 m/s to 1,962 m/s |

Specific Power (inc. radiators) | 1.2 kW_{thrust}/kg(833 kg/MW) |

Fusion Power | 1,959 MW |

Input Power | 115 MW |

Thrust Power | 1,500 MW |

Thermal Power (not useable for plasma thrust) | 574 MW |

Engine Mass | 1,250,000 kg |

Engine Length | 113 m |

Midplane Outer Radius | 1.0 m |

Neutron Wall Loading | 0.17 MW/m^{2} |

Central Cell on-axis magnetic field | 6.4 T |

Electron Density | 1.0×10^{21} m^{-3} |

^{3}He to Ddensity ratio | 1 |

Electron temperature | 87 keV |

Ion temperature | 105 keV |

Fuel Ion confinement time | 6 sec |

Ion confining electrostatic potential | 270 kV |

Efficiency | 77% |

ΔV | ? m/s |

Living Modules | |

Number modules | 36 |

Hull | Aluminum lithum alloy |

Hull Thickness | 4 cm |

Diameter | 4 m |

Length | 7.3 m |

Habitable Volume | 3,300 m^{3} |

Artificial gravity | 0.8g |

Centrifuge spin | 4.2 rpm |

Centrifuge diameter | 80 m |

Habitat Ring | |

×36 Living Modules | 320,200 kg |

Shadow Shield | 3,890,000 kg |

×4 Mass Elevators | 1,924,000 kg |

×4 Radial Arms | 178,000 kg |

Payload | 6,692,000 kg |

Total Hab Ring Mass | 13,000,000 kg |

Mass Schedule | |

Habitat Ring Mass | 13,000,000 kg |

Engine Mass | 1,250,000 kg |

Radiator Mass | 750,000 kg |

Fuel Mass | 1,730,000 kg |

Wet Mass | 16,730,000 kg |

Mass Ratio | 1.12 |

This is from the report Mars manned fusion spaceship (1991). It uses a Tandem mirror engine

There are 36 living modules composing the centrifuge ring. Each module is 4 meters in diameter and 7.3 meters long. The hull is an aluminum-lithium alloy 4 centimeters thick to shield from galactic cosmic radiation. So at a rough guess there is about 3,300 cubic meters of pressurized habitable volume.

Module types include airlocks, bathrooms, bedrooms, cafeteria, controls, library, life support, recreation, recycling, research, saferoom (storm cellar in case of solar proton storms I guess), and storage.

There is a pressure-tight spacedoor between each module. It is a damage control device to allow isolating a module in case of hull rupture/depressurization, toxic gases, or fire. Doors will handle 14.6 psi of pressure, low temperature, and will close automatically. To reduce mass each door is a sandwich of an aluminum honeycomb 13.5 cm thick between two sheets of titanium each 0.25 cm thick. The door is 187 cm high by 93.1 cm wide with a total mass of 10.7 kg. Corners are rounded to prevent curling and to press equal force around edge of seal. Doors are on tracks and can be opened/closed by spring, electric motor, or manually. If there is a pressure difference the door cannot be opened. Assuming a minimum 55 kPa atmospheric pressure to prevent suffocation, and a hull puncture the size of an entire door (1.67 m^{2}), the doors have to shut within 0.03 second to keep the two living modules adjacent to the breached modules above 55 kPa, and within 1.14 second to keep the entire habitat ring above 55 kPa.

Not shown is any sort of a landing craft, which presumably would be parked on the ring hub, nose-to-nose. Without a lander, the entire trip is kind of pointless.

The modules are on the rim of a centrifuge 80 meters in diameter rotating at 4.2 rpm to provide an artificial gravity of 0.8*g*. This provide enough gravity to reduce bone decalcification, and is below the 6 rpm spin nausea limit. This puts the modules under a shear stress of 22 MPa, which the aluminum-lithium allow can easily handle.

The centrifuge ring is supported by four radial supports. Each is 38 meters long, with an out side diameter of 4 meters with a 13.2 centimeter thickness.

As with all centrifuges, astronauts and other objects moving around will unbalance the centrifuge and make it unstable. The four centrifuge radial support arms have movable masses ("mass elevators") which dynamically ensure the centrifuge center of mass stays positioned on the centrifuge center of rotation. Assuming a maximum imbalance of 52.5% to 47.5%, and a radial arm length of 40 meters, each movable mass will need to be 481,000 kilograms. They will be made of cast iron, cylindrical with a radius of 1.8 meters and a length of 6.15 meters. To avoid problems with coriolis acceleration, the movable masses should have a velocity of no higher than 0.1 m/s when they are moving to correct an imbalance.

The tandem mirror fusion reactor is composed of 25 magnetic mirror cells. Each cell has 4 belt radiators for removing waste heat. There are 100 belt radiators total.

The specific power is 833 kg/MW_{thrust}, which is about an order of magnitude worse than the later ^{3}He-D Mirror Cell design (64 kg/MW_{thrust})

*Open-field magnetic confinement (Tandem mirror engine)*

From Critical Issues for SOAR: The Space Orbiting Advanced Fusion Power Reactor, Santarius et al (1988)

Maximum radiation dosage from the fusion reactor that the astronauts can be safely exposed to was set at 2.5 millirem per hour (0.025 millisievert/hr).

A shadow shield is set adjacent to the living modules. The shield is a ring-shaped steel tank full of boric acid. The shadow shield is 1.75 meters thick along the line of radiation flux, and has a total mass of 3,890,000 kilograms. The tank walls are 5 centimeters thick, so about 5% of the total shield mass is steel tank.

Alternatively the shadow shield can be placed so it encases the long reactor cylinder (a "reactor cover shield"). This would be lighter, but now the shadow shield has to cope with the intense waste heat from the reactor. The shield would be 1.37 meters thick and have a lower mass of 1,970,000 kilograms, plus the mass of the cooling system.

One calculation predicted a Terra-Mars trip would take 178 days at an acceleration of 1.6×10^{-4} *g* and a payload fraction of 0.40. But when I look at the report's reference for that statement, I discover that they are quoting a 1964 book by Ernst Stuhlinger (the designer of the Mars Umbrella Ship) called *Ion Propulsion for Space Flight*. In other words the report writers did not actually calculate the performance parameters of the Tandem Mirror fusion reactor.

## Hyde Fusion Rocket

Hyde Fusion Rocket | |
---|---|

Propulsion | Inertial Confinement Fusion |

Thrust | 40,000 N |

Exhaust Velocity | 2,650,000 m/s |

Thrust Power | 54 gigawatts |

Engine Specific Power | 110 kW/kg |

Pellet Ignition Rate | 100 Hz |

Magnetic Nozzle Efficiency | 65% |

Engine Mass | |

Engine Magnetic Nozzle | |

coil and matrix | 8.7 metric tons |

anti-burst structure | 8.5 metric tons |

coolant coil | 8.1 metric tons |

neutron shield | 44.4 metric tons |

gamma-ray shield | 56.3 metric tons |

lithium coolant | 27 metric tons |

heat radiators | 13 metric tons |

sub total | 166 metric tons |

Engine Driver | |

Driver module laser | 0.520 metric tons |

Driver module radiator | 0.435 metric tons |

Driver module total | 0.955 metric tons |

x200 Driver modules | 191 metric tons |

Driver system trusses | 12 metric tons |

Driver system optical system | 6 metric tons |

Driver system oscillator | 11 metric tons |

Power transmission lines | 5 metric tons |

Compulsator | 12 metric tons |

Capacitor banks | 25 metric tons |

Driver system sub total | 262 metric tons |

Engine | |

Total | 428 metric tons |

Misc. Mass | |

Cargo Payload (VIP Payload) | 1,458 metric tons (50 metric tons) |

Cargo Fuel (VIP Fuel) | 650 metric tons (2,058 metric tons) |

Fuel Tank | 16 metric tons |

Thrust Truss | 20 metric tons |

Radiation Shadow Shield | 17 metric tons |

Auxiliary reactor | 5 metric tons |

Total Mass | |

Wet Mass | 2,594 metric tons |

Cargo Mass Ratio (VIP Mass Ratio) | 1.33 (4.84) |

This is from *A Laser-Fusion Rocket for Interplanetary Propulsion* by Roderick A. Hyde (1983). I apologize for any mistakes but the document appears to be scanned from a poor photocopy of a pre-print that was almost unreadable. As you can see from the diagrams below.

**Pellets** of fusion fuel (with a coating of propellant) are injected into the reaction point at a rate of 100 pellets per second. There they are imploded by the **Driver** using a 2 megajoule? pulse of laser radiation from a krypton fluoride laser (which is only 6% efficient). The laser pulse is divided into 8 laser beams which are reflected by mirrors to converge at the reaction point from all directions. The laser pulse compresses the pellet, igniting the fusion reaction. Two krypton fluoride lasers will be used at 50 Hz, alternating pulses to make an effective pulse rate of 100 Hz. The **Magnetic nozzle** directs as much as it can of the exploding pellet's plasma energy into producing rocket thrust, and prevents as much as it can of the plasma energy from frying engine components.

Dr. Hyde estimates that this engine can carry 1,500 metric tons of payload, with an average trip-time of 6 weeks to Mars, 3 months to Jupiter, and 1 year to Pluto.

**Pellets**

For the fusion fuel inside the pellet, you want as much of the energy to be in hot plasma as possible. Any neutrons and x-rays produced are wasted energy, since they contribute nothing to the thrust and cause damage to the ship and crew. The report has a long section discussion the relative merits of various fusion fuels, but Dr. Hyde settles on Deuterium-Deuterium fusion. The pellets contain 15 milligrams of deuterium salted with 36 micromoles of tritium.

About 30% to 50% of the deuterium fuel will burn, the rest will be wasted. Deuterium has a specific energy of 345 megajoules per milligram. The engine is designed for 2000 megajoules per pulse, so for deuterium at 40% burnup each pellet will require 15 milligrams of deuterium. The pellet of deuterium will be coated with propellant to increase thrust (increasing the propellant mass flow mdot) so that the total pellet mass is 150 milligrams. Pretty much any element can be used for propellant, Dr. Hyde used spare deuterium. This means that by varying the amount of extra propellant the engine can shift gears, *i.e.,* trade exhaust velocity for thrust and vice versa. The on-board pellet factory can change this on the fly.

1280 megajoules will be in the form of charged particle fusion energy for thrust, about 710 megajoules will be wasted in the form of x-ray and neutron radiation (330 MJ of x-rays, 380 MJ of neutrons).

**Magnetic Nozzle**

The primary task of the thrust chamber's magnetic nozzle is to convert the exploding plasma into thrust. The secondary task is to generate the power required to energize the lasers in the driver. The tertiary task is to breed tritium for the fusion pellets, since the blasted stuff has an unstable half-life of barely 12 years.

A superconducting coil creates a magnetic field that reflects the exploding plasma. The coil is encased in neutron radiation shields, and has a heat radiator to keep the radiation shields from melting. The radiators are on the part of the coil farthest from the ignition point.

In a latter design described in a document I have as yet failed to lay my hands on, there are two coils instead of one: the S-coil and the B-coil. The S-coil is above the ignition point and the B-coil is below. The S-coil is smaller with a denser magnetic field, to encourage the plasma blast to exit out the weaker B-coil. The coils resemble slices of a cone

Since there is not much that can be done to stop the harmful x-rays and neutrons, the idea is to make the magnetic nozzle as "transparent" as possible. It is an open framework where all the components occupy a small fraction of the solid angle as seen from the fusion pellet explosion (just see the diagram below). You want to make all the components "edge on" to the explosion, which is why the coils look like conic sections. In other words, they are blade shields.

As the exploding plasma expands against the magnetic field of the thrust chamber, the field is moved. Induction coils (next to the nozzle coils) harvest this motion to generate electricity for the driver. 33 megajoules of electricity is generated, and stored in a compulsator flywheel for the laser driver to use for the next laser pulse.

Other engine designs try to turn all the plasma into electricity and use that to run an ion drive or something. This adds penalty mass in the form of the generator, and reduces the power available by the inefficiency of the generator. Dr. Hyde thinks it is better to just use the plasma directly as thrust.

The tritium breeder has to produce a minimum of 36 micromoles of tritium per pellet explosion. Otherwise the tritium supply will be operating at a loss, and will eventually run out. This is done with a tube full of liquid lithium-6 and lithium-7 with a loop near the detonation point. The lithium converts the neutrons from each blast into tritium. The trouble is that with the design of the lithium blanket there was a pathetic breeding ratio of only 54%, which mandates a neutron interception fraction of 0.055 in order to make 36 micromoles of tritium. The bottom line is that the liquid lithium will be heated at a hideous rate of 4.2 gigawatts, needing a huge heat radiator to prevent the rocket from vaporizing.

This means that the tritium breeding places a floor on vehicle heating; pellets should have a little tritium as possible. Dr. Hyde set it at 36 micromoles for reasons too complicated for me to understand.

Cross section view of the magnetic nozzle along the thrust axis. The curved lines are the outline of the plasma explosion at microsecond (μs) intervals after detonation. As you can see most of the plasma is traveling in the proper direction for exhaust. You can also see the small naughty jet of plasma trying to travel up the thrust axis to hit the ship in the rear.

The lithium (Li) loop tritium breeder is placed on the inner side of the magnetic nozzle coils, so they can soak up the neutrons and partially shield the coils. The loop and the coil are wrapped by a blade-shaped metal skin, which acts as an eddy current shield.

The magnetic nozzle is a high-energy type, unlike the low energy nozzle on a Daedalus starship. This means the magnetic field contains about five times the energy of the exploding pellet (radius of 6.5 meters with a current of 22 MA), where the Daedalus magnetic field is weaker than the pellet. High-energy types are more efficient at converting pellet explosion energy into thrust.

This is an axially-symmetric nozzle which means a jet of hot plasma will escape along the long axis, *i.e.,* right into the ship's backside. A smaller magnet is used to deflect this jet so it misses the ship's derrière

The magnetic nozzle is 65% efficient at converting the exploding plasma into thrust. Coupled with the 1280 megajoules of plasma energy per pellet detonation means that the entire engine converts about 42% of the total pellet energy into thrust.

The coil will have to be a superconductor, if for no other reason because 22 MA of current will vaporize a conventional coil. Dr. Hyde specified a vanadium-gallium (V_{3}Ga) superconductor with a 15.8 Tesla peak coil field at 4.8 K temperature will have a current density of 270 kA cm^{-2}. The coil will be embedded in a matrix of vanadium and aluminum. The coil and matrix will have a radius of 6.5 meters and a mass of 8.7 metric tons.

However, remember that the same charge of magnetic field repel each other. 15.8 freaking Teslas will be doing their darndest to expand the coil (read: make the coil violently explode in all directions). The technical term is "magnetic bursting force." This will be resisted by 8.5 metric tons of structural composite. So the total coil+structure mass is 17.2 metric tons.

Keeping the coil cooled down to 4.8 K when it is being exposed to 2 gigawatts of neutron and x-ray energy is somewhat of a challenge. The lithium loop will remove the heat created by neutron radiation in addition to breeding tritium. Dr. Hyde figures it can handle the 2000 watt heat load.

Even worse, some of the neutrons that enter the coil's lithium hydride (LiH) radiation shield will scatter right back out, thus they can hit the coil from its unprotected rear side. The radiation shield will have to cover one side of the coil that is not in direct line of sight of the detonation point (the side where radiation can be reflected off the payload's radiation shield right back at the coil).

And then there is x-rays and gamma-rays, requiring a lead coating on the radiation shield.

So the lithium loop will require an 8.1 metric ton refrigerator to reject the heat plus 10 tons of liquid lithium, the lithium hydride neutron radiation shield is about 44.4 metric tons, and the gamma-ray radiation shield is about 56.3 metric tons.

Total magnetic nozzle mass: 126 metric tons.

As previously mentioned the magnetic nozzle system has to cope with 4.2 gigawatts of waste heat, from x-rays hitting the lead shield and neutrons hitting the lithium loop. The lithium will be the thermal working fluid to move the heat to the heat radiators (then it will have its tritium harvested). It will be pumped by a 20 megawatt MHD pump utilizing the thrust chamber's magnetic field. At a given time there is 10 metric tons of liquid lithium inside the thrust chamber sopping up neutrons, but the total system has 27 metric tons. This includes the liquid lithium in the long pipes leading to the heat radiators, and inside the radiators themselves.

The heat radiators are an array of 7,800 heat pipes, each 11 meters long and using lithium at 1500 K. The array mass is 40 metric tons.

**Driver system**

Laser amplifier. The driver needs 200 of these.

The pellets are imploded by 2 megajoules worth of laser beam applied in 10 nanoseconds. Dr. Hyde considered electron beams, but they are hard to focus on a tiny pellet and also cause nasty bremsstrahlung radiation. Proton beams have no bremsstrahlung, but since the detonation point is going to be ten to twenty meters away the proton beam will bloom due to electrostatic repulsion and be impossible to focus on the pellet.

Dr. Hyde considers free electron lasers (FEL), carbon dioxide (CO_{2}) lasers, neodymium-doped glass (Nd:glass) lasers, and krypton fluoride (KrF) lasers. After a long discussion he figures the krypton fluoride laser is the least bad option.

Due to problems with heat rejection speed, Dr. Hyde decided to go with two laser systems alternatively firing at 50 Hz instead of one laser system firing at 100 Hz.

Each system will require 100 laser amplifiers (see diagram above). Each amplifier has a rotating cylinder with its lasers and a non-rotating heat pipe radiator. There are five lasers in the cylinder, firing at a rate of 10 Hz. Actually the cylinder is more like gas filled tube with five laser "buckets" on the rim. Between pulses the hot laser gas is exchanged with cool gas in the core, and the heat is rejected by liquid sodium heat pipes. The heat pipes radiate at a temperature of 900 K.

A module has a mass of 955 kilograms, of which 520 kilograms is laser and 435 kilograms is heat radiator. 100 modules per laser system and 2 laser systems means 200 modules are needed. Total mass is 191 metric tons.

In addition, the laser systems will need 12 metric tons of connecting trusses, 6 metric tons of optical system to combine and plus-stack the beams, and 11 metric tons for the oscillator system.

The laser driver will require 33 megajoules of energy per pulse. As described above, energy will be harvested from the engine and stored in a compulsator. 33 MJ will be extracted from the compulsator and placed in a capacitor bank, much like a camera strobe.

The power transmission lines connecting the engine and the compulsator have a mass of 5 metric tons, the compulsator has a mass of 12 metric tons, and the capacitor banks mass 25 metric tons.

**Miscellaneous Components**

There will be an neutron+gamma ray radiation shadow shield located 20 meters from the detonation point to protect the payload region. It will subtend a 3° half-angle, plus thin fins to shadow the thrust chamber heat radiators. Unfortunately the magnetic nozzle coil will scatter some radiation over the edge of the shield. Right behind the shield will be a magnet to deflect the naughty plasma jet.

The fusion pellets have to travel from the rear of the shadow shield to the detonation point during inter-pulse time. This means they have to have a speed of 2 kilometers per second. They will be propelled by a magnetic accelerator or laser ablation. Extreme precision will be required. In practice a pellet might be deliberately delivered slightly off axis from the detonation point in order to do thrust vectoring.

Behind the payload region is the pellet factory. It will take deuterium, tritium from the tritium breeder, and propellant and manufacture them into pellets. Dr. Hyde did not bother designing this but said he doubted it would be massive.

For cargo missions, Dr. Hyde figures the spacecraft will require 650 metric tons of deuterium fuel. If the acceleration is always below 0.1 *g* then the mass of the fuel tank would be about 16 metric tons.

The engine will be off in between missions and during coasting, so the engine will generate no power. An auxiliary nuclear fission reactor will be provided for housekeeping power and to restart the propulsion system. A 1 megawatt reactor with a mass of 5 metric tons will do.

There will be a truss to transmit thrust from its origin at the magnetic nozzle coil up to the payload. It has a mass of 20 metric tons. It has 8 primary thrust-bearing members. As with the lithium pipes (heat transfer and tritium breeding) the thrust-bearing members will be shadowed by the magnetic nozzle coil shield until the members reach the inner edge of the thrust chamber radiator (50 meters from the detonation point). At that location the members are laterally tied together by a structural ring, then fan out towards the laser driver radiating array. Upon reaching this site, the truss no longer has circular symmetry but is instead biased towards the radiation plane of the rocket. The thrust bearing members are hollow pipes tied together by a lateral truss to avoid buckling. It is rated for a maximum of 5,000 kilonewtons thrust.

**Vehicle Performance**

The important performance numbers to look at are the ratio of maximum exhaust power to engine mass (power-to-mass ratio) and the exhaust velocity.

The main limit on the power-to-mass ratio is the heat rejection capacity of the laser driver and thrust heat radiators (if you run the engine at a higher rate than the radiators can cope with the ship will melt or vaporize). The secondary limit is the actual mass of the engine.

Exhaust velocity is limited to a maximum of about 2.6×10^{6} m/s due to the energy limits of deuterium fusion. In practice it will be further limited by the energy wasted producing neutron and gamma-rays, inefficiency of magnetic nozzle converting plasma energy into thrust, and most importantly the fraction of the pellet mass used to implode the fuel.

The engine is pretty lousy for interstellar propulsion at least 20% c due to the the exhaust velocity (20% c is greater than 2.6×10^{6} m/s so mass ratio will be ugly).

However the engine will be marvelous for interplanetary travel. In that role the main limit is the power-to-mass ratio. Given a good ratio, the engine can be optimized to increase the thrust a little bit at the expense of the exhaust velocity (shifting gears). As a rule of thumb you want the thrust and wet mass of the spacecraft to be such that it can crank out a minimum of 5 milligees (0.05 m/s^{2}) of acceleration. Otherwise the spacecraft will take *years* to change orbit. It is worth it to up the thrust enough to allow this even if you are robbing the exhaust velocity.

**w = ƒ _{τ} * sqrt( (2 * E_{k}) / m_{p} )**

**P = (m _{p} * ν * w^{2}) / 2**

**P = ν * E _{k} * ƒ_{τ}^{2}**

**P = (F * w) / 2**

**α _{p} = P_{jet} / M_{e}**

**F = m _{p} * ν * w**

**mDot = m _{p} * ν**

where:

w= exhaust velocity (m/s) {2,650,000 m/s} which elsewhere in this site is symbolize by V_{e}

P= jet power, thrust power (W) {54,100,000,000 W = 54.1 GW} which elsewhere in this site is symbolize by F_{p}

α= power-to-mass ratio or specific power (W/kg) {110,000 W/kg = 110 kW/kg}_{p}

F= thrust (N) {40,000 N}

ƒ= efficiency of magnetic nozzle in converting charged particle energy into jet energy {0.65}_{τ}

E= charged particle fusion energy (J) {1,280,000,000 J}_{k}

m= pellet mass (kg) {0.00015 kg}_{p}

ν= pellet repetition rate (Hz) {100 Hz}

M= mass of engine (kg) {486,000 kg}_{e}

mDot= propellant mass flow (kg/s)

sqrt(x)= square root of x

x= x squared^{2}

In the following tables, a "VIP Mission" is one with the shortest possible trip time, but with a microscopic payload. A "Cargo Mission" is one with a longer trip time in exchange for a reasonable cargo. In the cargo mission, given the total starting mass of the spacecraft (2,592 metric tons), 4/16ths is fuel/propellant mass (648 metric tons), 9/16th is payload mass (1,458 metric tons), and 3/16ths is engine mass (486 metric tons). The VIP mission has the same total starting mass and engine mass. The difference is that the payload mass is reduced and the fuel mass is increased.

Over a given mission the exhaust velocity and thrust is varied by changing the pellet mass.

Note that an acceleration of 1 *g* is 981 cm/s/s. 5 milligees is about 5 cm/s/s

VIP Missions Table 4 | |||
---|---|---|---|

Parameter | Mars ♂ | Jupiter ♃ | Pluto ♇ |

Distance (AU) | 0.6 | 5.2 | 39.5 |

Transit Time (dys) | 9.4 | 39.8 | 153.9 |

Speed Max (km/s) | 165 | 339 | 667 |

Acceleration Max (cm/s/s) | 81.1 | 39.5 | 20.1 |

Exhaust Vel start (km/s) | 51 | 104 | 205 |

Exhaust Vel end (km/s) | 271 | 557 | 1,095 |

Pellet Mass start (gm) | 422 | 100 | 26 |

Pellet Mass end (gm) | 14.8 | 3.5 | 0.91 |

Cargo Missions Table 5 | |||
---|---|---|---|

Parameter | Mars ♂ | Jupiter ♃ | Pluto ♇ |

Distance (AU) | 0.6 | 5.2 | 39.5 |

Transit Time (dys) | 22.2 | 93.6 | 362 |

Speed Max (km/s) | 70 | 144 | 284 |

Acceleration Max (cm/s/s) | 14.7 | 7.11 | 3.63 |

Exhaust Vel start (km/s) | 281 | 577 | 1,135 |

Exhaust Vel end (km/s) | 375 | 770 | 1,135 |

Pellet Mass start (gm) | 13.8 | 3.3 | 0.85 |

Pellet Mass end (gm) | 7.8 | 1.8 | 0.48 |

The tables above were calculated by with the following equations, whose implications I have not fully digested.

For interplanetary travel, the capability of an Inertial-confinement Fusion Rocket (IFR) is limited more by its power-to-mass ratio, than bi its exhaust velocity. The limitation on exhaust power translates into a bound on the product of exhaust speed

"w"and acceleration"a", i.e., onaw. While a large value ofwwill eventually enable the rocket to reach a high speed, the lowameans that doing so takes up a lot of time and distance. When the goal is to travel a given distance"D"as quickly as possible, the optimum technique involves accepting a lowerwvalue in exchange for higher acceleration. This dialing ofwcan be accomplished in an IFR by placing excess propellant mass outside of the fusion pellet. The extra material lowers the exhaust velocity of the pelet, while increasing its impulse. Pellet-nozzle expansion calculations have been performed for different overall pellet masses, and shown no change in nozzle efficiency.We have used three models, of increasing sophistication and opacity, to analyze the performance of this IFR. The first is the classic power-limited model, in which gravity and exhaust velocity limits are neglected. This case is easy to solve, and indicates the the pertinent scaling and operational modes. Next the

wconstraint is included. The resulting zero-gee motion can also be analytically solved, but in less useful form. This solution is then used as the starting point when numerically solving the 2D problem in which solar graviyt is included along with thewandawconstraints.By neglecting solar gravity and vehicle exhaust velocity limits, we gain a simple insight into the performance capabilities of an IFR. Suppose one wishes to travel a distance

"D"in time"T", starting and stopping at rest. The rocket has an initial mass of"M, of which the powerplanet accounts for a fraction_{0}""β"and is characterized by a power-to-mass ratio of"η". The optimum tradeoff betweenaandwoccurs for the time dependent acceleration:The payload fraction

"λ"can be shown to be given byNote that

D, T,andηappear only in the dimensionless parameterα. The trip time is seen to vary with the 2/3 power of distance, and with the inverse cube root of the power-to-mass ratio. There are two interesting operational modes suggested by Eq. 2. The "VIP" mode yields the shortest possible trip time, but a vanishing payload. For this mode:For economical operation, one is willing to accept a longer trip time in exchange for a large payload fraction

λ. The "Cargo" mode results from maximizing the payload throughputλ / Tby optimizing overTand the choice ofβ. This optimum occurs atα= 1/16 andβ= 3/16, resulting in a payload fractionλ= 9/16 and a fuel fraction of 1/4 (4/16). For this mode:In Table 4 we demonstrate the VIP mode capabilities of this rocket, and show Cargo performance in Table 5. For purposes of comparison, the VIP mode numbers assume the same powerplant fraction,

β= 3/16, which is optimal for cargo carrying; so the payload of the Cargo mission is swapped for more fuel in the VIP mission. The rocket exhaust power and exhaust velocity are given by:(ed note: those two equations were already presented above)

For the current design, the nozzle efficiency

ƒis 0.65, so the power_{τ}Pis 54.1 GW. Using the powerplant of Table 3, we find a power-to-mass of 110 Wgm. The examples illustrated in Tables 4 and 5 span the range of solar system mission; Martian close approach to show high acceleration capability, Pluto transit to show the opposite extreme, and an average Jupiter mission. The Tables list the distance, trip time, maximum speed, maximum acceleration, the exhaust speed at the beginning and end, and the overall pellet mass at beginning and end.^{-1}The potential of this IFR for solar system propulsion is graphically illustrated by the trip times shown in Tables 4 and 5. A quick trip to Mars can be made in 9 days, while even in Cargo mode, Pluto can be reached in a year.

In Cargo mode, the rocket can deliver 1,500 metric tons per mission; while the VIP method still permits delivery of ≈ 50 metric ton payloads.While enlightening, the above analysis is incomplete. The acceleration profile of Eq. 1 requires a zero acceleration and infinite exhaust velocity at the midpoint of the trajectory. Hence, the exhaust speed constraint will be violated during these trajectories. This will certainly occur in the middle of the trips, and for longer missions can occur throughout the journey. When a limitation on

wis imosed on the trajectory optimization problem, its solution is no longer as transparent as Eq. 2; but analytic results can still be derived.(ed note: for more details see the report)

This is apparently from a different but related study by Hyde. Note there are two coils instead of one. Note similarity to Luke Campbell's blade shields.

*Apparently from "Prospects for Rocket Propulsion with Laser Induced Fusion Microexplosions" by R. Hyde, L. Wood, and J. Nuckolls (1972)*

Images from "Comparison of Fusion/Antiproton Propulsion Systems for Interplanetary Travel by Stanley K. Borowski (1987)

click for larger imageDiagram by Roderick Hyde

## HOPE (Z-Pinch Fusion)

Z-Pinch HOPE ship | |
---|---|

Specific Power | 6.6 kW/kg (6,553 W/kg) |

Thrust Power | 3.6 gigawatts |

Propulsion | Z-Pinch fusion |

Specific Impulse | 19,346 s |

Exhaust Velocity | 189,780 m/s |

Mass Flow | 0.2 kg/s |

Thrust | 38,120 N |

Dry Mass | 552,000 kg |

Payload | 150,000 m |

Length | 126 m |

Diameter | 47 m |

Mars 90 day mission | |

Wet Mass | 635,227 kg |

Mass Ratio | 1.15 |

Total ΔV | 27,500 m/s |

Mars 30 day mission | |

Wet Mass | 887,300 kg |

Mass Ratio | 1.61 |

Total ΔV | 93,200 m/s |

Jupiter mission | |

Wet Mass | 663,100 kg |

Mass Ratio | 1.20 |

Total ΔV | 36,100 m/s |

550 AU mission | |

Wet Mass | 738,400 kg |

Mass Ratio | 1.34 |

Total ΔV | 57,200 m/s |

Z-Pinch Pulsed Plasma Propulsion Technology Development Final Report. Like all the others, they started with the HOPE study, replaced the HOPE Magnetized Target Fusion engine with their own engine, and compared the two.

*Z-Pinch freighter card from the game High Frontier (Colonization Expansion).*

## ICAN-II

ICAN-II | |
---|---|

ΔV | 100,000 m/s |

Specific Power | 34 kW/kg (34,400 W/kg) |

Thrust Power | 11.9 gigawatts |

Propulsion | Antimatter Catalyzed Micro-Fission |

Specific Impulse | 13,500 s |

Exhaust Velocity | 132,000 m/s |

Wet Mass | 707,000 kg |

Dry Mass | 345,000 kg |

Mass Ratio | 2 |

Mass Flow | 1.36 kg/s |

Thrust | 180,000 newtons |

Initial Acceleration | 0.255 g |

Payload | 82,000 kg |

Length | 72 m |

Diameter | 190 m wide |

This design for an antiproton-catalyzed microfission/fusion propulsion spacecraft is from the University of Pennsylvania.

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 1×10^{11} 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/s^{2} 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 7×10^{14} antiprotons per nanogram, and 1×10^{11} antiprotons needed to ignite one fuel pellet, that's enough to ignite about 453,000 fuel pellets.

## Magneto Inertial Fusion Drive Rocket

Engine Specs | |
---|---|

Engine | Magneto Inertial Fusion |

Fuel | Deuterium |

Propellant | Lithium foil |

Power | D-D Fusion |

Delay Between Fusion Pulses | 13.3 sec |

Specific Impulse | 5,000 sec |

Exhaust Velocity | 49,000 m/s |

Mass Ratio | 1.7 |

ΔV | 26,000 m/s |

Jet Power | 36 MW |

Thrust | 1,470 N |

Propellant mass flow | 0.03 kg/s |

Specific Power (Jet power/inert mass) | 2.4 kW/kg |

Fusion Gain | 200 |

Fusion Input Power | 400 kW |

Mass Budget | |

Structure | 3.4 metric tons |

Propellant Tank | 0.1 metric ton |

FRC Formation | 0.5 metric ton |

Propellant Feed | 1.2 metric tons |

Energy Storage (capacitors 1 J/g) | 2.5 metric tons |

Liner Driver Coils | 0.3 metric tons |

Switches and Cables | 1.2 metric tons |

Solar Panels 400kW at Mars @200 W/kg | 2.0 metric tons |

Thermal Management (heat radiators) | 1.1 metric tons |

Nozzle | 0.2 metric tons |

Margin (20%) | 2.5 metric tons |

INERT MASS(spacecraft) | 15 metric tons |

Payload (Crew Habitat) | 33 metric tons |

Payload (Lander Aeroshell) | 16 metric tons |

Payload (Lander rockets) | 14 metric tons |

PAYLOAD MASS | 63 metric tons |

DRY MASS(inert+payload) | 78 metric tons |

Propellant | 56 metric tons |

WET MASS(dry+propellant) | 134 metric tons |

Initial Acceleration | 0.011 m/s (0.001 g) |

Payload fraction | 47% |

Tankage fraction | 10% |

Mission | |

Terra-Mars Transit | 82.9 days |

Stay Time | 30 days |

Mars-Terra Transit | 97.1 days |

TOTAL MISSION TIME | 210 days |

This is from **Electromagnetically Driven Fusion Propulsion**, J. Slough, Pancotti, A., Kirtley, D., Votroubek, G., International Electric Propulsion Conference, IEPC-372 (2013).

This fusion ship uses John Slough *et al's* innovative Magneto Inertial Fusion engine. The engine has most of the advanages of both magnetic confinement and inertial confinement fusion with very little of the disadvantages. Instead of trying to crush the fusion fuel with wobbly magnetic fields or a spherical firing squad of lasers, then attempting to heat the propellant by toasting it over the explosion, it tries a more clever method.

Instead it magnetically crushes a foil ring of lithium metal (called a "liner") such that it also crushes a blob of fusion fuel in a mighty fist of metal. Then as the fusion explosion occurs, the lithium becomes propellant, conveniently totally enclosing the blast and doing a fantastic job of converting fusion energy into propellant energy. This also allows the rocket to use open cycle cooling, so it does not need acres of heat radiators like other fusion rockets.

In addition, carrying inert rolls of compact lithium foil propellant is infintely easier than trying to keep huge cryogenic tanks of liquid hydrogen from boiling dry.

Each lithium foil liner has a mass of something between 0.28 to 0.41 kilograms. The crush speed is about 3 kilometers per second, resulting in a solid cylinder of lithium with a fusion explosion going off in its heart.

Using a fusion rocket means the entire mission will take about 210 days, instead of the 540+ days you'd need with a fission rocket. Which means the crew won't max out their career radiation exposure limit in one lousy mission.

For the specified mission a specific impulse of 5,000 seconds is needed. A complicated equation (in the paper) calculates this mandates a fusion gain factor of 200. This means if you want 36 megawatts of jet power coming out of the engine, you will have to feed in 36,000,000 / 200 = **180 kilowatts** of electricity. This can be supplied with a low-mass arrangement of a solar photovoltaic array charging a capacitor energy storage bank *(instead of being forced to use a weighty nuclear reactor or something)*. Remember that sunlight is weaker at Mars orbit, you'll need an array rated for 400 kilowatts at Terra orbit in order to eke out 180 kW at Mars.

The crew habitat module appears to be a bog-standard inflatable TransHab module, which is hardly surprising. It can house a crew of six for about 18 months in about 33 metric tons. The rest of the payload is a 30 metric ton Mars Excursion Vehicle. Basically it is using the payload package specified in NASA's Mars Design Reference Architecture 5.0.

And this rocket is totally resuable, unlike those insane designs using fission rocket staging.

**TRANSIT HABITAT**is a TransHab module

**SPLINE TRUSS**is the backbone of the ship

**LINER/PROPELLANT**are the big rolls of lithium foil propellant**SHADOW SHIELD**protects ship from radiation

**FRC FORMATION**makes the puff of fusion fuel for detonation (stands for Field Reversed Configuration if anybody cares)

**SHOCK ABSORBERS**are needed since this engine pulses BANG! --- BANG! --- BANG! at 13.3 second intervals instead of a steady burn

**LINER/PROPELLANT INJECTOR**converts a length of lithium foil into a ring and throws it over the compression coils

**MAIN COMPRESSION COILS**grabs the ring of lithium foil and brutally squeezes it over the puff of fusion fuel

**MAGNETICALLY INSULATED EXPANDER**channels the blast of lithium plasma into a rocket exhaustWhite area is protected by the shadow shield. Note how radiators are trimmed at an angle to keep them inside the protective shadow.

## MICF Fusion Spacecraft

DT Fuel | Catalyzed DD Fuel | |
---|---|---|

Fuel Exhaust Velocity | 776 km/s | 344 km/s |

Tungsten Exhaust Vel | 43.8 km/s | 35.9 km/s |

Effective Specific Impulse | 4,510 s | 3,700 s |

Effective Exhaust Vel | 44,200 m/s | 36,300 m/s |

Firing Rate ω | ≤ 6,422/s | ≤ 5,254/s |

Thrust | 412ω N | 233ω N |

Thrust Power | 9.70ω MW | 4.627ω MW |

Pellet and Plasma | ||

DT Fuel | Catalyzed DD Fuel | |

Fusion Fuel Inner Radius | 0.25 cm | |

Fusion Fuel Outer Radius | 0.30 cm | |

Metal Shell Outer Radius | 0.547 cm | 0.495 cm |

Laser Energy | 2.59 MJ | 4.56 MJ |

Initial Plasma Density | 5×10^{21}cm^{-3} | 3×10^{21}cm^{-3} |

Initial Plasma Temperature | 11.785 keV | 40 keV |

Pellet Mass | 8.75 g | 6.03 g |

Propellant Mass Flow | 0.00875ω kg/s | 0.00603ω kg/s |

Energy Gain Factor | 724 | 82 |

Average Ion Energy | 1.10 keV | 0.735 keV |

Reaction Chamber Volume | 4.189×10^{3} cm^{3} | |

Nozzle Throat Area | 19.63 cm^{2} | |

Nozzle Throat Radius | 2.5 cm | |

Mars Ship | ||

DT Fuel | Catalyzed DD Fuel | |

Round Trip | 138 days | 171 days |

Firing Rate ω | 100 | |

Thrust | 41,200 N | 23,300 N |

Inert Mass | 564 metric tons | |

Payload Mass | 100 metric tons | |

Dry Mass | 664 metric tons |

This is from An Inertial Fusion Propulsion Scheme For Solar System Exploration by Terry Kammash and David Galbraith (1991)

This is another clever scheme to combine inertial confinement fusion (IC) and magnetic confinement fusion (MC). Remember that in both of the conventional schemes the longer you can confine the fusion plasma, the more of it will burn in nuclear fusion, and the more energy you will get out of a unit of fuel.

Conventional IC fusion has a naked pellet of fusion fuel surrounded by a circular firing squad (nay, *spherical*) of lasers. The laser pressure crushes the fuel until it ignites into fusion. Unfortunately the confinement lifetime is dictated by the speed of sound in the plasma, leading to lamentably short confinements.

Conventional MC fusion tries to confine hot fusion fuel plasma in a magnetic field. The complicated arrangement of magnetic fields still cannot prevent the plasma from wriggling out between the magnetic lines of force like a swarm of greased piglets. A material metal wall is *not* used to confine the plasma because

- to the star-core hot fusion plasma the metal wall is colder than winter midnight at Antarctica. It instantly cools the plasma below fusion temperatures
- to the metal wall the star-core hot fusion plasma is like an oxy-acetylene cutting torch on steroids. The metal wall's warranty will be terminated with extreme prejudice.

The clever Magnetically Insulated Inertial Confinement Fusion (MICF) scheme turns the concepts on their heads.

**FUEL PELLET**

Blue: Tungsten Shell (Metal Shell)

Green: Fusion Fuel (Halo)

Red Flare: Hollow Core (Plasma Core)

Red Arrow: Laser Beam

Green Arrow: Fusion Fuel Inner Radius

Blue Arrow: Fusion Fuel Outer Radius

Violet Arrow: Metal Shell Outer Radius**MAGNETIC FIELD FORMATION INSIDE FUEL PELLET**

Unlike IC fusion the fuel is not a naked pellet. Instead it is a layer of fuel *inside* a hollow sphere of tungsten. There is a single hole allowing the entry of a 2.59 megaJoule laser bolt. Inside the sphere the bolt vaporizes the fusion fuel into plasma. Fusion is ignited.

The clever part is the geometry of the bolt and the plasma create a magnetic field which thermally insulates the tungsten from the hot plasma. Instead of the confinement lifetime being dictated by the speed of sound in the plasma, it is instead dictated by the shock speed in the tungsten.

The bottom line the confinement time is about two orders of magnitude (100 times) longer than with MC or IC fusion. The plasma burns longer and produces more fusion energy. With Deuterium-Tritium (DT) fusion fuel the expected fusion energy gain factor is a whopping 724.

MICF ENGINE

with pellet detail at lower left

Like most IC fusion engines the MICF engine has four main parts: pellet injector, laser, reaction chamber, and magnetic nozzle.

Pellets are injected at a predetermined rate (ω) into the reaction chamber, where they are ignited by a laser bolt. The fusion energy turns the fuel and the metal shell into high velocity ions which expand adiabatically into immaterial magnetic nozzles where the ions escape and create thrust. "Adiabatically" means without touching any parts of the engine, touching would roast the engine and rob the ions of thrust.

For DT fuel ω has a maximum of **6,422 pellets per second**, the report analyzes a Mars rocket with a conservative ω of 100. For DT fuel the thrust is **412ω Newtons** (with an implied multiplication sign between the 412 and the ω). If ω is 100 the thrust is 41,200 N, at the maximum ω of 6,422 the thrust would be 2,645,864 N. If you tried popping off fuel pellets faster than the maximum ω the ions wouldn't have enough time to escape out the nozzle. Ions from several ignitions would start piling up inside the reaction chamber and things would turn ugly real fast.

DT fuel is the easiest known fuel to ignite into fusion (Lawson criterion of only 1) and the fusion products have an admirably high exhaust velocity. Unfortunately the blasted reaction machine-guns deadly neutrons in all directions, giving the crew cancer, transmuting the structure of the engine into dangerous radioisotopes, making structural members brittle like uncooked spaghetti, and heating up everything nearby like an open blast furnace. This is because 79% of the fusion energy is turned into neutrons.

Not to mention the fact that if 79% of the fusion energy is expressed as neutrons, this basically means that 79% of the fusion energy **is being totally wasted.** Neutrons do not contribute to the engine's thrust, at all.

Not that the MICF is special in this respect, pretty much any fusion spacecraft on this page will have the exact same problem with DT fuel.

But other fusion fuels have other problems. Deuterium-Helium^{3} has only 5% of its energy expressed as neutron, but the blasted stuff is sixteen times harder to ignite, needing sixteen times as much laser energy, which need more than sixteen times the mass of laser generators, which is very bad since Every Gram Counts. The report also looked at catalyzed Deuterium-Deuterium fusion, by looking at the table here you can see how disappointing it is. For one thing is it *thirty* times harder to ignite.

Going with DT fuel seems the lesser of two evils. At least the neutron heat can be disposed of with standard heat radiators. The heat gradient can at least be used to generate electricity so the 79% of the fusion energy is only *partially* wasted. Such power generation is typically 40% efficient. Not fantastic but worth-while.

**MERIDONAL MAGNETIC NOZZLE**

## Pegasus

*artwork by Daren Horley*

click for larger image

Pegasus | |
---|---|

Thrust Power | 118 GW |

ΔV | 80,000 m/s |

Engine | Fusion |

Chamber Temp | 100,000,000°C |

Exhaust Velocity | 952,000 m/s |

Thrust | 248,000 N |

Propellant Mass Flow | 0.26 kg/s |

Length | 1.3 km |

Total Lander Mass (payload) | 152 metric tons |

Food Mass | 57 metric tons |

Oxygen Mass | 80 metric tons |

Engine Mass | ?? |

Structral Mass | ?? |

Dry Mass | >289 metric tons |

Propellant Mass | <111 metric tons |

Wet Mass | 400 metric tons |

Mass Ratio | <1.38 |

The *Pegasus* is from a BBC science fiction "documentary" called Space Odyssey: Voyage to the Planets. The science was remarkably hard in the show, though details were scanty.

The ship design inspired the *Antares* for the much more mediocre show Defying Gravity.

The only hard facts about the *Pegasus* I could find were:

- The ship was "as long as 12 football fields."
*British*football pitch ×12, length is 1,300 meters - The ship mass is 400 metric tons
- The engine is powered by nuclear fusion
- Engine chamber temperature is "100 million degrees". Since this is a British show I'm going to presume Celsius, not Fahrenheit.
- Propellant is liquid hydrogen, heated by the fusion reaction
- Engine has 158 million horsepower. I calculate that as 118 gigawatts thrust power
- Ship has an aeroshield on the nose, presumably for aerobraking. Shield is composed of steel, carbon fibre, and beryllium.
- Ship has a "top speed" of 288,000 km/s. I'm going to presume that means a deltaV of 80,000 m/s
- Before the mission huge orbital propellant depots were sited around each planet by unmanned ships to increase ship's delta V
- Crew size of five
- Mission duration six years
- Interior volume could hold 10 jumbo jets. Best estimate of interior volume of a 747
*(that I could find with a five-minute Google search)*is 1,035 cubic meters, external volume close to that. So ship volume 10,350 cubic meters. - Consumables are 57 tonnes of food and 80 tonnes of oxygen.
- Cargo is five landing vehicles (each optimized for a different planet) with combined mass of 152 tonnes. Plus unmanned probes.

There is a centrifuge for artificial gravity. It provides 0.5 g's.

There is a storm cellar to shelter from solar proton storms. In addition, there is an artificial magnetic field to protect against Jupiter's radiation belts.

*Thus endeth the canon knowledge.*

Now here come my wild conjectures. Using similarly wild assumptions. Feel free to change my assumptions and recalculate.

Since this is a fusion engine that heats hydrogen, it is an Afterburner Fusion Engine.

It is stated that the wet mass is 400 metric tons. We do not know the mass of all the dry mass elements but the masses we are given total to 239 metric tons. The actual dry mass will be bigger.

Mass Ratio is wet mass divided by dry mass. So we know the ** maximum mass ratio is 1.38**, it will be lower than that.

Exhaust velocity is **V _{e} = ΔV / ln[R]** where

**V**is exhaust velocity,

_{e}**Δ**is delta V, and

*V***R**is mass ratio.

**Δ**is 80,000 m/s,

*V***R**is 1.38

*(or less)*so

**Exhaust velocity = 952,000 meters per second**.

Thrust is **F = (2 * F _{p}) / V_{e}** where

**F**is thrust,

**F**is thrust power, and

_{p}**V**is exhaust velocity.

_{e}**V**is 952,000 m/s, I'll assume that

_{e}**F**is 118,000,000,000 watts (118 gigawatts), so

_{p}**Thrust = 248,000 Newtons**.

Acceleration is **A = F / M _{c}** where

**A**is acceleration and

**M**is ship's current mass. Ship's initial mass is 400,000 kg (400 metric tons) and thrust is 248,000 N so

_{c}**Initial Acceleration = 0.62 m/s**or 0.063

*g*

Propellant mass flow is **mDot = F / V _{e}**, so

**Propellant Mass Flow = 0.26 kilograms per second**.

**LANDERS**

**HERMES**

Io Lander

Height: 10m, Mass 15 tonnes

*Hermes*, named after the Greek messenger god, is a single-person lander designed to land on Jupiter's Moon Io. It has enough air and water supplies to sustain the astronaut for 36 hours.

To protect itself from Jupiter's harshest radiation belts, the lander is specially built with radiation-hardened electronics and has two triangular windows made of aluminised 12-layer glass-polythene laminate with 10cm thick hydrogen-rich shield shutters.

*Hermes*also has five legs which are only strong enough to support it on the 1/6th gravity environment on Io's surface. Powerful floodlights are available to illuminate the landing site during an Ionian night.**CLYDE**

Pluto Lander

Height 15m, Mass 28 tonnes

The*Clyde*lander, named after the American astronomer who discovered Pluto — Clyde Tombaugh — is a nuclear-powered lander designed to maintained a crew of two for two weeks.

Its ultra-thin titanium skin with thick aerogel on the interior insulates it against the numbing chill of the planet.

Powerful floodlights illuminate the telescope construction site during the 26-hour Plutonian nights.**ARES**

Mars Lander

Height 25m, Mass 45 tonnes

Named after the Greek god of war,*Ares*has been designed to support a crew of three astronauts for up to a month. It carries an electronically powered Martian rover vehicle for surface exploration and has an inner core storm shelter formed from multi-laminate polythene.

The Mars Lander has a launch engine — toroidal aerospike — capable of reaching the Mars escape velocity of 5 km per second within five minutes.

It uses a paraglider canopy the size of a football field to steer itself towards the landing site.**MESSIER**

Comet Lander

Height 12m, Mass 29 tonnes

The*Messier*comet lander is named after the French astronomer who surveyed many comets during the 18th century. It carries bullet-proof shielding to protect it from debris clouds, and a set of three rocket-propelled harpoons to harness the comet.

Multiple motors positioned above and below the spacecraft push it towards the ultra-low gravity environment of the comet’s surface

It has also been designed with a multi-laminate self-repairing fuselage to offer extra protection against cometary debris.**ORPHEUS**

Height 25m, Mass 35 tonnes

The*Orpheus*lander, named after the poet and musician of Greek myth who visited the underworld to try to rescue his wife, has therefore been designed to withstand the harsh Venusian environment.

Its small porthole windows are hewn from a single diamond — the only material that can weather the corrosive sulphuric acid clouds.

The launch engine — a toroidal aerospike — is capable of reaching the Venus escape velocity of over 10km per second in just under eight minutes.

## Pulsed Fission Fusion

Engine | ||
---|---|---|

Engine | PuFF | |

Specific Impulse | 20,000 sec | |

Exhaust Velocity | 196,000 m/s | |

Thrust | 29,400 N | |

Thrust Power | 2.88 GW | |

Specific Power | 96 kW/kg | |

Mass Budget | ||

Subsystem | Mars Express (mT) | TAU Mission (mT) |

Magnetic Nozzle | 14.83 | 14.83 |

Radiation Shielding | 14.01 | 14.01 |

D-T Tankage | 5.0 | 5.0 |

Li Tankage | 1.45 | 0.94 |

Truss | 2.71 | 2.09 |

Other Primary Structures | 0.64 | 0.49 |

Secondary Structures | 0.13 | 0.10 |

Capacitor Banks | 2.10 | 2.10 |

Marx Generator Circuitry | 0.13 | 0.13 |

RCS Wet Mass | 1.03 | 0.79 |

Low Temp Heat Rejection | 1.30 | 1.30 |

Medium Temp Heat Rejection | 14.82 | 14.82 |

High Temp Heat Rejection | 1.26 | 1.26 |

LN2 Seed Coil Cooling | 8.41 | 8.41 |

Auxiliary Power | 4.40 | 4.40 |

Avionics | 0.39 | 0.39 |

Payload | 25.00 | 10.00 |

Dry Mass (less MGL) | 94.87 | 77.57 |

Mass Growth Allowance (30%) | 40.66 | 35.21 |

TOTAL DRY MASS | 135.53 | 112.78 |

Fuel | 56.02 | 37.03 |

TOTAL WET MASS | 191.55 | 149.81 |

Performance | ||

Mass Ratio | 1.41 | 1.33 |

ΔV | 67,300 m/s | 55,900 m/s |

*Uses same space frame as Hope Z-Pinch Fusion*

This is from The Pulsed Fission-Fusion (PuFF) Propulsion System and Phase I Final Report.

For purposes of the report, the PuFF engine was mounted on a Hope Z-Pinch Fusion design, and two missions were calculated. The Mars Express mission is a high-speed transit. The TAU (Thousand Astronomical Unit) mission is an interstellar precursor mission concept. The TAU would put a telescope about 950 AU further away from Sol than Pluto, where it could make ultra-precise parallax measurements to determine the distance to nearby stars.

Segment | Days |
---|---|

S1 Terra Escape | 0.6 |

S2 Trans Martian Insertion | 2.6 |

Coast | 31.4 |

S3 Mars Deceleration | 0.8 |

S4 Mars Capture | 2.1 |

TOTAL | 37 |

**Mars Express Mission**

Segment | Days |
---|---|

Terra Escape | 0.4 |

Deorbit | 1.4 |

Coast to Sol | 48 |

Sol Oberth Burn | 2.5 |

Milestone | Years |

Heliopause | 5 |

275 AU | 10 |

Solar Gravitational Lens | 20 |

1,000 AU | 36 |

**Thousand AU Mission**

## Santarius Fusion Rocket

D-^{3}HeTandem Mirror Engine | |
---|---|

Engine | Tandem mirror |

Fuel | Deuterium Helium 3 |

Thrust | 3,678 N to 37,500 N |

Specific Impulse | 10^{5} sec to200 sec |

Exhaust Velocity | 981,000 m/s to 1,962 m/s |

Specific Power (inc. radiators) | 1.2 kW/kg |

Fusion Power | 1,959 MW (2 TW) |

Input Power | 115 MW |

Thrust Power | 1,500 MW |

Thermal Power (not useable for plasma thrust) | 574 MW |

Total Mass | 1,250,000 kg |

Total Length | 113 m |

Central Cell Outer Radius | 1.0 m |

Neutron Wall Loading | 0.17 MW/m^{2} |

Central Cell on-axis magnetic field | 6.4 T |

Electron Density | 1.0×10^{21} m^{-3} |

^{3}He to Ddensity ratio | 1 |

Electron temperature | 87 keV |

Ion temperature | 105 keV |

Fuel Ion confinement time | 6 sec |

Ion confining electrostatic potential | 270 kV |

This is from Lunar He-3, fusion propulsion, and space development by John Santarius (1992). It uses a Tandem mirror engine.

Dr. Santarius figures that **Deuterium-Helium 3** is the best choice for fusion fuel. Deuterium-Deuterium has a lower power density. Deuterium-Tritium reaction emits lots of deadly neutrons and would require more radiation shield mass. Hydrogen-Boron is too difficult to ignite and produces almost all of its power as thermal bremsstrahlung radiation instead of the more desirable fast charged particles. Helium 3-Helium 3 is also far too difficult to ignite.

*Open-field magnetic confinement (Tandem mirror engine)*

From Critical Issues for SOAR: The Space Orbiting Advanced Fusion Power Reactor, Santarius et al (1988)

The fusion reaction chamber is linear, with a magnetic mirror closing each end. The mirror at the exhaust nozzle is weaker, so the star-core hot fusion reaction products shoot out the nozzle (we hope). Dr. Santarius puts it *"Thrust is produced by driving one end cell more vigorously to increase axial confinement on that end, thereby unbalancing the end loss of plasma."* Which is more precise than what I said, but harder to understand.

Each central cell has a 6.4 Tesla magnet made of a Niobium-Titanium (NbTi) superconductor.

The magnetic mirror end-cell magnets are much stronger. Each mirror has a 12 Tesla Niobium-tin (Nb_{3}Sn) magnet, and a 24 Tesla composite magnet (16 Tesla from a Nb_{3}Sn magnet plus 8 Tesla from a normal conducting copper electromagnet energized with 8 megawatts of power).

The engine can "shift gears" (trade thrust for specific impulse) over an unusually broad range by using three different operating modes. Specific impulse ranges from 10^{5} seconds to 200 seconds, while the thrust-to-weight ratio varies correspondingly from 3×10^{-4} to 0.03 (thrust of 375 Newtons to 37,500 Newtons).

**Fuel Plasma Exhaust:**The fusion reaction products are also the propellant. This has the highest specific-impulse/exhaust velocity, but the lowest thrust since the propellant mass-flow is so minuscule.

See Pure Fusion Engines**Mass-Augmented Exhaust:**a low-field magnetic valve is added and reaction mass is injected into the fusion reaction. This increases the thrust by upping the propellant mass flow, at the cost of cooling the exhaust which lowers the specific impulse.

See Afterburner Fusion Engines**Thermal Exhaust:**This uses the fusion reaction's thermal radiation (bremsstrahlung and synchrotron) to indirecty heat a blanket of reaction mass, which becomes the thrust exhaust. This has the lowest specific-impulse but highest thrust, similar to chemical propulsion.

See Dual-Mode Fusion Engine

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

**Reduction of flight time via fusion rocket**

Chemical Rocket vs Fusion in Sports Car Mode.

For each planetary mission, chem and fusion spacecraft have identical payload fractions*(equal to chem rocket from other graph)*.

The point is that the fusion rocket gets to the destination*much*quicker.**Increase of payload via fusion rocket**

Chemical Rocket vs Fusion in Truck Mode.

For each planetary mission, chem and fusion spacecraft have identical flight times*(equal to chem rocket from other graph)*.

The point is that the fusion rocket can haul*lots*more payload.**Payload fraction vs. Round-Trip time**

Terra-Mars mission

Specific Power*(α)*1 kW_{thrust}/kg

Left half of curve is Sports Car Mode, right half is Truck Mode

Chemical | D-^{3}He Fusion | |
---|---|---|

Payload (each way) | 11,800 | 11,800 |

Propellant | 47,200 | 2,000 |

Fusion Reactor | — | 1,000 |

D-^{3}He fuel burned | — | 0.08 |

Nonpayload mass orbited | 47,200 | 3,000 |

The point being that D-^{3}He fuel is so compact and energetic that the entire fusion spacecraft is **44,200 metric tons lighter** than the chemical spacecraft.

## VISTA

VISTA | |
---|---|

Wet Mass | 6,000,000 kg |

Dry Mass | 1,835,000 kg |

Mass Ratio | 3.27 |

ΔV | 200,000 m/s |

Thrust | 2.4 × 10^{5}N |

Exhaust Velocity | 170,000 m/s |

Thrust Power | 20.4 gigawatts |

Specific Power | 11.1 kW/kg |

Propulsion | Inertial Confinement D-T Fusion |

Width | 170 m |

Height | 100 m |

VISTA is the Vehicle of Interplanetary Space Transport Application, from a study by the Lawrence Livermore National Laboratory. It looks like a tiny flying saucer in the diagrams but it is actually freaking huge. Blasted spacecraft is taller than Godzilla.

Tiny pellets with a deuterium-tritium compount core surrounded by about 50 grams of propellant drop out of the bottom of the cone. At the pellet target position a battery of laser modules zap the pellet with enough energy to initiate a fusion explosion. The propellant blast bounces off the 12-Tesla superconducting magnetic coil to provide thrust. Thrust is throttled by varying the pellet detonation rate from 0 to 30 detonations per second.

With 100 metric tons of payload, VISTA can travel to Mars and back to Terra in six months flat.

Unfortunately about 75% of the fusion energy is wasted, creating no thrust (escaping as neutrons and x-rays). But the remaining 25% is more than powerful enough to give the ship 200 kilometers per second of delta V. The spacecraft is shaped like a cone in an attempt to minimize how much of the wasted energy hits the ship as deadly radiation (only about 4% of the wasted energy irradates the spacecraft).

*D-T VISTA Inertial Fusion Gigawatt Thruster patent card from the game High Frontier (Colonization expansion).*

*Artist Unknown**VISTA model created by ZZZ as a mod for Kerbal Space Program*