(cache) Engine List - Atomic Rockets

Introduction

Artwork by Dean Ellis (for The Last Hurrah Of The Golden Horde)

There is a nice basic overview of propulsion systems here.

You can spend lots of time researching spacecraft propulsion systems. But you are in luck, I've got some data for you. Most of this is from Philip Eklund's out of print boardgame Rocket Flight, the impressive Spaceship Handbook, and the indispensable Space Propulsion Analysis and Design. The rest is from various places I found around the internet, and no, I didn't keep track of where I got them. Use at your own risk.

Philip Eklund has a new boardgame out called High Frontier, which has the Atomic Rockets seal of approval (be sure to get the expansion pack as well). It has even more cutting-edge but scientifically accurate propulsion systems, which will eventually find there way onto this web page. (more details here, here, here, and here.)

If you don't like the values in the table, do some research to see if you can discover values you like better. Also note that the designs in the list are probably optimized for high exhaust velocities at the expense of thrust. There is a chance that some can be altered to give enough thrust for lift-off at the expense of exhaust velocity. Or you can just give up and go beg Mr. Tyco Bass for some atomic tri-tetramethylbenzacarbonethylene. Four drops should do the trick.

Some engines require electricity in order to operate. These have their megawatt requirements listed under "Power Requirements". With these engines, the Engine Mass value includes the mass of the power plant (unless the value includes "+pp", which means the mass value does NOT include the mass of the power plant). The power plant mass can be omitted if the spacecraft relies on beamed power from a remote power station. Alas, I could find no figures on the mass of the power plant. If the plant is nuclear, it probably has a mass of around 0.5 to 10 tons per megawatt. If it is beamed power the mass is of course zero. Efficiency is the percentage of the power requirements megawatts that are actually turned into thrust. The rest becomes waste heat and has to be removed with heat radiators.

T/W >1.0 = Thrust to Weight ratio greater than one? This boils down to: can this engine be used to take off from Terra's surface? If the answer is "no" use it only for orbit to orbit maneuvers. It is calculated by figuring if the given thrust can accelerate the engine mass greater than one gee of acceleration. As a rule of thumb, a practical spacecraft capable of lifting off from the Earth's surface will require a T/W of about 50 to 75.

Most propulsion systems fall into two categories: SUV and economy. SUV propulsion is like an SUV automobile: big and muscular, but the blasted thing gets a pathetic three miles to the gallon. Economy propulsion has fantastic fuel economy, but has trouble climbing low hills. In the world of rockets, good fuel economy means a high "specific impulse" (I_sp) and high exhaust velocity. And muscle means a high thrust.

The only vaguely possible propulsion system that has both high exhaust velocity and high thrust is the Nuclear Salt Water Rocket, and not a few scientist have questions about its feasibility. Well, actually there is also Project Orion, but that has other problems (see below). In science fiction, one often encounters the legendary "fusion drive" or "torchship", which is a high exhaust velocity + high thrust propulsion system that modern science isn't sure is even possible.

From **On Torchships** comment by Eric (2010)

The Drive Table

Download it here

All drives listed in the table whose names end in "MAX" require some sort of technological breakthrough to to prevent the engine from vaporizing and/or absurdly large reaction chamber sizes.

If these figures result in disappointing rocket performance, in the name of science fiction you can tweak some of them and claim it was due to a technological advance. You are allowed to tweak anything who's name does not end in "MAX". You can alter the Thrust, Engine Mass, and/or the Eff, but no other values. If there is a corresponding "MAX" entry for the engine you are tweaking, you cannot alter any of the values above the "MAX" entry (i.e., you are not allowed to tweak NTR-SOLID-DUMBO's thrust above 7,000,000, which is the value in the NTR-SOLID MAX entry).

The engines are sorted by thrust power, since that depends on both exhaust velocity and thrust. So engines that high in both of those parameters will be towards the end of the list. This is useful for designers trying to make spacecraft that can both blast-off from a planet's surface and do efficient orbital transfers.

If one was trying to design a more reasonable strictly orbit-to-orbit spacecraft one would want the engine list sorted by exhaust velocity. And surface-to-orbit designers would want the list sorted by thrust.

Propulsion	Code	Thrust Power (MW)	Exhaust Velocity (m/s)	Specific Impulse (s)	Thrust (N)	Engine Mass (kg)	T/W
DAWN mission NSTAR	ESTAT	1.37e-06	30,411	3,100	9.00e-05	26	3.60e-07
Resistojet	ETHERM	7.25e-04	2,900	296	1
Radioisotope	NTR SOLID	5.85e-03	7,800	795	2
ArcJet	ETHERM	2.00e-02	20,000	2,039	2
HOPE Cargo MPD	EMAG	4.32e-01	78,500	8,002	11
HOPE Tanker MPD	EMAG	4.32e-01	78,500	8,002	11
HOPE Crew MPD	EMAG	1	78,500	8,002	28
Magneto Inertial Fusion (low)	PULSE	3	50,420	5,140	103
VASIMR (low gear)	EMAG	6	29,000	2,956	400	10,000	0.004
VASIMR (high gear)	EMAG	6	294,000	29,969	40	10,000	4.08e-04
VASIMR (med gear)	EMAG	6	147,000	14,985	80	10,000	8.15e-04
Space Shuttle RCS	CHEM LIQUID	6	3,100	316	3,870	4	106.620
Mirror Steamer	BEAM	13	9,810	1,000	2,600	20,977	0.013
Monatomic-H MITEE	NTR SOLID	15	12,750	1,300	2,350	200	1.198
HybridMITEE	ETHERM	15	17,660	1,800	1,700	10,000	0.017
Propulsion	Code	Thrust Power (MW)	Exhaust Velocity (m/s)	Specific Impulse (s)	Thrust (N)	Engine Mass (kg)	T/W
AIM	PULSE	16	598,000	60,958	55
Solar Moth	BEAM	18	9,000	917	4,000	100	4.077
Umbrella Ship	ESTAT	20	80,442	8,200	490
ArcJet	ETHERM	31	19,620	2,000	3,200	22,369	0.015
Hall Effect	ESTAT	32	19,620	2,000	3,300	85,469	0.004
Pulsed Plasmoid Thruster	PULSE	43	78,480	8,000	1,100	83,611	0.001
Ponderomotive VASIMR	EMAG	44	39,240	4,000	2,250	43,796	0.005
Wakefield E-Beam	ETHERM	45	19,620	2,000	4,600	41,837	0.011
Ablative Laser	BEAM	47	39,240	4,000	2,400	22,222	0.011
MPD T-Wave	EMAG	47	78,480	8,000	1,200	82,675	0.001
Tungsten Resistojet	ETHERM	49	9,810	1,000	9,900	42,601	0.024
NASA space tug	CHEM LIQUID	49	4,400	449	22,400	199,600	0.011
Mass Driver	OTHER	51	9,810	1,000	10,400	163,000	0.007
Ion Drive	ESTAT	57	78,480	8,000	1,444	120,149	0.001
MET Steamer Amplitrons	ETHERM	59	9,810	1,000	12,000	123,302	0.010
NERVA (CO or N2)	NTR SOLID	65	2,649	270	49,000	10,000	0.499
Basic MITEE	NTR SOLID	69	9,810	1,000	14,000	200	7.136
NERVA (CO2)	NTR SOLID	81	3,306	337	49,000	10,000	0.499
NERVA (H2O)	NTR SOLID	99	4,042	412	49,000	10,000	0.499
HOPE FFRE	NTR FRAG	111	5,170,000	527,013	43
Werka FFRE	NTR FRAG	111	5,170,000	527,013	43	113,400	3.90e-05
NERVA (NH3)	NTR SOLID	125	5,101	520	49,000	10,000	0.499
D-D Fusion Inertial	PULSE	126	78,480	8,000	3,200	243,333	0.001
NERVA (CH4)	NTR SOLID	155	6,318	644	49,000	10,000	0.499
Dusty Plasma (550AU)	NTR FRAG	165	15,000,000	1,529,052	22	9,000	2.49e-04
Propulsion	Code	Thrust Power (MW)	Exhaust Velocity (m/s)	Specific Impulse (s)	Thrust (N)	Engine Mass (kg)	T/W
Colloid Thruster	ESTAT	172	43,000	4,383	8,000	20,000	0.041
LARS	NTR LIQUID	196	19,620	2,000	20,000	1,000	2.039
NERVA (H2)	NTR SOLID	198	8,093	825	49,000	10,000	0.499
Laser Thermal	BEAM	260	40,000	4,077	13,000	20,000	0.066
Mass Driver	OTHER	300	30,000	3,058	20,000	150,000	0.014
Lighter	CHEM LIQUID	309	4,410	450	140,000
LANTR (high gear)	NTR SOLID	309	9,221	940	67,000
Magneto Inertial Fusion (high)	PULSE	348	50,420	5,140	13,800
SNRE Peewee	NTR SOLID	367	8,829	900	73,000	2,400	3.06
H-B Cat Inertial	PULSE	369	156,960	16,000	4,700	65,089	0.007
Aluminum/LOX rocket	CHEM LIQUID	388	2,649	270	292,600	56,000	0.533
NERVA (H)	NTR SOLID	392	16,000	1,631	49,000	10,000	0.499
Kuck Mosquito	CHEM LIQUID	484	4,400	449	220,000
Vortex Confined (H2)	NTR GAS OP	494	19,620	2,000	50,400	114,116	0.045
LH2/LOX rocket	CHEM LIQUID	540	4,905	500	220,000	26,667	0.841
VCR Light Bulb (H2)	NTR GAS CL	553	19,620	2,000	56,400	72,566	0.079
LANTR (low gear)	NTR SOLID	584	6,347	647	184,000
Dual-mode Fission (H2)	NTR SOLID	612	9,810	1,000	124,700	33,000	0.385
Polywell Fusor	FUSION	658	19,620	2,000	67,100	54,000	0.127
Cermet NERVA (H2)	NTR SOLID	659	9,810	1,000	134,400	32,546	0.421
Z-Pinch Microfission	PULSE	667	156,960	16,000	8,500	193,333	0.004
Dual-mode PB (H2)	NTR SOLID	847	9,810	1,000	172,700	58,000	0.304
Bimodal NTR Solid (NASA)	NTR SOLID	898	8,980	915	200,000	6,672	3.056
Ion	ESTAT	1,050	210,000	21,407	10,000	400,000	0.003
D-T Fusion	FUSION	1,188	22,000	2,243	108,000	10,000	1.101
NERVA Deriv (H2)	NTR SOLID	1,350	8,085	824	334,061	10,100	3.372
Propulsion	Code	Thrust Power (MW)	Exhaust Velocity (m/s)	Specific Impulse (s)	Thrust (N)	Engine Mass (kg)	T/W
Antimatter Bottle	PULSE	1,362	78,480	8,000	34,700	180,000	0.020
Metastable He*	CHEM	1,376	43,000	4,383	64,000	10,000	0.652
Resuable Nuclear Shuttle	NTR SOLID	1,376	8,000	815	344,000
Metastable Helium	CHEM	1,567	29,430	3,000	106,500
n-6Li Microfission	PULSE	1,570	156,960	16,000	20,000	106,667	0.019
Pebble Bed (H2)	NTR SOLID	1,590	9,530	971	333,617	1,700	20.005
Vapor Core (H2)	NTR VAPOR	1,617	9,800	999	330,000	6,830	4.925
Twisted ribbon NTR	NTR SOLID	1,650	9,420	960	330,000	5,260	6.4
3He-D Mirror Cell	FUSION	1,664	313,920	32,000	10,600	106,667	0.010
Cermet (H2)	NTR SOLID	2,030	9,120	930	445,267	9,000	5.043
Tokamak MC	FUSION	2,231	66,800	6,809	66,800	197,000	0.035
Widmer Mars Mission	NTR SOLID	2,320	8,000	815	580,000
Antimatter Solid max	AM SOLID	2,374	10,791	1,100	440,000
Dusty Plasma (0.5LY)	NTR FRAG	2,580	15,000,000	1,529,052	344	9,000	0.004
Proton RD-253 x1	CHEM LIQUID	2,836	3,100	316	1,830,000	1,260	148.051
Discovery II	FUSION	3,123	347,000	35,372	18,000
MPD	EMAG	3,140	314,000	32,008	20,000	1,540,000	0.001
HOPE Z-Pinch	PULSE	3,617	189,780	19,346	38,120	95,138	0.041
HELIOS 2nd Stage	NTR SOLID	3,826	7,800	795	981,000
NTR Gas/Closed (H2)	NTR GAS CL	4,540	20,405	2,080	445,000	56,800	0.799
Dumbo (CO or N2)	NTR SOLID	4,636	2,649	270	3,500,000	5,000	71.356
Atomic V-2	NTR SOLID	4,714	8,980	915	1,050,000	4,200	25.484
ORION Fission	PULSE	5,654	43,000	4,383	263,000	200,000	0.134
Dumbo (CO2)	NTR SOLID	5,786	3,306	337	3,500,000	5,000	71.356
THS Fusion Pulse high gear	PULSE	6,000	300,000	30,581	40,000	4,000	1.019
THS Fusion Pulse low gear	PULSE	6,000	150,000	15,291	80,000	4,000	2.039
Propulsion	Code	Thrust Power (MW)	Exhaust Velocity (m/s)	Specific Impulse (s)	Thrust (N)	Engine Mass (kg)	T/W
Dumbo (H2O)	NTR SOLID	7,074	4,042	412	3,500,000	5,000	71.356
Dumbo (NH3)	NTR SOLID	8,927	5,101	520	3,500,000	5,000	71.356
ORION Fusion	PULSE	10,658	73,000	7,441	292,000	200,000	0.149
Dumbo (CH4)	NTR SOLID	11,056	6,318	644	3,500,000	5,000	71.356
Saturn-V F-1 x1	CHEM LIQUID	11,541	2,982	304	7,740,500	9,153	86.206
ACMF (ICAN-II)	PULSE	11,919	132,435	13,500	180,000	27,000	0.680
Space Shuttle SSME x3	CHEM LIQUID	12,115	4,444	453	5,452,200	9,531	58.313
Dumbo (H2)	NTR SOLID	14,163	8,093	825	3,500,000	5,000	71.356
Solid rocket	CHEM SOLID	15,000	3,000	306	10,000,000
Proton RD-253 x6	CHEM LIQUID	16,228	3,100	316	10,470,000	7,560	141.174
VISTA	PULSE	20,400	170,000	17,329	240,000
Project Orion	PULSE	21,731	19,620	2,000	2,215,200	203,680	1.109
Nuclear DC-X NERVA	NTR SOLID	27,272	9,810	1,000	5,560,000	199,600	2.840
Dumbo (H)	NTR SOLID	28,000	16,000	1,631	3,500,000	5,000	71.356
Mini-Mag Orion (DRM-3)	PULSE	29,853	93,000	9,480	642,000	199,600	0.328
Antimatter Plasma (H2O)	AM PLASMA	29,890	980,000	99,898	61,000	500,000	0.012
H-B Fusion	FUSION	29,890	980,000	99,898	61,000	300,000	0.021
Mini-Mag Orion (DRM-1)	PULSE	29,906	93,164	9,497	642,000	119,046	0.550
APCP Space Shuttle SRB x2	CHEM SOLID	31,200	2,600	265	24,000,000	1,180,000	2.073
ORION USAF 10m	PULSE	32,900	32,900	3,354	2,000,000	107,900	1.889
NTR Solid MAX	NTR SOLID	42,000	12,000	1,223	7,000,000	15,000	47.571
Gasdynamic Mirror	FUSION	46,060	1,960,000	199,796	47,000
Nuclear DC-X LANTR	NTR SOLID	49,206	5,900	601	16,680,000	199,600	8.519
NTR Liquid max	NTR GAS OP	56,000	16,000	1,631	7,000,000	70,000	10.194
Luna	NTR LIQUID	56,650	10,300	1,050	11,000,000	9,000	124.589
Propulsion	Code	Thrust Power (MW)	Exhaust Velocity (m/s)	Specific Impulse (s)	Thrust (N)	Engine Mass (kg)	T/W
Saturn-V F-1 x5	CHEM LIQUID	58,054	3,000	306	38,702,500	45,765	86.206
NTR Gas/Open (H2)	NTR GAS OP	61,250	35,000	3,568	3,500,000	200,000	1.784
Tanker	NTR GAS OP	61,803	35,316	3,600	3,500,000
AV:T high gear	PULSE	102,138	832,928	84,906	245,250
NTR Gas/Open 2nd Gen	NTR GAS OP	125,000	50,000	5,097	5,000,000	200,000	2.548
Mini-Mag Orion	PULSE	146,795	157,000	16,004	1,870,000	199,600	0.955
NTR Gas MAX	NTR GAS OP	147,000	98,000	9,990	3,000,000	15,000	20.387
NTR Gas/Coaxial (H2)	NTR GAS OP	157,156	17,658	1,800	17,800,000	127,000	14.287
Antimatter Plasma (H2)	AM PLASMA	192,080	7,840,000	799,185	49,000	500,000	0.010
He3-D Fusion	FUSION	192,080	7,840,000	799,185	49,000	1,200,000	0.004
MC-Fusion MAX	FUSION	200,000	8,000,000	815,494	50,000	600	8.495
Salt-water Zubrin	NTR GAS OP	341,266	78,480	8,000	8,696,900	495,467	1.789
NSWR (20% UTB)	NTR GAS OP	425,700	66,000	6,728	12,900,000	33,000	39.848
Liberty Ship	NTR GAS CL	560,700	30,000	3,058	37,380,000	378,000	10.080
Cargo Tug Slingshot	ESTAT	764,400	280,000	28,542	5,460,000
IBS Agamemnon	ESTAT	1,100,000	220,000	22,426	10,000,000
ORION battleship	PULSE	1,560,000	39,000	3,976	80,000,000	1,700,000	4.797
AV:T low gear	PULSE	2,541,895	104,116	10,613	48,828,125
Epstein Drive	FUSION	5,500,000	11,000,000	1,100,000	1,000,000
Propulsion	Code	Thrust Power (MW)	Exhaust Velocity (m/s)	Specific Impulse (s)	Thrust (N)	Engine Mass (kg)	T/W
ORION 10k ton adv	PULSE	24,000,000	120,000	12,232	400,000,000	3,250,000	12.546
NSWR (90% UTB) MAX	NTR GAS OP	30,550,000	4,700,000	479,103	13,000,000
ORION MAX	PULSE	39,200,000	9,800,000	998,981	8,000,000	8,000	101.937
Antimatter Beam MAX	AM BEAM	500,000,000	100,000,000	10,193,680	10,000,000	10,000	101.937
IC-Fusion MAX	PULSE	500,000,000	10,000,000	1,019,368	100,000,000	1,000,000	10.194

Antimatter

Antimatter requirements for different propulsion concepts
From Antimatter Production for Near-term Propulsion Applications
click for larger image
Propellant requirements for various antimatter propulsion concepts
Solid Core (1,000 secs)
Gas Core (2,000 secs)
Plasma Core (10⁵ secs)
Beamed Core (10⁷ secs)
ACMF (13,500 secs)
AIM (61,000 - 67,000 secs)
From Antimatter Production for Near-term Propulsion Applications
click for larger image
Antiproton mass requirements for various antimatter propulsion concepts
From Antimatter Production for Near-term Propulsion Applications
click for larger image

Solid Core

AM: Solid
Thrust Power	2.4 GW
Exhaust velocity	10,791 m/s
Thrust	440,000 n
T/W >1.0	yes

Basically a NERVA design where a tungsten target replaces the reactor. 13 micrograms per second of antiprotons are annihilated. The gamma rays and pions are captured in the tungsten target, heating it. The tungsten target in turn heats the hydrogen. Produces high thrust but the specific impulse is limited due to material constraints (translation: above a certain power level the blasted tungsten melts)

Image courtesy of Positronics Research, LLC

Gas Core

AM: Gas
Exhaust Velocity	24,500 m/s
Specific Impulse	2,497 s
Fuel	Antimatter: antihydrogen
Reactor	Liquid Core
Remass	Water
Remass Accel	Thermal Accel: Reaction Heat
Thrust Director	Magnetic Nozzle

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
Thrust	61,000 N
Thrust Power	29.9 GW
Mass Flow	0.06 kg/s
T/W	0.01
Remass	Water
Specific Power	17 kg/MW

AM: Plasma
Hydrogen
Exhaust Velocity	7,840,000 m/s
Specific Impulse	799,185 s
Thrust	49,000 N
Thrust Power	0.2 TW
Mass Flow	0.01 kg/s
T/W	0.01
Remass	Liquid Hydrogen
Specific Power	3 kg/MW

AM: Plasma
Both
Total Engine Mass	500,000 kg
Fuel	Antimatter: antihydrogen
Reactor	Plasma 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 = (T_normalized / ΔT) * B_vol

where

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

The propellant mass flow is:

mDot_p = (m_p * n_p * B_vol) / ΔT

where

mDot_p = hydrogen propellant mass flow (kg)
m_p = atomic mass of hydrogen (kg) = 1.672621777×10⁻²⁷
n_p = hydrogen density (atoms/cm³)
B_vol = volume of magnetic bottle (cm³)
ΔT = pulse rate (seconds)

And obviously the antimatter mass flow is:

mDot_p = (m_p * n_p * B_vol) / ΔT

where

mDot_p = antiproton fuel mass flow (kg)
m_p = rest mass of antiproton (kg) = 1.672621777×10⁻²⁷
n_p = antiproton density (antiproton/cm³)
B_vol = 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).

Beam Core

AM: Beam
Exhaust Velocity	100,000,000 m/s
Specific Impulse	10,193,680 s
Thrust	10,000,000 N
Thrust Power	500.0 TW
Mass Flow	0.10 kg/s
Total Engine Mass	10,000 kg
T/W	102
Fuel	Antimatter: antihydrogen
Reactor	Antimatter Catalyzed
Remass	Reaction Products
Remass Accel	Annihilation
Thrust Director	Magnetic Nozzle
Specific Power	2.00e-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.

Image courtesy of NASA

Positron Ablative

Positron Ablative
Exhaust velocity	49,000 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

Image courtesy of Positronics Research, LLC

Beamed Power

Laser Thermal

Laser Thermal
Exhaust Velocity	40,000 m/s
Specific Impulse	4,077 s
Thrust	13,000 N
Thrust Power	0.3 GW
Mass Flow	0.33 kg/s
Total Engine Mass	20,000 kg
T/W	0.07
Thermal eff.	30%
Total eff.	30%
Fuel	External Laser
Reactor	Collector Mirror
Remass	Seeded Hydrogen
Remass Accel	Thermal Accel: Collector Mirror
Thrust Director	Nozzle
Specific Power	77 kg/MW

Similar to Solar Moth, but uses a stationary ground or space-station based laser instead of the sun. Basically the propulsion system leaves the power plant at home and relies upon a laser beam instead of an incredibly long extension cord.

As a rule of thumb, the collector mirror of a laser thermal rocket can be much smaller than a comparable solar moth, since the laser beam probably has a higher energy density than natural sunlight.

With the mass of the power plant not actually on the spacecraft, more mass is available for payload. Or the reduced mass makes for a higher mass ratio to increase the spacecraft's delta V. The reduced mass also increases the acceleration. In some science fiction novels, combat "motherships" will have batteries of lasers, used to power hordes of ultra-high acceleration missiles and/or fighter spacecraft.

The drawback include the fact that there is a maximum effective range you can send a worthwhile laser beam from station to spacecraft, and the fact that the spacecraft is at the mercy of whoever is controlling the laser station.

Propellant is hydrogen seeded with alkali metal. As always the reason for seeding is that hydrogen is more or less transparent so the laser beam will mostly pass right through without heating the hydrogen. The seeding make the hydrogen more opaque so the blasted stuff will heat up. Having said that, the Mirror Steamer has an alternate solution.

The equations for delta V and mass ratio are slightly different for a Solar Moth or Laser Thermal rocket engine:

Δ_v = sqrt((2 * Bp * Bε) / mDot) * ln[R]

R = e^{(Δ_v/sqrt((2 * Bp * Bε) / mDot)}

where

Δ_v = ship's total deltaV capability (m/s)
R = ship's mass ratio
Bp = Beam power (watts) of either laser beam or solar energy collected
Bε = efficiency with which engine converts beam power into exhaust kinetic energy (0.0 to 1.0, currently about 0.3)
ln[x] = natural logarithm of x, the "ln" key on your calculator
e^x = antilog base e or inverse of natural logarithm of x, the "e^x" key on your calculator

Mirror Steamer Robonaut patent card from the game High Frontier.

*From High Frontier. Artwork by Philip Eklund*

Ablative Laser
Exhaust Velocity	39,240 m/s
Specific Impulse	4,000 s
Thrust	2,400 N
Thrust Power	47.1 MW
Mass Flow	0.06 kg/s
Total Engine Mass	22,222 kg
T/W	0.01
Frozen Flow eff.	88%
Thermal eff.	90%
Total eff.	79%
Fuel	External Laser
Reactor	Collector Mirror
Remass	Graphite
Remass Accel	Thermal Accel: Collector Mirror
Thrust Director	Nozzle
Specific Power	472 kg/MW

Laser Sail

A Laser Sail is a photon sail beam-powered by a remote laser installation.

As an important point, the practical minimum acceleration for a spacecraft is about 5 milligees. Otherwise it will take years to change orbits. Photo sails can only do up to 3 milligees, but a laser sail can do 5 milligees easily.

Solar Moth

Solar Moth
Exhaust Velocity	9,000 m/s
Specific Impulse	917 s
Thrust	4,000 N
Thrust Power	18.0 MW
Mass Flow	0.44 kg/s
Total Engine Mass	100 kg
T/W	4
Thermal eff.	65%
Total eff.	65%
Fuel	Solar Photons
Reactor	Collector Mirror
Remass	Liquid Hydrogen
Remass Accel	Thermal Accel: Collector Mirror
Thrust Director	Nozzle
Specific Power	6 kg/MW

Solar thermal rocket. 175 meter diameter aluminum coated reflector concentrates solar radiation onto a window chamber hoop boiler, heating and expanding the propellant through a regeneratively-cooled hoop nozzle. The concentrating mirror is one half of a giant inflatable balloon, the other half is transparent (so it has an attractive low mass).

The advantage is that you have power as long as the sun shines and your power plant has zero mass (as far as the spacecraft mass is concerned). The disadvantage is it doesn't work well past the orbit of Mars. The figures in the table are for Earth orbit.

The solar moth might be carried on a spacecraft as an emergency propulsion system, since the engine mass is so miniscule.

The equations for delta V and mass ratio are slightly different for a Solar Moth or Laser Thermal rocket engine:

Δ_v = sqrt((2 * Bp * Bε) / mDot) * ln[R]

R = e^{(Δ_v/sqrt((2 * Bp * Bε) / mDot)}

where

Δ_v = ship's total deltaV capability (m/s)
R = ship's mass ratio
Bp = Beam power (watts) of either laser beam or solar energy collected
Bε = efficiency with which engine converts beam power into exhaust kinetic energy (0.0 to 1.0)
ln[x] = natural logarithm of x, the "ln" key on your calculator
e^x = antilog base e or inverse of natural logarithm of x, the "e^x" key on your calculator

For the Solar Moth in the data block Bε = 0.63, for the Mirror Steamer Bε = 0.87

Bp = M_area * (☉_constant * (1 / (☉_dist²)))

where

Bp = Beam power (watts) of solar energy collected
M_area = total area of collecting mirrors (m²)
☉_dist = distance between Sun and spacecraft (Astronomical Units, Earth = 1.0)
☉_constant = Solar Constant (w/m²)

1.0 astronomical units is defined as 149,597,870,700 meters.

1 / (☉_dist²) is the sunlight energy density. In Earth's orbit, the density is 1.0, at Mars orbit it is 0.44 (44%), at Jupiter orbit it is 0.037, at Neptune orbit it is 0.001, at Mercury orbit it is 6.68

The Solar Constant varies from 1,361 w/m² at solar minimum and 1,362 w/m² at solar maximum.

Sunlight bounces from primary reflector to secondary reflector. Then it travels to the "transfer optics", a diagonal mirror that bounces the sunlight into the thermal collector on the rocket engine.
From Solar Rocket System Concept Analysis (1979)
Off-axis parabolic inflatable mirror concentrates sunlight on the cavity aperture of the rocket engine.
From Solar Rocket System Concept Analysis (1979)
From Solar Rocket System Concept Analysis (1979)
Click for larger image. Apologies for how fuzzy the image is.
From Solar Rocket System Concept Analysis (1979)
Interior mirrored surface prevents misfocused sunlight from frying the spacecraft like an ant under a magnifying glass on a sunny day.
From Solar Rocket System Concept Analysis (1979)
From Solar Rocket System Concept Analysis (1979)

*Mirror Steamer Robonaut patent card from the game High Frontier.*

Rocketdyne heat exchanger thruster. Hydrogen propellant. Temperature 2,700 K. Thrust 3.7 newtons. Exhaust velocity 7,800 m/sec.
From NASA SP-509
Robot Asteroid Prospector (RAP)
Solar thermal propulsion (the two mirrored dishes, solar moth with water propellant) also supplies process heat for mining and refining, and one megawatt of electricity from a Stirling cycle engine.
From Asteroid Mining AIAA-2013-5304
Art by Frank Tinsley. Click for larger image
Painting by Professor Sol Dember

Chemical

A barely contained chemical explosive. Noted for very high thrust and very low exhaust velocity. One of the few propulsion systems where the fuel and the propellant are the same thing. There is a list of chemical propellants here

Solid Rocket

Space Shuttle solid rocket boosters

Space Shuttle SRB x2
Exhaust Velocity	2,600 m/s
Specific Impulse	265 s
Thrust/Engine	12,000,000 N
Number Thrusters	x2
Thrust	24,000,000 N
Thrust Power	31.2 GW
Mass Flow	9,231 kg/s
Total Engine Mass	1,180,000 kg
T/W	2
Fuel	Chemical Solid: APCP
Reactor	Combustion Chamber
Remass	Reaction Products
Remass Accel	Thermal Accel: Reaction Heat
Thrust Director	Nozzle
Specific Power	38 kg/MW

Liquid Rocket

Methane-Oxygen

Chemical: Methane-Oxygen
Exhaust Velocity	3,700 m/s
Specific Impulse	377 s

Methane and oxygen are burned resulting in an unremarkable specific impulse of about 377 seconds. However, this is the highest performance of any chemical rocket using fuels that can be stored indefinitely in space. Chemical rockets with superior specific impulse generally use liquid hydrogen, which will eventually leak away by escaping between the the molecules composing your fuel tanks. Liquid methane and liquid oxygen will stay put.

People tend to sneer at chemical rockets because of their abysmal specific impulse. Surprisingly, they are perfectly adequate for missions to Mars or cis-Lunar space provided there is a network of orbital propellant depots suppled by in-situ resource allocation. See Sabatier reaction below.

Hydrogen-Fluorine

Chemical: LH2/Fluorine
Exhaust Velocity	4,700 m/s
Specific Impulse	479 s

Hydrogen-Oxygen

Chemical: LH2/LOX
Exhaust Velocity	4,400 m/s
Specific Impulse	449 s
Space Shuttle SSME x3
Propulsion System	Chemical: LH2/LOX
Exhaust Velocity	4,444 m/s
Specific Impulse	453 s
Thrust/Engine	1,817,400 N
Number Thrusters	x3
Thrust	5,452,200 N
Thrust Power	12.1 GW
Mass Flow	1,227 kg/s
Total Engine Mass	9,531 kg
T/W	58
Specific Power	1 kg/MW
NASA space tug
Propulsion System	Chemical: LH2/LOX
Thrust	22,400 N
Thrust Power	49.3 MW
Mass Flow	5 kg/s
Total Engine Mass	199,600 kg
T/W	0.01
Wet Mass	32,000 kg
Dry Mass	14,000 kg
Mass Ratio	2.29 m/s
ΔV	3,637 m/s
Specific Power	4,050 kg/MW
Lighter
Propulsion System	Chemical: LH2/LOX
Exhaust Velocity	4,410 m/s
Specific Impulse	450 s
Thrust	140,000 N
Thrust Power	0.3 GW
Mass Flow	32 kg/s
Wet Mass	56,300 kg
Dry Mass	25,898 kg
Mass Ratio	2.17 m/s
ΔV	3,424 m/s
Kuck Mosquito
Propulsion System	Chemical: LH2/LOX
Exhaust Velocity	4,400 m/s
Specific Impulse	449 s
Thrust	220,000 N
Thrust Power	0.5 GW
Mass Flow	50 kg/s
Wet Mass	350,000 kg
Dry Mass	100,000 kg
Mass Ratio	3.50 m/s
ΔV	5,512 m/s

Hydrogen and oxygen are burned resulting in close to the theoretical maximum specific impulse of about 450 seconds. However, liquid hydrogen cannot be stored permanently in any tank composed of matter. The blasted stuff will escape atom by atom between the molecules composing the fuel tanks.

Space Shuttle main engines

NASA space tug
Kuck Mosquito

Lighter

LH2/LOX Rocket
Exhaust Velocity	4,905 m/s
Specific Impulse	500 s
Thrust	220,000 N
Thrust Power	0.5 GW
Mass Flow	45 kg/s
Total Engine Mass	26,667 kg
T/W	0.84
Frozen Flow eff.	55%
Thermal eff.	98%
Total eff.	54%
Fuel	Chemical: Single-H/LOX
Reactor	Combustion Chamber
Remass	Reaction Products
Remass Accel	Thermal Accel: Reaction Heat
Thrust Director	Nozzle
Specific Power	49 kg/MW

RP-1 - Oxygen

Chemical: RP-1/LOX
Exhaust Velocity	3,500 m/s
Specific Impulse	357 s
Saturn-V F-1 x1
Exhaust Velocity	2,982 m/s
Specific Impulse	304 s
Thrust	7,740,500 N
Thrust Power	11.5 GW
Mass Flow	2,596 kg/s
Total Engine Mass	9,153 kg
T/W	86
Fuel	Chemical: RP-1/LOX
Reactor	Combustion Chamber
Remass	Reaction Products
Remass Accel	Thermal Accel: Reaction Heat
Thrust Director	Nozzle
Specific Power	1 kg/MW
Saturn-V F-1 x5
Exhaust Velocity	3,000 m/s
Specific Impulse	306 s
Thrust/Engine	7,740,500 N
Number Thrusters	x5
Thrust	38,702,500 N
Thrust Power	58.1 GW
Mass Flow	12,901 kg/s
Total Engine Mass	45,765 kg
T/W	86
Fuel	Chemical Liquid: RP-1/LOX
Specific Power	1 kg/MW

RP-1 is Rocket Propellant-1 or Refined Petroleum-1) is a highly refined form of kerosene outwardly similar to jet fuel, used as rocket fuel. It is not as powerful as liquid hydrogen but it is a whole lot less trouble. Compared to LH₂ it is cheaper, stabler at room temperature, non-cryogenic less of an explosive hazard, and denser.

NASA uses it a lot.

Saturn-V F-1
Saturn-V F-1

Saturn-V F-1
Saturn-V F-1

Hypergolic Fuels

Chemical: UDMH/N₂0₄
Exhaust Velocity	3,267 m/s
Specific Impulse	333 s
Chemical: MMH/N₂0₄
Exhaust Velocity	3,296 m/s
Specific Impulse	336 s
Space Shuttle RCS
Thrust	3,870 N
Thrust Power	6.0 MW
Mass Flow	1 kg/s
Total Engine Mass	4 kg
T/W	107
Fuel	Chemical: MMH/N204
Specific Power	1 kg/MW
Proton RD-253 x1
Thrust	1,830,000 N
Thrust Power	2.8 GW
Mass Flow	590 kg/s
Total Engine Mass	1,260 kg
T/W	148
Fuel	Chemical: UDMH/N204
Specific Power	0.44 kg/MW
Proton RD-253 x6
Thrust/Engine	1,745,000 N
Number Thrusters	x6
Thrust	10,470,000 N
Thrust Power	16.2 GW
Mass Flow	3,377 kg/s
Total Engine Mass	7,560 kg
T/W	141
Fuel	Chemical: UDMH/N204
Specific Power	0.47 kg/MW

Unsymmetrical dimethylhydrazine (UDMH) + nitrogen tetroxide (N₂0₄ or "NTO") and Monomethylhydrazine (MMH) + NTO are very important chemical rocket fuels.

Both are hypergolic, meaning the stuff explodes on contact with each other instead of needing a pilot light or other ignition system as do other chemical fuels. This means one less point of failure and one less maintenance nightmare on your spacecraft. Being hypergolic also prevents large amounts of fuel and oxidizer accumulating in the nozzle, which can cause a hard start or engine catastrophic failure (fancy term for "engine goes ka-blam!"). It is also non-cryogenic, liquid at room temperature and pressure. This means it is a storable liquid propellant, suitable for space missions that last years.

"Ah, what's the catch?" you ask.

The catch is that the mix is hideously corrosive, toxic, and carcinogenic. It is also easily absorbed through the skin. If UDMH escapes into the air it reacts to form dimethylnitrosamine, which is a persistent carcinogen and groundwater pollutant. MMH is only fractionally less bad.

This is the reason for all those technicians wearing hazmat suits at Space Shuttle landings. The Shuttle used MMH/NTO in its reaction control thrusters. Upon landing the techs had to drain the hellish stuff before it leaked and dissoved some innocent bystander.

In the words of Troy Campbell, hypergolic fuels are tanks full of explosive cancer.

Hybrid Rocket

Aluminum-Oxygen

Chemical: Aluminum-Oxygen
Exhaust Velocity	2,800 m/s
Specific Impulse	285 s
Fuel	Chemical: Aluminum/LOX
Reactor	Combustion Chamber
Remass	Reaction Products
Remass Accel	Thermal Accel: Reaction Heat
Thrust Director	Nozzle

Aluminum and oxygen are burned resulting in an unremarkable specific impulse of about 285 seconds. However, this is of great interest to any future lunar colonies. Both aluminum and oxygen are readily available in the lunar regolith, and such a rocket could easily perform lunar liftoff, lunar landing, or departure from a hypothetical L5 colony for Terra (using a lunar swingby trajectory). The low specific impulse is more than made up for by the fact that the fuel does not have to be imported from Terra. It can be used in a hybrid rocket (with solid aluminum burning in liquid oxygen), or using ALICE (which is a slurry of nanoaluminium powder mixed in water then frozen).

Of course the aluminum oxide in lunar regolith has to be split into aluminum and oxygen before you can use it as fuel. But Luna has plenty of solar power. As a rule of thumb, in space, energy is cheap but matter is expensive.

Image courtesy of NASA

From High Frontier. Artwork by Philip Eklund
From High Frontier. Artwork by Philip Eklund

Aluminum/LOX rocket
Exhaust Velocity	2,649 m/s
Specific Impulse	270 s
Thrust	292,600 N
Thrust Power	0.4 GW
Mass Flow	110 kg/s
Total Engine Mass	56,000 kg
T/W	0.53
Frozen Flow eff.	79%
Thermal eff.	98%
Total eff.	77%
Fuel	Chemical: APCP
Reactor	Combustion Chamber
Remass	Reaction Products
Remass Accel	Thermal Accel: Reaction Heat
Thrust Director	Nozzle
Specific Power	145 kg/MW

ISRU Metal-Oxygen

From Propulsion Fuels From Indigenous Lunar And Asteroidal Metals by William N. Agosto and John H. Wickman

Table 1: Metal/Oxygen Combustion Properties
hydrogen	1.39×10⁷	457
aluminum	1.63×10⁷	270
calcium	1.41×10⁷	213
iron	4.7×10⁶	184
magnesium	1.83×10⁷	260
silicon	1.58×10⁷	272
titanium	1.17×10⁷	255

Metastable

Atomic Hydrogen

100% Atomic Hydrogen
Exhaust velocity	20,600 m/s
15% Atomic Hydrogen in solid H₂
Exhaust velocity	7,300 m/s
Single-H/LOX
Exhaust Velocity	4,600 m/s
Specific Impulse	469 s

Atomic hydrogen is also called free-radical hydrogen or "single-H". The problem is that it instantly wants to recombine. The least unreasonable way of preventing this is to make a solid mass of frozen hydrogen (H₂) at liquid helium temperatures which contains 15% single-H by weight.

Free Radical Hydrogen
Exhaust velocity	39,240 m/s
Thrust	73,900 N
Specific Power	55 kg/MW
Engine Power	2,000 MW
Frozen Flow eff.	77%
Thermal eff.	94%
Thrust Power	1448 MW

Metallic Hydrogen

Metallic Hydrogen
Specific Impulse	1,700 sec
Exhaust Velocity	16,700 m/s
Reaction Chamber Temperature	6,000 K
Density	700 kg/m³
Energy of Recombination	216 MJ/kg

Most of the data here is from Metallic Hydrogen: The Most Powerful Rocket Fuel Yet to Exist by Isaac F. Silvera and John W. Cole.

Hydrogen (H₂) subjected to enough pressure to turn it into metal (mH), then contained under such pressure. Release the pressure and out comes all the stored energy that was required to compress it in the first place.

It will require storage that can handle millions of atmospheres worth of pressure. The mass of the storage unit might be enough to negate the advantage of the high exhaust velocity.

Or maybe not. The hope is that somebody might figure out how to compress the stuff into metal, then somehow release the pressure and have it stay metallic. In Properties of Metallic Hydrogen under Pressure the researchers showed that hydrogen would be a metastable metal with a potential barrier of ~1 eV. That is, if the pressure on metallic hydrogen were relaxed, it would still remain in the metallic phase, just as diamond is a metastable phase of carbon. This will make it a powerful rocket fuel, as well as a candidate material for the construction of Thor's Hammer.

Then that spoil-sport E. E. Salpeter wrote in "Evaporation of Cold Metallic Hydrogen" a prediction that quantum tunneling might make the stuff explode with no warning. Since nobody has managed to make metallic hydrogen they cannot test it to find the answer.

Silvera and Cole figure that metallic hydrogen is stable, to use it as rocket fuel you just have to heat it to about 1,000 K and it ~~explodes~~ recombines into hot molecular hydrogen.

Recombination of hydrogen from the metallic state would release a whopping 216 megajoules per kilogram. TNT only releases 4.2 megajoules per kg. Hydrogen/oxygen combustion in the Space Shuttle main engine releases 10 megajoules/kg. This would give metallic hydrogen an astronomical specific impulse (I_sp) of 1,700 seconds. The shuttle only had 460 seconds, NERVA had 800, and the pebble bed NTR had 1,000 seconds. Yes, this means metallic hydrogen has more specific impulse than a freaking solid-core nuclear thermal rocket.

I_sp of 1,700 seconds is big enough to build a single-stage-to-orbit heavy lift vehicle, which is the holy grail of boosters.

The cherry on top of the sundae is that metallic hydrogen is about ten times more dense (700 kg/m³) than that pesky liquid hydrogen (70.8 kg/m³). The high density is a plus, since liquid hydrogen's annoyingly low density causes all sorts of problems. Metallic hydrogen also probably does not need to be cryogenically cooled, unlike liquid hydrogen. Cryogenic cooling equipment cuts into your payload mass.

The drawback is the metallic hydrogen reaction chamber will reach a blazing temperature of at least 6,000 K. By way of comparison the temperatures in the Space Shuttle main engine combustion chamber can reach 3,570 K, which is about the limit of the state-of-the-art of preventing your engine from evaporating.

It is possible to lower the combustion chamber temperature by injecting cold propellant like water or liquid hydrogen. The good part is you can lower the temperature to 3,570 K so the engine doesn't melt. The bad part is this lowers the specific impulse (nothing comes free in this world). But even with a lowered specific impulse the stuff is still revolutionary.

At 100 atmospheres of pressure in the combustion chamber it will be an I_sp of 1,700 sec with a temperature of 7,000 K. At 40 atmospheres the temperature will be 6,700 K, still way to high.

Injecting enough water propellant to bring the temperature down to 3,500 to 3,800 K will lower the I_sp to 460 to 540 seconds. Doing the same with liquid hydrogen will lower the I_sp to 1,030 to 1,120 seconds.

Metallic Hydrogen (mH)
cooled with Liquid Hydrogen (H₂)
or Water (H₂O)
Dilutant	-	H₂	H₂	H₂	H₂	H₂	H₂	H₂	H₂	H₂O	H₂O	H₂O	H₂O
I_sp (s)	1700	1091?	1120	1089	1058	1029	1022	962	911	538	512	489	467
Chamber Temp (K)	7000	3925	3800	3700	3600	3500	3673	3448	3240	3800	3700	3600	3500
Mix Ratio (H₂/mH)	-	1.50	1.87	2.09	2.33	2.59	2.00	2.50	3.00	10.76	12.22	13.79	15.44

Metastable He^*

Metastable He^*
Exhaust Velocity	43,000 m/s
Specific Impulse	4,383 s
Thrust	64,000 N
Thrust Power	1.4 GW
Mass Flow	1 kg/s
Total Engine Mass	10,000 kg
T/W	0.65
Fuel	Metastable He*
Reactor	Combustion Chamber
Remass	Reaction Products
Remass Accel	Thermal Accel: Reaction Heat
Thrust Director	Nozzle
Specific Power	7 kg/MW

Spin-polarized triplet helium. Two electrons in a helium atom are aligned in a metastable state (one electron each in the 1s and 2s atomic orbitals with both electrons having parallel spins, the so-called "triplet spin state", if you want the details). When it reverts to normal state it releases 0.48 gigjoules per kilogram. Making the stuff is easy. The trouble is that it tends to decay spontaneously, with a lifetime of a mere 2.3 hours. And it will decay even quicker if something bangs on the fuel tank. Or if the ship is jostled by hostile weapons fire. To say the fuel is touchy is putting it mildly. The fuel is stored in a resonant waveguide to magnetically lock the atoms in their metastable state but that doesn't help much. There were some experiments to stablize it with circularly polarized light, but I have not found any results about that.

Metastable He IV-A

Metastable He IV-A
Exhaust Velocity	21,600 m/s
Specific Impulse	2,202 s
Total Engine Mass	10,000 kg
Fuel	Metastable He IV-A
Reactor	Combustion Chamber
Remass	Reaction Products
Remass Accel	Thermal Accel: Reaction Heat
Thrust Director	Nozzle
Meta from Saturn Rukh
Exhaust Velocity	30,900 m/s
Specific Impulse	3,150 s

Meta-helium would be such a worthwhile propulsion system that scientists have been trying real hard to get the stuff to stop decaying after a miserable 2.3 hours. One approach is to see if metastable helium can be formed into a room-temperature solid if bonded with diatomic helium molecules, made from one ground state atom and one excited state atom. This is called diatomic metastable helium. The solid should be stable, and it can be ignited by heating it. The exhaust velocity is about half that of pure He^* which is disappointing, but not as disappointing as a dust-mote sized meteorite blowing your ship into atoms.

Theoretically He IV-A would be stable for 8 years, have a density of 0.3 g/cm³, and be a solid with a melting point of 600 K (27° C). The density is a plus, liquid hydrogen's annoying low density causes all sorts of problems.

Dr. Robert Forward in his novel Saturn Rukh suggested bonding 64 metastable helium atoms to a single excited nitrogen atom, forming a stable super-molecule called Meta. Whether or not this is actually possible is anybody's guess. In theory it would have a specific impulse of 3150 seconds.

Metastable Helium
Exhaust Velocity	29,430 m/s
Specific Impulse	3,000 s
Thrust	106,500 N
Thrust Power	1.6 GW
Mass Flow	4 kg/s
Frozen Flow eff.	90%
Thermal eff.	87%
Total eff.	78%
Fuel	Metastable He IV-A
Reactor	Combustion Chamber
Remass	Reaction Products
Remass Accel	Thermal Accel: Reaction Heat
Thrust Director	Nozzle

Electromagnetic (Plasma)

Electromagnetic ion thrusters use the Lorentz force to move the propellant ions.

Electrodeless plasma

Electrodeless Plasma Thruster

Helicon Double Layer (HDLT)

Helicon Double Layer Thruster

Magnetoplasmadynamic (MPD)

Magnetoplasmadynamic
Exhaust Velocity	314,000 m/s
Specific Impulse	32,008 s
Thrust	20,000 N
Thrust Power	3.1 GW
Mass Flow	0.06 kg/s
Total Engine Mass	1,540,000 kg
T/W	1.00e-03
Thermal eff.	79%
Total eff.	79%
Fuel	4GWe input
Remass	Helium
Remass Accel	Electromagnetic Acceleration
Specific Power	490 kg/MW
HOPE Cargo MPD
Propulsion System	MPD
Exhaust Velocity	78,500 m/s
Specific Impulse	8,002 s
Thrust	11 N
Number Thrusters	2
Thrust Power	0.4 MW
Mass Flow	1.40e-04 kg/s
Fuel	60MWe input
Remass	Helium
Wet Mass	242,000 kg
Dry Mass	182,000 kg
Mass Ratio	1.33 m/s
ΔV	22,367 m/s
HOPE Tanker MPD
Propulsion System	MPD
Exhaust Velocity	78,500 m/s
Specific Impulse	8,002 s
Thrust	11 N
Number Thrusters	2
Thrust Power	0.4 MW
Mass Flow	1.40e-04 kg/s
Fuel	60MWe input
Remass	Helium
Wet Mass	244,000 kg
Dry Mass	184,000 kg
Mass Ratio	1.33 m/s
ΔV	22,155 m/s
HOPE Crew MPD
Propulsion System	MPD
Exhaust Velocity	78,500 m/s
Specific Impulse	8,002 s
Thrust	28 N
Number Thrusters	4
Thrust Power	1.1 MW
Mass Flow	3.57e-04 kg/s
Fuel	60MWe input
Remass	Helium
Wet Mass	262,000 kg
Dry Mass	188,000 kg
Mass Ratio	1.39 m/s
ΔV	26,054 m/s

Magnetoplasmadynamic thruster, a travelling wave plasma accelerator. Propellant is potassium seeded helium.

Self-Field Magnetoplasmadynamic Thruster
Propellant is accelerated by magnetic field created by discharge current between anode and cathode.
Applied-Field Magnetoplasmadynamic Thruster
Propellant is accelerated by an external applied magnetic field. Used when the discharge current is too weak to make worthwhile magnetic field.

MPD T-Wave
Exhaust Velocity	78,480 m/s
Specific Impulse	8,000 s
Thrust	1,200 N
Thrust Power	47.1 MW
Mass Flow	0.02 kg/s
Total Engine Mass	82,675 kg
T/W	1.00e-03
Frozen Flow eff.	90%
Thermal eff.	81%
Total eff.	73%
Fuel	60MWe input
Remass	Regolith
Remass Accel	Electromagnetic Acceleration
Specific Power	1,756 kg/MW

Pulsed Inductive (PIT)

Pulsed inductive thruster

A puff of propellant is directed at the spiral drive coil. Capacitors deliver a 1 microsecond jolt to the coil, creating a radial magnetic field. The field induces a circular electric field in the propellant, ionizing it and causing the ions to move perpendicular to the magnetic field. This accelerates the ions, creating thrust.
There are no electrodes to erode, and thrust can be scaled up by increasing pulse rate.

Pulsed Plasma (PPT)

Pulsed plasma thruster

The spring pushes the slab of teflon propellant into the discharge chamber. There an arc vaporizes a layer of teflon. The ablated teflon is accelerated away by the arc's magnetic field.

Pulsed Plasmoid Thruster
Exhaust Velocity	78,480 m/s
Specific Impulse	8,000 s
Thrust	1,100 N
Thrust Power	43.2 MW
Mass Flow	0.01 kg/s
Total Engine Mass	83,611 kg
T/W	1.00e-03
Frozen Flow eff.	90%
Thermal eff.	80%
Total eff.	72%
Fuel	60MWe input
Remass	Regolith
Remass Accel	Thermal Accel: Reaction Heat
Thrust Director	Magnetic Nozzle
Specific Power	1,937 kg/MW

VASIMR

VASIMR
VASIMR (high gear)
Exhaust Velocity	294,000 m/s
Specific Impulse	29,969 s
Thrust	40 N
Thrust Power	5.9 MW
Mass Flow	1.36e-04 kg/s
Total Engine Mass	10,000 kg
T/W	4.08e-04
Specific Power	1,701 kg/MW
VASIMR (med gear)
Exhaust Velocity	147,000 m/s
Specific Impulse	14,985 s
Thrust	80 N
Thrust Power	5.9 MW
Mass Flow	5.44e-04 kg/s
Total Engine Mass	10,000 kg
T/W	8.15e-04
Specific Power	1,701 kg/MW
VASIMR (low gear)
Exhaust Velocity	29,000 m/s
Specific Impulse	2,956 s
Thrust	400 N
Thrust Power	5.8 MW
Mass Flow	0.01 kg/s
Total Engine Mass	10,000 kg
T/W	4.08e-03
Specific Power	1,724 kg/MW
All
Thermal eff.	60%
Total eff.	60%
Fuel	19.6MWe input
Remass	Liquid Hydrogen
Remass Accel	Electromagnetic Acceleration
Thrust Director	Magnetic Nozzle

Some classify this as an electromagnetic plasma, some as an electrodeless electrothermal

The variable specific impulse magnetoplasma rocket is a plasma drive with the amusing ability to "shift gears." This means it can trade exhaust velocity for thrust and vice versa. Three "gears" are shown on the table. There are more details here and here.

VASIMR has been suggested for use in a space tug aka Orbital Transfer Vehicle. A VASIMR powered tug could move 34 metric tons from Low Earth Orbit (LEO) to Low Lunar Orbit (LLO) by expending only 8 metric tons of argon propellant. A chemical rocket tug would require 60 metric tons of liquid oxygen - liquid hydrogen propellant. Granted the VASIMR tug would take six month transit time as opposed to the three days for the chemical, but there are always trade offs.

Artwork by Nick Kaloterakis

Ponderomotive VASIMR
Exhaust Velocity	39,240 m/s
Specific Impulse	4,000 s
Thrust	2,250 N
Number Thrusters	15
Thrust/Engine	150 N
Thrust Power	44.1 MW
Mass Flow	0.06 kg/s
Total Engine Mass	43,796 kg
T/W	5.00e-03
Frozen Flow eff.	90%
Thermal eff.	80%
Total eff.	72%
Fuel	60MWe input
Remass	Liquid Hydrogen
Remass Accel	Electromagnetic Acceleration
Thrust Director	Magnetic Nozzle
Specific Power	992 kg/MW

Electrostatic

Electrostatic ion thrusters use the Coulomb force to move the propellant ions.

Electrostatic Propellant

When I was a little boy, the My First Big Book of Outer Space Rocketships type books I was constantly reading usually stated that ion drives would use mercury or cesium as propellant. But most NASA spacecraft are using xenon. What's the story?

Ionization energy represents a large percentage of the energy needed to run ion drives. The ideal propellant is thus easy to ionize and has a high mass/ionization energy ratio. In addition, the propellant should not erode the thruster to any great degree to permit long life; and should not contaminate the vehicle.

Many current designs use xenon gas, as it is easy to ionize, has a reasonably high atomic number, is inert and causes low erosion. However, xenon is globally in short supply and expensive.

Older designs used mercury, but this is toxic and expensive, tended to contaminate the vehicle with the metal and was difficult to feed accurately.

Other propellants, such as bismuth and iodine, show promise, particularly for gridless designs, such as Hall effect thrusters.

Gridded Electrostatic Ion Thrusters typically use xenon.

Hal Effect Thrusters typically use xenon, bismuth and iodine

Field-Emission Electric Propulsion typically use caesium or indium as the propellant due to their high atomic weights, low ionization potentials and low melting points.

Pulsed Inductive Thrusters typically use ammonia gas.

Magnetoplasmadynamic Thrusters typically use hydrogen, argon, ammonia or nitrogen.

If you want the ultimate in in-situ resource utilization, design an ion drive that can use asteroid dust for propellant.

From **EARTHLIGHT** by Arthur C. Clarke (1955)

From **POWERING CISLUNAR SPACEFLIGHT WITH NEO POWDER** by Ronald P. Menich (2014)

From **MORE ENHANCED GRAVITY TRACTOR MUSINGS: ISRU PROPELLANTS** by Jonathan Goff (2015)

Colloid

ESTAT: Colloid
Exhaust Velocity	43,000 m/s
Specific Impulse	4,383 s
Thrust	8,000 N
Thrust Power	0.2 GW
Mass Flow	0.19 kg/s
Total Engine Mass	20,000 kg
T/W	0.04
Thermal eff.	85%
Total eff.	85%
Fuel	200MWe input
Remass	Colloid
Remass Accel	Electrostatic Acceleration
Specific Power	116 kg/MW

Similar to Ion, but utilizing tiny droplets instead of ions.

Field-Emission Electric (FEEP)

Field-emission electric propulsion, a type of Colloid thruster.

They typically use caesium or indium as the propellant due to their high atomic weights, low ionization potentials and low melting points.

Hall Effect (HET)

Hall Effect Thruster

In a Hall thruster the attractive negative charge is provided by an electron plasma at the open end of the thruster instead of a grid.

Ion

Ion
Exhaust Velocity	210,000 m/s
Specific Impulse	21,407 s
Thrust	10,000 N
Thrust Power	1.1 GW
Mass Flow	0.05 kg/s
Total Engine Mass	400,000 kg
T/W	3.00e-03
Thermal eff.	96%
Total eff.	96%
Fuel	800MWe input
Remass	Argon
Remass Accel	Electrostatic Acceleration
Specific Power	381 kg/MW
DAWN mission NSTAR
Propulsion System	Ion
Exhaust Velocity	30,411 m/s
Specific Impulse	3,100 s
Thrust	9.00e-05 N
Thrust Power	1.4 W
Mass Flow	2.96e-09 kg/s
Total Engine Mass	26 kg
T/W	3.60e-07
Fuel	Solar Photons
Reactor	Photovoltaic array
Remass	Xenon
Remass Accel	Electrostatic Acceleration
Wet Mass	1,210 kg
Dry Mass	785 kg
Mass Ratio	1.54 m/s
ΔV	13,159 m/s
Specific Power	1.86e+07 kg/MW
Umbrella Ship
Propulsion System	Ion
Exhaust Velocity	80,442 m/s
Specific Impulse	8,200 s
Thrust	490 N
Thrust Power	19.7 MW
Mass Flow	0.01 kg/s
Fuel	Fission: Uranium 235
Reactor	Nuclear Power Reactor (electric)
Remass	Cesium
Remass Accel	Electrostatic Acceleration
Wet Mass	660,000 kg
Dry Mass	328,000 kg
Mass Ratio	2.01 m/s
ΔV	56,247 m/s

Gridded Electrostatic Ion Thruster. Potassium seeded argon is ionized and the ions are accelerated electrostatically by electrodes. Other propellants can be used, such as cesium and buckyballs. Though it has admirably high exhaust velocity, there are theoretical limits that ensure all Ion drives are low thrust.

It also shares the same problem as the other electrically powered low-thrust drives. In the words of a NASA engineer the problem is "we can't make an extension cord long enough." That is, electrical power plants are weighty enough to make the low thrust an even larger liability. A high powered ion drive will generally be powered by a nuclear reactor, Nuclear Electric Propulsion (NEP). Low powered ion drives can get by with solar power arrays, all ion drive space probes that exist in the real world use that system. Researchers are looking into beamed power systems, where the ion drive on the spaceship is energized by a laser beam from a remote space station.

If you are interested in the technical details about why ion drives are low thrust, read on.

Ions from the charged particle source are accelerated by being attracted to the exit grid. After the grid electrons are added from the neutralizer source to make a charge-neutral exhaust flow. Otherwise the engine would accumulate such a negative charge that the exhaust would refuse to leave the engine.

NASA NSTAR for Deep Space 1

The three spheres on the top look suspiciously like two habitat modules on an artificial gravity centrifuge.
Artwork by Lee Ames for Man's Reach Into Space by Roy Gallant (1959)
Note the beam neutralizers between the pad-like ion engines.
Artwork by Lee Ames for Man's Reach Into Space by Roy Gallant (1959)
Artwork by Lee Ames for Man's Reach Into Space by Roy Gallant (1959)
Sorry, this is the highest resolution I could find.
Impression by a Convair artist of an ion-rocket space-ship.

Ion Drive
Exhaust Velocity	78,480 m/s
Specific Impulse	8,000 s
Thrust	1,444 N
Number Thrusters	x361
Thrust/Engine	4 N
Thrust Power	56.7 MW
Mass Flow	0.02 kg/s
Total Engine Mass	120,149 kg
T/W	1.00e-03
Frozen Flow eff.	96%
Thermal eff.	99%
Total eff.	95%
Fuel	60MWe input
Remass	Magnesium
Remass Accel	Electrostatic Acceleration
Specific Power	2,120 kg/MW

( IBS Agamemnon )

IBS Agamemnon
Propulsion System	Ion
Exhaust Velocity	220,000 m/s
Specific Impulse	22,426 s
Thrust	10,000,000 N
Thrust Power	1.1 TW
Mass Flow	45 kg/s
Fuel	Deuterium-Deuterium Fusion
Reactor	Fusion Power Reactor(electric)
Remass	Cadmium
Remass Accel	Electrostatic Acceleration
Wet Mass	100,000,000 kg
Dry Mass	28,000,000 kg
Mass Ratio	3.57 m/s
ΔV	280,052 m/s
Ship Mass	8,000,000 kg
Cargo Mass	20,000,000 kg
Length	400 m
Length spin arm	100 m
Cargo Tug Slingshot
Propulsion System	Ion
Exhaust Velocity	280,000 m/s
Specific Impulse	28,542 s
Thrust	5,460,000 N
Thrust Power	764.4 GW
Mass Flow	20 kg/s
Fuel	Deuterium-Deuterium Fusion
Reactor	Fusion Power Reactor(electric)
Remass	Cadmium
Remass Accel	Electrostatic Acceleration
Wet Mass	512,600,000 kg
Dry Mass	501,600,000 kg
Mass Ratio	1.02 m/s
ΔV	6,074 m/s

Fictional Interplanetary BoostShip Agamemnon from Jerry Pournelle's short story "Tinker". This fictional ship is a species of Ion drive utilizing cadmium and powered by deuterium fusion. Looking at its performance I suspect that in reality no Ion drive could have such a high thrust. The back of my envelope says that you'd need one thousand ultimate Ion drives to get this much thrust.

Artwork by Rick Sternbach (1975). Click for larger image

Electrothermal

ArcJet

ArcJet
Exhaust Velocity	20,000 m/s
Specific Impulse	2,039 s
Thrust	2 N
Thrust Power	20.0 kW
Mass Flow	1.00e-04 kg/s
Fuel	100kWe input
Remass	Liquid Hydrogen
Remass Accel	Thermal Accel: Arc Heater
Thrust Director	Nozzle

Hydrogen propellant is heated by an electrical arc.

Constricted Arcjet

Arcjet with applied magnetic field
The magnetic field rotates the plasma to alow even heating

Microwave Electrothermal

Microwave Electrothermal Thruster

Resistojet

Resistojet
Exhaust Velocity	2,900 m/s
Specific Impulse	296 s
Thrust	1 N
Thrust Power	0.7 kW
Mass Flow	2.00e-04 kg/s
Thermal eff.	80%
Total eff.	80%
Fuel	100kWe input
Remass	Liquid Hydrogen
Remass Accel	Thermal Accel: Resistance Heater
Thrust Director	Nozzle

In a resistojet, ropellant flows over a resistance-wire heating element (much like a space heater or toaster) then the heated propellant escapes out the exhaust nozzle. They are mostly used as attitude jets on satellites, and in situations where energy is more plentiful than mass.

Wakefield E-Beam

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.

Deuterium-Tritium

Exhaust Velocity	22,000 m/s
Specific Impulse	2,243 s
Thrust	108,000 N
Thrust Power	1.2 GW
Mass Flow	5 kg/s
Total Engine Mass	10,000 kg
T/W	1
Fuel	Deuterium-Tritium Fusion
Specific Power	8 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 Velocity	980,000 m/s
Specific Impulse	99,898 s
Thrust	61,000 N
Thrust Power	29.9 GW
Mass Flow	0.06 kg/s
Total Engine Mass	300,000 kg
T/W	0.02
Fuel	Hydrogen-Boron Fusion
Specific Power	10 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?"

Diagram from Alex H.Y. Cheung

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 Velocity	7,840,000 m/s
Specific Impulse	799,185 s
Thrust	49,000 N
Thrust Power	0.2 TW
Mass Flow	0.01 kg/s
Total Engine Mass	1,200,000 kg
T/W	4.00e-03
Fuel	Helium3-Deuterium Fusion
Specific Power	6 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

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
Fuel	D-³He (spin polarized)
Specific Impulse	20,000 s
Mass Flow	0.308 kg/s
Engine Alpha	5.75 kW/kg
Engine Mass	1,033,000 kg
Payload Mass	200,000 kg

Sample Inertial Confinement Fusion Rocket
Fuel	Cat-DD
Specific Impulse	270,000 s
Mass Flow	0.015 kg/s
Engine Alpha	110 kW/kg
Engine Mass	486,000 kg
Payload Mass	200,000 kg

Sample Tokamak Fusion Rocket
One-way continuous-burn constant-I_sp trajectory
Mission	Distance D_AB (A.U.)	Mass Ratio R_M	Initial Mass M_i (mT)	Propellant Mass M_p (mT)	Payload Mass M_L/M_i (%)	Travel Time τ_AB (days)	Initial Acceleration a_i (10^-3 g₀)
Mars	0.524	1.732	2,135	902	9.4	33.0	~2.9
Ceres	1.767	2.497	3,079	1,846	6.5	69.4	2.0
Jupiter	4.203	3.590	4,427	3,194	4.5	120.0	~1.4

Sample Tokamak Fusion Rocket
Round-trip trajectory
Mission	Mass Ratio R_M	Propellant Mass M_p^A→B (mT)	Propellant Mass M_p^B→A (mT)	Propellant Mass M_p^A→A (mT)	Initial Mass M_i (mT)	Travel Time τ_AB (days)	Travel Time τ_BA (days)	Travel Time τ_RT (days)
Mars	2.664	1,149	902	2,051	3,284	43.2	33.9	77.1
Ceres	4.667	2,675	1,846	4,521	5,754	100.5	69.4	169.9
Jupiter	7.783	5,169	3,194	8,363	9,596	194.3	120.0	314.3

Sample Inertial Confinement Fusion Rocket
Round-trip continuous-burn constant-I_sp trajectory
Mission	Distance D_AB (A.U.)	Mass Ratio R_M	Initial Mass M_i (mT)	Propellant Mass M_p^A→A (mT)	Payload Mass M_L/M_i (%)	Travel Time τ_AB (days)	Travel Time τ_RT (days)
Mars	0.524	1.104	757.3	71.3	26.4	27.7	55.0
Ceres	1.767	1.196	820.5	134.5	24.4	53.1	103.7
Jupiter	4.203	1.309	898	212.0	22.3	84.6	163.6
Saturn	8.539	1.453	997	311.0	20.1	125.5	239.8
Uranus	18.182	1.689	1,159	473.0	17.3	194.1	364.7
Neptune	29.058	1.901	1,304	618.0	15.3	257.3	476.9
Pluto	38.518	2.063	1,415	729.0	14.1	306.6	562.7

The above tables were calculated with the following equations:

W_f = M_f * g₀

M_B = M_f + M_p^B→A

1 / α = M_i / M_B

1 / β = M_B / M_f

P_f = M_p / M_i

R_M = 1 / (α * β) (two way)

R_M = 1 / β (one way)

τ_AB = (I_sp / (F / W_f)) * (1 / β) * ((1 / α) -1) (equation 10)

τ_BA = (I_sp / (F / W_f)) * (1 / β - 1) (equation 11)

τ_RT = τ_AB + τ_BA (equation 12a)

τ_RT = (I_sp / (F / W_f)) * (1 / (α * β) - 1) (equation 12b)

D_AB(m) = ((g₀ * I_sp²) / (F / W_f))) * (1 / β) * ((1 / sqrt(α)) - 1)² (equation 13a)

D_BA(m) = ((g₀ * I_sp²) / (F / W_f))) * ((1 / sqrt(β)) - 1)² (equation 14)

D_AB(m) = D_BA(m) (equation 13b)

where:

α_p = engine alpha (W/kg)
D_AB = distance between A and B (meters)
D_BA = distance between B and A (meters)
I_sp = engine specific impulse (seconds)
IMEO = initial mass in Earth orbit (kg)
M_B = dry mass plus just propellant to travel from B to A (kg)
M_L = mass of payload (kg)
M_W = mass of engine (kg)
M_f = dry mass (kg)
M_i = initial mass in Earth orbit (kg)
M_p^A→A = mass of propellant used traveling round-trip from A to B to A (kg)
M_p^A→B = mass of propellant used traveling one-way from A to B (kg)
M_p^B→A = mass of propellant used traveling one-way from B to A (kg)
ṁ_p = propellant mass flow (kg/s)
P_f = propellant mass fraction
R_M = spacecraft mass ratio
τ_AB = time to travel one way from A to B (seconds)
τ_BA = time to travel one way from B to A (seconds)
τ_RT = time to travel round trop from A to B to A (seconds)
W_f = dry weight (Newtons)

Inertial Confinement

Inertial Confinement Fusion is in the Pulse section.

Electrostatic Inertial

Magnetic Confinement

MC-Fusion
Thrust Power	200 GW
Exhaust velocity	8,000,000 m/s
Thrust	50,000 n
Engine mass	0.6 tonne
T/W >1.0	yes
Gasdynamic Mirror
Exhaust Velocity	1,960,000 m/s
Specific Impulse	199,796 s
Thrust	47,000 N
Thrust Power	46.1 GW
Mass Flow	0.02 kg/s
Fuel	Deuterium-Tritium Fusion
Reactor	Magnetic Confinement Linear
Remass	Liquid Hydrogen
Remass Accel	Thermal Accel: Reaction Heat
Thrust Director	Magnetic Nozzle

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 Velocity	1,960,000 m/s
Specific Impulse	199,796 s
Thrust	47,000 N
Thrust Power	46.1 GW
Mass Flow	0.02 kg/s
Fuel	Deuterium-Tritium Fusion
Reactor	Magnetic Confinement Linear
Remass	Liquid Hydrogen
Remass Accel	Thermal Accel: Reaction Heat
Thrust Director	Magnetic Nozzle

Also known as "Open-field magnetic confinement".

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

Open-field magnetic confinement (Mirror)
Open-field magnetic confinement (Mirror)
Open-field magnetic confinement (Mirror)

Open-field magnetic confinement (Tandem mirror engine)
From Critical Issues for SOAR: The Space Orbiting Advanced Fusion Power Reactor, Santarius et al (1988)
Open-field magnetic confinement (Field Reversed Configuration)

Toroidal Fusion

Also known as "Closed-field magnetic confinement".

Closed-field magnetic confinement (Tokamak)
Closed-field magnetic confinement (Tokamak)

Click to open website. — Discovery II *from NASA report.*

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.
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 lowest thrust/propellant mass flow and the 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
Fuel Plasma Exhaust = Pure Fusion
Mass Augmented Exhaust = Fusion Afterburner
Thermal Exhaust = Dual-Mode
Thrust To Weight Ration * 1,250,000 = Thrust (N)

Santarius Fusion Rocket
D-³He Fusion
Mode	Specific Impulse	Thrust
Pure Fusion	1×10⁶ sec	88 N
Afterburner	5×10⁵ sec to 1×10⁴ sec	125 N to 5,000 N
Dual-Mode	7×10² 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:

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

where

V_e = 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:

V_e = sqrt(2 * E_p)

where

E_p = fraction of fuel that is transformed into energy
V_e = exhaust velocity (percentage of the speed of light)

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

Afterburner Fusion Engines

Discovery II fusion reactor and engine. This uses a fusion afterburner

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 P_therm = F² / (1.7 * (F / V_e))

eq.2 mDot = F² / (1.7 * P_therm)

eq.3 P_therm = F² / (1.7 * mDot)

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

eq.5 V_e = F / mDot

eq.6 mDot = F / V_e

where:

F = thrust (newtons)
P_therm = Thermal power (watts)
mDot = propellant mass flow (kg/s) spent fusion product propellant + cold reaction mass
V_e = 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 P_therm. 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 P_therm 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 P_therm 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.

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

( AV:T Fusion )

AV:T Fusion
Cruise mode
Exhaust Velocity	832,928 m/s
Specific Impulse	84,906 s
Thrust	245,250 N
Thrust Power	0.1 TW
Mass Flow	0.29 kg/s
Fuel	Helium3-Deuterium Fusion
Combat mode
Exhaust Velocity	104,116 m/s
Specific Impulse	10,613 s
Thrust	48,828,125 N
Thrust Power	2.5 TW
Mass Flow	469 kg/s
Fuel	Helium3-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.

Radiators extended to signal surrender.

( THS Fusion Pulse )

Fusion Pulse low gear
Exhaust Velocity	150,000 m/s
Specific Impulse	15,291 s
Thrust	80,000 N
Mass Flow	0.53 kg/s
T/W	2
Fusion Pulse high gear
Exhaust Velocity	300,000 m/s
Specific Impulse	30,581 s
Thrust	40,000 N
Mass Flow	0.13 kg/s
T/W	1
Both
Thrust Power	6.0 GW
Total Engine Mass	4,000 kg
Fuel	Helium3-Deuterium Fusion
Specific Power	1 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.

Artwork by Win Barker
Artwork by Win Barker

( Epstein Drive )

Epstein Drive
Thrust Power	5.5 TW
Exhaust Velocity	11,000,000 m/s
Specific Impulse	1,100,000 s
Thrust	1,000,000 N
Mass Flow	0.09 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. ( V_e = 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 / V_e )

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

Video "The Rocket Science of 'The Expanse'" by Scott Manley
click to play video

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.

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 M_e = 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
I_sp = (ΔV / ln(R)) / g₀
I_sp = (5,933,000 / ln(3.0)) / 9.81
I_sp = 551,000 seconds

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

Wet Mass
M = R * M_e
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
F_p = (F * V_e ) / 2
F_p = (3,700,000 * 6,000,000 ) / 2
F_p = 11,100,000,000,000 Watts = 11 TW

Nuclear Thermal

These use the heat generated from a nuclear reaction to heat up propellant. The nuclear reaction is controlled by adjusting the amount of free neutrons inside the mass of fissioning material.

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

Figure 11-11 from NUCLEAR SPACE PROPULSION by Holmes F. Crouch. Note neutron isolation shield.
An interpretation by master artist William Black. Note neutron isolation shield (10).

Solid Core

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

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

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

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

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

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

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

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

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

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

"The enlisted men get to go out and shovel whatever they can find into the propellant tanks"
NERVA testing. From nuclearspace.com.

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

NERVA

NERVA
Thrust Power	0.198-0.065 GW
Exhaust velocity	See Table
Thrust	49,000 n
Engine mass	10 tonne
T/W >1.0	no
NERVA (H2)
Exhaust Velocity	8,093 m/s
Specific Impulse	825 s
Thrust	49,000 N
Thrust Power	0.2 GW
Mass Flow	6 kg/s
Total Engine Mass	10,000 kg
T/W	0.50
Fuel	Fission: Uranium 235
Reactor	Solid Core
Remass	Liquid Hydrogen
Remass Accel	Thermal Accel: Reaction Heat
Thrust Director	Nozzle
Specific Power	50 kg/MW
Resuable Nuclear Shuttle
Propulsion System	NERVA
Exhaust Velocity	8,000 m/s
Specific Impulse	815 s
Thrust	344,000 N
Thrust Power	1.4 GW
Mass Flow	43 kg/s
Wet Mass	170,000 kg
Dry Mass	30,000 kg
Mass Ratio	5.67 m/s
ΔV	13,877 m/s
Widmer Mars Mission
Propulsion System	NERVA
Exhaust Velocity	8,000 m/s
Specific Impulse	815 s
Thrust	580,000 N
Thrust Power	2.3 GW
Mass Flow	72 kg/s
Wet Mass	400,000 kg
Dry Mass	150,000 kg
Mass Ratio	2.67 m/s
ΔV	7,847 m/s
HELIOS 2nd Stage
Propulsion System	NTR Solid
Exhaust Velocity	7,800 m/s
Specific Impulse	795 s
Thrust	981,000 N
Thrust Power	3.8 GW
Mass Flow	126 kg/s
Wet Mass	100,000 kg
Dry Mass	6,800 kg
Mass Ratio	14.71 m/s
ΔV	20,968 m/s
Atomic V-2
Propulsion System	NTR Solid
Exhaust Velocity	8,980 m/s
Specific Impulse	915 s
Thrust	1,050,000 N
Thrust Power	4.7 GW
Mass Flow	117 kg/s
Total Engine Mass	4,200 kg
T/W	25
Wet Mass	42,000 kg
Dry Mass	17,000 kg
Mass Ratio	2.47 m/s
ΔV	8,122 m/s
Specific Power	1 kg/MW

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

SNRE Peewee

SNRE "Peewee-class" Engine
Exhaust Velocity	8,829 m/s
Specific Impulse	900 s
Thrust	73,000 N
Thrust Power	367 MW_t
Mass Flow	kg/s
Total Engine Mass	2,400 kg
T/W	3.06
Fuel	Fission: Uranium 235
Max Enrichment	93% U-235 wt
Num Fuel Elements	564
Num Tie-tube Elements	241
Fissle Loading	0.6 g U per cm³
Max Fuel Temp	2,860 K
U-235 Mass	59.6 kg
Reactor	Solid Core
Remass	Liquid Hydrogen
Remass Accel	Thermal Accel: Reaction Heat
Thrust Director	Nozzle
Specific Power	6.5 kg/MW
Engine Length	4.46
Fuel Length	0.89 m
Pressure Vessel Diameter	0.98m

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

They looked at a 33,000 Newton engine but it was a bit too small to do anything useful, even in a cluster of three. A 73,000 Newton engine on the other hand could perform quite a few proposed missions.

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

NERVA Derivative

NERVA Deriv
Exhaust Velocity	8,085 m/s
Specific Impulse	824 s
Thrust	334,061 N
Thrust Power	1.4 GW
Mass Flow	41 kg/s
Total Engine Mass	10,100 kg
T/W	3
Fuel	Fission: Uranium 235
Reactor	Solid Core
Remass	Liquid Hydrogen
Remass Accel	Thermal Accel: Reaction Heat
Thrust Director	Nozzle
Specific Power	7 kg/MW

DUMBO

General Dumbo
Thrust Power	14.0-4.6 GW
Exhaust velocity	See Table
Thrust	3,500,000 n
Engine mass	5 tonne
T/W >1.0	yes
Dumbo (H2)
Exhaust Velocity	8,093 m/s
Specific Impulse	825 s
Thrust	3,500,000 N
Thrust Power	14.2 GW
Mass Flow	432 kg/s
Total Engine Mass	5,000 kg
T/W	71
Fuel	Fission: Uranium 235
Reactor	Solid Core
Remass	Liquid Hydrogen
Remass Accel	Thermal Accel: Reaction Heat
Thrust Director	Nozzle
Dumbo Model A
Engine mass	0.7 tonne
Thrust	400,000 n
Propellant mass flow	52 kg/sec
Exhaust velocity	7,700 m/sec
Engine Height	0.6 m
Engine Radius	0.3 m
Engine Volume	0.2 m³
T/W	58
Dumbo Model B
Engine mass	2.8 tonne
Thrust	3,560,000 n
Propellant mass flow	460 kg/sec
Exhaust velocity	7,700 m/sec
Engine Height	0.6 m
Engine Radius	1.0 m
Engine Volume	1.8 m³
T/W	130
Dumbo Model C
Engine mass	2.1 tonne
Thrust	400,000 n
Propellant mass flow	48 kg/sec
Exhaust velocity	8,300 m/sec
Engine Height	0.6 m
Engine Radius	0.4 m
Engine Volume	0.3 m³
T/W	20

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

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

(bad photocopy of a ) Rough schematic of Dumbo engine. Liquid hydrogen propellant enters top and flows through beryllium neutron reflector, cooling it. Flows upward through a Cold Gas Entrance into interior of a reactor tube. Hydrogen seeps through walls of tube, being heated by fissioning uranium. Hot hydrogen escapes through hot gas exit holes in bottom, entering exhaust nozzle. Beryllium reflector will have control drums (not shown)
Cross section of a reactor tube, showing the channels the hydrogen escapes through. Every other channel is filled with uranium, the other channels the hydrogen passes through while being heated. Hydrogen travels from center of tube through the channels to the outside.
Model "A" Dumbo. These models are not optimized, they are simply to compare and contrast how engine performance changes with number of reactor tubes and use of either molybdenum or tungsten. This model has 19 reactor tubes and uses molybdenum. The "moderator" is the layer of the reactor tube wall containing uranium. Flow of hydrogen propellant is as per the description in the rough schematic.
Model "B" Dumbo. Again this is not optimized. The main difference from the model "A" is that it has 169 reactor tubes instead of only 19.
Model "C" Dumbo. Again this is not optimized. This has 19 reactor tubes like the model "A", but uses tungsten instead of molybdenum. Because tungsten requires more moderator, the hydrogen flow is the opposite of the "A" and "B". Instead the cool hydrogen starts outside of the reactor tube, and is heated as it flows to the interior of the tube.

Pebble Bed

Pebble Bed
Exhaust Velocity	9,530 m/s
Specific Impulse	971 s
Thrust	333,617 N
Thrust Power	1.6 GW
Mass Flow	35 kg/s
Total Engine Mass	1,700 kg
T/W	20
Fuel	Fission: Uranium 235
Reactor	Solid Core
Remass	Liquid Hydrogen
Remass Accel	Thermal Accel: Reaction Heat
Thrust Director	Nozzle
Specific Power	1 kg/MW

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

Cermet

Prismatic CERMET Reactor Concept. Click for larger image

Cermet NERVA
Exhaust Velocity	9,120 m/s
Specific Impulse	930 s
Thrust	445,267 N
Thrust Power	2.0 GW
Mass Flow	49 kg/s
Total Engine Mass	9,000 kg
T/W	5
Fuel	Fission: Uranium 235
Reactor	Solid Core
Remass	Liquid Hydrogen
Remass Accel	Thermal Accel: Reaction Heat
Thrust Director	Nozzle
Specific Power	4 kg/MW

Pulsed Solid-core NTR

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

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

Pulse mode can be used two ways:

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

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

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

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

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

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

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

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

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

How Does It Work?

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

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

Amplification Factor

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

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

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

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

N ≅ 6×10^-3 * [ ΔT/t ]

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

Direct Thrust Amplification Details

Thrust power is:

F_p = (F * V_e ) / 2

Thrust is:

F = mDot * V_e

Specific Impulse is:

I_sp = V_e / g₀

where:

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

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

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

The limit on the increase in thrust power is N.

Specific Impulse Amplification Details

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

I_spPulse = I_spS * sqrt[ (f_n * N) + 1]

where:

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

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

A sequence for a stationary-pulsed-stationary maneuver for a pulsed thermal nuclear rocket
During the stationary mode (working at constant nominal power), the fuel temperature is always constant (solid black line), and the propellant is coming cold (blue doted lines) heated in the chamber and exhausted in the nozzle (red doted line).
When amplification in thrust or specific impulse is required, the nuclear core is "switched on" to a pulsed mode. In this mode, the fuel in continuously quenched and instantaneously heated by the pulses.
Once the requirements for high thrust and specific impulse are not required, the nuclear core is "switched on" to the initial stationary mode.
Pulsed nuclear thermal rocket unit cell concept for I_sp amplification
In this cell, hydrogen-propellant is heated by the continuous intense neutronic pulses in the propellant channels. At the same time, the unwanted energy from the fission fragments is removed by a solidary cooling channel with lithium or other liquid metal.

Project Timberwind

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

NTR Comparison
	NERVA	Timberwind 45
Engine Mass	6,803 kg	1,500 kg
Thrust (Vac)	333.6 kN	392.8 kN
Specific Impulse	850 s	1,000 s
Burn Time	1,200 s	449 s
T/W	5	30 !!!

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

	Timberwind 45	Timberwind 75	Timberwind 250
Diameter	4.25 m	2.03 m	8.70 m
Thrust (Vac)	392.8 kN	735.5 kN	2,451.6 kN
Specific Impulse	1,000 s	1,000 s	1,000 s
Engine Mass	1,500 kg	2,500 kg	8,300 kg
T/W	30	30	30
Burn Time	449 s	357 s	493 s

Russian Twisted Ribbon

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

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

Twisted Ribbon Engines
	RD-0140	NPPS
Thrust (vac) (kN)	35.28	68
Propellant	H₂ + Hexane	H₂
Propellant Mass Flow (kg/s)	~4	~7.1
Specific Impulse (vac) (s)	~900	~920
Core outlet temparture (K)	3,000	2,800 to 2,900
Chamber Pressure (10⁵ Pa)	70	60
U²³⁵ enrichment (%)	90	90
Fuel Composition	(U,Nb,Zn)C	U-Zr-C-N
Fuel Element Form	Twisted ribbon	Twisted ribbon
Generated electrical power (kW)	N/A	50
Working fluid for power loop (% by mass)	N/A	93% Xe + 7% He
Max temp for power loop (K)	N/A	1,500
Max press for power loop (10⁵ Pa)	N/A	9
Working fluid flow rate (kg/s)	N/A	1.2
Thermal power - propulsion mode (MW)	196	340
Thermal power - power mode (MW)	N/A	0.098
Core length (mm)	800	700
Core diameter (mm)	500	515
Engine length (mm)	3,700	No Data
Engine diameter (mm)	1,200	No Data
Lifetime - propulsion mode (h)	1	5
Lifetime - power mode (yr)	N/A	2
Mass (kg)	2,000*	1,800**

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

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

RD-0140 rocket engine
NPPS bi-modal NTR
1 Nozzle
2 Rotary drum
3 Fuel assembly
4 Outlet to turbogenerator (TG)
5 He+Xe mixture supply from TG
6 Radial reflector
7 Preheating fuel assembly
8 Radiation shield
9 Rotary drum actuator
10 Radiation safety bar actuator
11 Nozzle plug actuator
12 H₂ inlet

Video clip about RD-0140 (in Russian)
click to play video

Figure 6
Twisted Ribbon fuel assembly configuration

LANTR

LANTR
LANTR NERVA mode
Exhaust Velocity	9,221 m/s
Specific Impulse	940 s
Thrust	67,000 N
Thrust Power	0.3 GW
Mass Flow	7 kg/s
Remass	Liquid Hydrogen
LANTR LOX mode
Exhaust Velocity	6,347 m/s
Specific Impulse	647 s
Thrust	184,000 N
Thrust Power	0.6 GW
Mass Flow	29 kg/s
Remass	Hydrogen + Oxygen
LANTR Both
Fuel	Fission: Uranium 235
Reactor	Solid Core
Remass Accel	Thermal Accel: Reaction Heat
Thrust Director	Nozzle
Special	Low-High Gear
Nuclear DC-X NERVA
High Gear
Exhaust Velocity	9,810 m/s
Specific Impulse	1,000 s
Thrust/Engine	1,112,000 N
Thrust	5,560,000 N
Thrust Power	27.3 GW
Mass Flow	567 kg/s
T/W	3
Remass	Hydrogen
Specific Power	7 kg/MW
Low Gear
Exhaust Velocity	5,900 m/s
Specific Impulse	601 s
Thrust/Engine	3,336,000 N
Thrust	16,680,000 N
Thrust Power	49.2 GW
Mass Flow	2,827 kg/s
T/W	9
Remass	Water
Remass Accel	Thermal Accel: Reaction Heat
Thrust Director	Nozzle
Specific Power	4 kg/MW
Both
Number Thrusters	x5
Total Engine Mass	199,600 kg
Fuel	Fission: Uranium 235
Special	Low-High Gear
Wet Mass	460,000 kg

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

O/H MR = oxygen-to-fuel mixture ratio
15 klbf = 66,700 newtons
Engine mass = 2,300 kg
Engine weight = 22,563 kg⋅m/s²
Thrust (newtons) = 22,563 × T/W_eng
e.g., at 1.0 oxygen-to-fuel mixture ratio the thrust will be 22,563 × 4.8 = 108,000 newtons

Porkjet's LANTR mod for the game Kerbal Space Program
Porkjet's LANTR mod for the game Kerbal Space Program
Porkjet's LANTR mod for the game Kerbal Space Program. Left to right: LANTR in NERVA mode, LANTR in afterburner mode, Nuclear Lightbulb

Bi-Modal NTR

Bimodal NTR Solid (NASA)
Propulsion System	NTR Solid Bimodal
Exhaust Velocity	8,980 m/s
Specific Impulse	915 s
Thrust/Engine	66,667 N
Number Thrusters	x3
Thrust	200,000 N
Thrust Power	0.9 GW
Mass Flow	22 kg/s
Total Engine Mass	6,672 kg
T/W	3
Fuel	Fission: Uranium 235
Reactor	Solid Core
Remass	Liquid Hydrogen
Remass Accel	Thermal Accel: Reaction Heat
Thrust Director	Nozzle
Special	Bimodal
Wet Mass	80,000 kg
Dry Mass	26,830 kg
Mass Ratio	2.98 m/s
ΔV	9,811 m/s
Specific Power	7 kg/MW

A useful refinement is the Bimodal NTR.

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

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

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

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

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

Pretty ingenious, eh?

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

Bimodal NTR schematic
ORANGE: NERVA thermal propulsion
BLUE: Brayton electrical power generation
Note ion drive ("electric propulsion") at lower right

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

Trimodal schematic
Brayton electrical power generation in leftmost column
H₂ for Brayton and NERVA in second from left column
Nuclear reactor in second from right column
LANTR O₂ afterburner system in rightmost column
from A Revolutionary Lunar Space Transportation System Architecture Using Extraterrestrial Lox-augmented NTR Propulsion
click for larger image
TRITON Trimodal schematic
ORANGE LINES: H₂ feed for NERVA
PINK LINES: Brayton electrical power generation
GREEN LINES: LANTR O₂ afterburner system

TRITON Trimodal
TRITON Trimodal and Brayton radiator

MITEE

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

Basic

Basic MITEE
Exhaust Velocity	9,810 m/s
Specific Impulse	1,000 s
Thrust	14,000 N
Thrust Power	68.7 MW
Mass Flow	1 kg/s
Total Engine Mass	200 kg
T/W	7
Fuel	Fission: Uranium 235
Reactor	Solid Core
Remass	Liquid Hydrogen
Remass Accel	Thermal Accel: Reaction Heat
Thrust Director	Nozzle
Specific Power	3 kg/MW

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

Monatomic H

Monatomic-H MITEE
Exhaust Velocity	12,750 m/s
Specific Impulse	1,300 s
Thrust	2,350 N
Thrust Power	15.0 MW
Mass Flow	0.18 kg/s
Total Engine Mass	200 kg
T/W	1
Fuel	Fission: Uranium 235
Reactor	Solid Core
Remass	Liquid Hydrogen
Remass Accel	Thermal Accel: Reaction Heat
Thrust Director	Nozzle
Specific Power	13 kg/MW

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

Hybrid

HybridMITEE
Exhaust Velocity	17,660 m/s
Specific Impulse	1,800 s
Thrust	1,700 N
Thrust Power	15.0 MW
Mass Flow	0.10 kg/s
Total Engine Mass	10,000 kg
T/W	0.02
Fuel	Fission: Uranium 235
Reactor	Solid Core
Remass	Single-H
Remass Accel	Thermal Accel: Reaction Heat
Thrust Director	Nozzle
Specific Power	666 kg/MW

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

Liquid Core

Liquid Core 1
Exhaust Velocity	16,000 m/s
Specific Impulse	1,631 s
Thrust	7,000,000 N
Thrust Power	56.0 GW
Mass Flow	438 kg/s
Total Engine Mass	70,000 kg
T/W	10
Fuel	Fission: Uranium 235
Reactor	Liquid Core
Remass	Water
Remass Accel	Thermal Accel: Reaction Heat
Thrust Director	Nozzle
Specific Power	1 kg/MW
Liquid Core 2
Exhaust velocity	14,700 to 25,500 m/s

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

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

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

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

LARS

LARS
Exhaust Velocity	19,620 m/s
Specific Impulse	2,000 s
Thrust	20,000 N
Thrust Power	0.2 GW
Mass Flow	1 kg/s
Total Engine Mass	1,000 kg
T/W	2
Fuel	Fission: Uranium 235
Reactor	Liquid Core
Remass	Liquid Hydrogen
Remass Accel	Thermal Accel: Reaction Heat
Thrust Director	Nozzle
Specific Power	5 kg/MW
Luna
Propulsion System	LARS
Exhaust Velocity	10,300 m/s
Specific Impulse	1,050 s
Thrust	11,000,000 N
Thrust Power	56.6 GW
Mass Flow	1,068 kg/s
Total Engine Mass	9,000 kg
T/W	125
Fuel	Fission: Uranium 235
Remass	Water
Thrust Director	Nozzle
Wet Mass	226,000 kg
Dry Mass	45,000 kg
Mass Ratio	5.02 m/s
ΔV	16,623 m/s

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

Vapor Core

Vapor Core
Thrust Power	1.6 GW
Exhaust velocity	9,800 to 11,800 m/s
Thrust	330,000 n
Propellant mass flow	30 kg/sec
Reactor thermal power	1,400 to 1,800 MW
Total engine mass	6.83 tonne
Fuel element mass total	1.35 tonne
Forward reflector mass	0.60 tonne
Aft reflector mass	0.51 tonne
Radial reflector mass	2.47 tonne
Radiation shield mass	0.9 tonne
Total reactor mass	5.83 tonne
Misc. engine component mass	0.9 tonne
T/W	5
Fuel	Fission: Uranium Hexafluoride
Reactor	Vapor Core
Remass	Liquid Hydrogen
Remass Accel	Thermal Accel: Reaction Heat
Thrust Director	Nozzle
Specific Power	4 kg/MW

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

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

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

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

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

Reflectors
Side	Composition	Thickness	Mass
Forward	Beryllium oxide	15 cm	0.60 tonne
Aft	C-C Composite	25 cm	0.51 tonne
Radial	Beryllium oxide	15 cm	2.47 tonne

Schematic of NVTR Fuel Element

CORE: 2000 fuel elements
Radius	0.5 m
Height	1.5 m
Fuel channel per element	12 to 32
Hydrogen channel per element	12 to 32
Critical mass	20 kg
Hydrogen pressure	100 atm
UF₄ pressure	100 atm
Fuel center temperature	4,500 K

P= psia, T=deg-R, W=lb_m/s, H=BTU/lb_m, S=BTU/lb_m-R. Flowrates indicated are for one-half of system

Design Values
Pump Flowrate (Total)	75.20 lb_m/s
Pump Discharge Pressure	3,924 psia
Pump Efficiency	80.01%
Turbopump RPM	70,000 RPM
Turbopump Power (each)	9,836 HP
Turbine Inlet Temperature	481 deg-R
Turbine Pressure Ratio	1.69
Turbine Flow Rate (each)	33.77 lb_m/s
Reactor Thermal Power	1,769 MW
Fuel Element and Reflector Power	1,716 MW
Nozzle Chamber Temperature	5,580 deg-R
Chamber Pressure (Nozzle Stagnation)	1,500 psia
Nozzle Expansion Area Ratio	500:1
Vacuum Specific Impulse (Delivered)	997.8 sec
Heat Loads
Nozzle-con (total)	30.05 MW
Nozzle-div (total)	22.97 MW
Reflector (total)	35.0 MW

Typical NVTR Engine Parameters
Nozzle Area Ratio	500
Fuel Pressure	100 atm
Average Fuel Temperature	4000 K
Maximum Element Heat Flux	420 W/cm²
Nomial Element Length	150 cm
Fuel Volume Fraction	0.15
Coolant Volume Fraction	0.15
Moderator Volume Fraction	0.70
Fuel Element Power	0.9 MWt
Element Heat Transfer Area	2141 cm²
Reactor Core L/D	1.5
Fuel Channel Diameter	0.142 cm
Fuel Channel Sectional Area	0.0158 cm²
Total Fuel Channel Area Per Element	0.505 cm²
Fuel Element Sectional Area	3.464 cm²
Element Diameter (across flats)	2.2 cm
Coolant Channel Diameter	0.142 cm
Coolant Channel Sectional Area	0.0158 cm²
Total Coolant Channel Area Per Element	0.505 cm²
Core Volume	1.2 m³
Core Volume Density	1,500 MW/m³
Fuel Element Mass, Total	1.35 MT
Forward Reflector Mass	0.60 MT
Aft Reflector Mass	0.51 MT
Radial Reflector Mass	2.47 MT
Radiation Shield Mass	0.90 MT
Total Reactor Mass	5.83 MT
Misc. Engine Components Mass	0.9 MT
Total Engine Mass	6.83 MT
Engine F/W	5.0

Gas Core

Closed Cycle

Gaseous Core NTR closed 1
Exhaust Velocity	20,405 m/s
Specific Impulse	2,080 s
Thrust	445,000 N
Thrust Power	4.5 GW
Mass Flow	22 kg/s
Total Engine Mass	56,800 kg
T/W	0.80
Fuel	Fission: Uranium Hexafluoride
Reactor	Gas Core Closed-Cycle
Remass	Liquid Hydrogen
Remass Accel	Thermal Accel: Reaction Heat
Thrust Director	Nozzle
Specific Power	13 kg/MW
Gaseous Core NTR closed 2
Thrust Power	0.6 to 231 GW
Exhaust velocity	10,800 to 31,400 m/s
Thrust	117,700 to 14,700,000 n
Engine mass	30 to 300 tonne
Engine T/W	0.4 to 5.0
Operating Pressure	400 to 1600 atm
NASA report nuclear lightbulb
Thrust Power	3.7 GW
Engine Power	4.6 GW
Exhaust velocity	18,300 m/s
Thrust	409,000 n
Engine mass	32 tonne
Engine T/W	1.3
Operating Pressure	500 atm
Propellant mass flow	22.3 kg/s
Liberty Ship
Propulsion System	Nuclear Lightbulb
Exhaust Velocity	30,000 m/s
Specific Impulse	3,058 s
Thrust/Engine	5,340,000 N
Number Thrusters	x7
Thrust	37,380,000 N
Thrust Power	560.7 GW
Mass Flow	1,246 kg/s
Total Engine Mass	378,000 kg
T/W	10
Fuel	Fission: Uranium Hexafluoride
Wet Mass	2,700,000 kg
Dry Mass	1,600,000 kg
Mass Ratio	1.69 m/s
ΔV	15,697 m/s
Specific Power	0.67 kg/MW

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

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

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

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

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

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

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

Image from NASA Report, Studies of Specific Nuclear Light Bulb and Open-Cycle Vortex-Stabilized Gaseous Nuclear Rocket Engines. Warning: I did the color-coding myself, I may have gotten some of the details incorrect.
Image by me, attempting to work from the blueprints
Image by me, attempting to work from the blueprints
Image by me, attempting to work from the blueprints
Porkjet's Nuclear Lightbulb mod for the game Kerbal Space Program
Porkjet's Nuclear Lightbulb mod for the game Kerbal Space Program. Left to right: LANTR in NERVA mode, LANTR in afterburner mode, Nuclear Lightbulb

cw3brett's KSP images using Porkjet's Nuclear Lightbulb mod
cw3brett's KSP images using Porkjet's Nuclear Lightbulb mod
cw3brett's KSP images using Porkjet's Nuclear Lightbulb mod

NASA Report

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

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

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

*Colored diagram of a primary circuit inlet.*

Uranium fuel

The total fissioning uranium in all seven vortexes be about 25.2 pounds of uranium (about 3.6 pounds per cavity). You would ordinarily need more to ensure nuclear criticality, but the required amount is brought down by the beryllium oxide neutron reflector encasing each cavity. The average uranium fuel density is 0.409 lb/ft³. The total density of the neon-uranium mix inside the vortex is about 0.56 lb/ft³. A unit of neon gas will spend about 3.8 seconds inside the cavity. A unit of uranium will spend about 19 seconds inside the cavity. This implies a uranium fuel flow rate of 0.19 lb/sec per cavity.
According to my slide rule, if the array of seven cavities is producing 4,600 megawatts, it means that the array is burning a miniscule total of 0.055 grams (0.00012 pounds) of uranium fuel per second (0.0079 grams per cavity per second). It still needs the full 3.6 pounds per cavity to be present in order to burn the fraction of a gram.
The theoretical maximum specific impulse possible is 2230 seconds. Due to this designs incomplete expansion, transpiration coolant flow in the nozzle, presence of tungsten seeding, and friction losses the specific impulse is reduced to 84% or 1870 seconds. Total propellant flow (allowing for tungsten seeds and transpiration cooling) is 49.3 lb/sec. This would result in a thrust of 92,000 pounds force. For complicated reasons you can find in the report, this implies that the exhaust nozzles are 0.0875 feet in diameter at the throat expanding to 2.04 feet diameter at the exit.

Uranium refueling

Careful readers may have noticed how the description avoids mentioning the details on how one gets the uranium into the lightbulbs. This is because it is quite a difficult problem, and each of the proposed solutions has drawbacks. The basic problem is old reliable: all the atomic fireworks inherent in ²³⁵U will happen if you merely let too much of it accumulate in one place. You have to store it diffuse and somehow bring it together in the lightbulb.
Method #1 Store it as uranium hexafluoride gas. This would be in large tanks of low pressure (i.e., low density) and with the tanks full of neutron absorbing foam. Pump enough into the lightbulb, a chain reaction will start, and well before the reaction reaches 13,000°R the uranium will have separated from the fluorine.
The problem is that now you have the insanely dangerous task of dealing with 13,000°R fluorine gas. At room temperature the blasted stuff will violently react with any element in the known universe except helium and neon. A temperature of 13,000°R makes it about 13,000 times as deadly. It will explosively corrode away anything solid in its path like molten lead on facial tissue. Chemist Derek Lowe sarcastically notes that "At seven hundred freaking degrees, fluorine starts to dissociate into monoatomic radicals, thereby losing its gentle and forgiving nature." You can read more about the suicidal risk of dealing with hot fluorine in his amusing blog post.
Method #2 Store it as sub-critical chunks of uranium, melt them, and inject the molten uranium into the lightbulb. Uranium melts at 1403°K, which is difficult but not impossible. The plan is to somehow turn the molten uranium into a sort of aerosol mist suspended in hot neon.
The problem is that the molten uranium wants to plate itself all over the melter and the aerosol spray equipment. Which is annoying if the material in question is something like lead, but disasterous if the material is radioactive and fissionable.
Method #3 is to store the uranium cold as finely divided dust. As dust it is pumpable, injectable, and it will not plate over everything. Inside the lightbulb the uranium dust will be rapidly heated to vaporization by the nuclear reaction. This method does not have any major problems, except for the common problem of how to protect the transparent wall from being vaporized by the heat.
Again, the uranium delivery system seems to be totally missing from the blueprint. The only bit present is the short stub of the injector at the top of each lightbulb.

*Propellant flow through a primary circuit inlet.*

Open Cycle

*Four Mars Missions for analysis, with gas-core engine characteristics. In the graphs below, the trip-time curves imply engines with the characteristics listed in the above tables.*

Coaxial

Coaxial
Exhaust Velocity	17,658 m/s
Specific Impulse	1,800 s
Thrust	17,800,000 N
Thrust Power	0.2 TW
Mass Flow	1,008 kg/s
Total Engine Mass	127,000 kg
T/W	14
Fuel	Fission: Uranium Hexafluoride
Reactor	Gas Core Open-Cycle
Remass	Liquid Hydrogen
Remass Accel	Thermal Accel: Reaction Heat
Thrust Director	Nozzle
Specific Power	1 kg/MW
NASA-Lewis
Thrust Power	0.495GW
Exhaust velocity	22,000 m/s
Specific Impulse	2,200 s
Thrust	45,000 n
Engine mass	66,000 kg
T/W	0.68
Diameter	5 m
Length	5 m
Fuel Temp	20,000° R
Propellant Temp	10,000° R

Gaseous core coaxial flow fission / nuclear thermal rocket.

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

No, the concept does not work very well (i.e., huge amounts of nuclear fuel escape), and it seems to have been abandoned.

Circa 1960 NASA-Lewis concept for a gas core nuclear rocket engine. From The Unwanted Blog.

Open Cycle

Open Cycle
Propulsion System	Gas Core NTR
Exhaust Velocity	35,000 m/s
Specific Impulse	3,568 s
Thrust	3,500,000 N
Thrust Power	61.2 GW
Mass Flow	100 kg/s
Total Engine Mass	200,000 kg
Fuel	Fission: Uranium Hexafluoride
Reactor	Gas Core Open-Cycle
Remass	Liquid Hydrogen
Remass Accel	Thermal Accel: Reaction Heat
Thrust Director	Nozzle
Specific Power	3 kg/MW
Engine mass	30-200 tonne
T/W	11.9 to 1.8
Open Cycle 2
Propulsion System	Gas Core NTR
Exhaust Velocity	50,000 m/s
Specific Impulse	5,097 s
Thrust	5,000,000 N
Thrust Power	0.1 TW
Mass Flow	100 kg/s
Fuel	Fission: Uranium Hexafluoride
Remass	Liquid Hydrogen
Specific Power	2 kg/MW
Engine mass	30-200 tonne
T/W	17.0 to 2.5
Open Cycle 3
Thrust Power	GW
Exhaust velocity	25,000 to 69,000 m/s
Thrust	19,600 to 108,000 n
Engine mass	40 to 110 tonne
T/W	0.05 to 0.10
Operating Pressure	400 to 2000 atm
Open Cycle MAX
Exhaust Velocity	98,000 m/s
Specific Impulse	9,990 s
Thrust	3,000,000 N
Thrust Power	0.15 TW
Mass Flow	31 kg/s
Total Engine Mass	15,000 kg
T/W	20
Fuel	Fission: Uranium Hexafluoride
Tanker
Propulsion System	Gas Core NTR Open-cycle
Exhaust Velocity	35,316 m/s
Specific Impulse	3,600 s
Thrust	3,500,000 N
Thrust Power	61.8 GW
Mass Flow	99 kg/s
Fuel	Fission: Uranium Hexafluoride
Remass	Liquid Hydrogen
Wet Mass	433,000 kg
Dry Mass	268,000 kg
Mass Ratio	1.62 m/s
ΔV	16,943 m/s

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

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

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

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

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

You can find more details here.

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

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

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

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

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

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

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

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

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

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

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

From NASA Report, Gas Core Reactors - A New Look TM X-67823
From NASA Report, Mars Exploration Studies 1988 Volume 2
From NASA Report, High-Specific-Impulse Gas-Core Reactors TM X-2243
From NASA Report, High-Specific-Impulse Gas-Core Reactors TM X-2243
From NASA Report, Reactor Moderation, Pressure Vessel, and Heat Rejection System of an Open-Cycle Gas-Core Nuclear Rocket Concept TM X-2772
From NASA Report, Reactor Moderation, Pressure Vessel, and Heat Rejection System of an Open-Cycle Gas-Core Nuclear Rocket Concept TM X-2772
From NASA Report, Reactor Moderation, Pressure Vessel, and Heat Rejection System of an Open-Cycle Gas-Core Nuclear Rocket Concept TM X-2772
From NASA Report, Reactor Moderation, Pressure Vessel, and Heat Rejection System of an Open-Cycle Gas-Core Nuclear Rocket Concept TM X-2772
Nexus gas core heavy lift vehicle (1964). Isp of 2220 seconds, payload delivery of one million pounds to lunar orbit. From The Unwanted Blog
Nexus with chemical first stage, and gas core second stage. From The Unwanted Blog
CGI 3D rendering of the Nexus engines created by William Black
CGI 3D rendering of the Nexus engines created by William Black

From NUCLEAR PROPULSION &MDASH; A VITAL TECHNOLOGY FOR THE EXPLORATION OF MARS AND THE PLANETS BEYOND (1987)

Vortex Confined

From US Patent 3714782 Gasous Nuclear Rocket Engine (1969)

Nuclear Salt Water

From "Nuke Your Way to the Stars" by John Cramer in Analog Mid-December 1992. Artist unknown.

NSWR
20% UTB
Exhaust Velocity	66,000 m/s
Specific Impulse	6,728 s
Thrust	12,900,000 N
Thrust Power	425.7 GW
Mass Flow	195 kg/s
Total Engine Mass	33,000 kg
T/W	40
Fuel	Fission: Uranium Tetrabromide
Reactor	Gas Core Open-Cycle
Remass	Water
Remass Accel	Thermal Accel: Reaction Heat
Thrust Director	Pusher Plate
Specific Power	0.08 kg/MW
90% UTB
Exhaust Velocity	4,700,000 m/s
Specific Impulse	479,103 s
Thrust	13,000,000 N
Thrust Power	30.6 TW
Mass Flow	3 kg/s

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

From AIAA 90-2371 Nuclear Salt Water Rockets: High Thrust at 10,000 sec I_sp

Salt-water Zubrin thrust card from the game High Frontier. Performance is so good that some players do not allow them to be used in the game. Only drawback is they require **lots** of heat radiators, and it is difficult to perform the research which allows them to be constructed.

From **The Last Great War** by Matthew Lineberger *(not yet published)*

Fission Fragment

George Chapline
Exhaust velocity	980,000 m/s

All of the other nuclear thermal rockets generate heat with nuclear fission, then transfer the heat to a working fluid which becomes the reaction mass. The transfer is always going to be plagued by inefficiency, thanks to the second law of thermodynamics. What if you could eliminate the middleman, and use the fission heat directly with no transfer?

That what the fission fragment rocket does. It uses the hot split atoms as reaction mass. The down side is that due to the low mass flow, the thrust is minuscule. But the up side is that the exhaust velocity is 5% the speed of light! 15,000,000 kilometers per second, that's like a bat out of hell. With that much exhaust velocity, you could actually have a rocket where less than 50% of the total mass is propellant (i.e., a mass ratio below 2.0).

The fission fragment is one of the few propulsion systems where the reaction mass has a higher thermal energy than the fuel elements. The other notable example being the Pulsed NTR.

Dr. Chapline's design use thin carbon filaments coated with fission fuel (coating is about 2 micrometers thick). The filaments radiated out from a central hub, looking like a fuzzy vinyl LP record. These revolving disks were spun at high speed through a reactor core, where atoms of nuclear fuel would undergo fission. The fission fragments would be directed by magnetic fields into an exhaust beam.

The drawback of this design is that too many of the fragments fail to escape the fuel coat (which adds no thrust but does heat up the coat) and too many hit the carbon filaments (which adds no thrust but does heat up the filaments). This is why the disks spin at high speed, otherwise they'd melt.

Fission-fragment propulsion as proposed by Dr. George Chapline.
a fissionable filaments, b revolving disks, c reactor core, d fragments exhaust
Fission fragment concept as proposed by Dr. George Chapline. The reactor consists of thin carbon filaments coated with nuclear fuel rotated at high speed through the core. Courtesy of LLNL (1986)

Dusty Plasma
550AU
Thrust	22 N
Thrust Power	0.2 GW
Mass Flow	1.00e-06 kg/s
T/W	2.49e-04
Specific Power	55 kg/MW
0.5LY
Thrust	344 N
Thrust Power	2.6 GW
Mass Flow	2.30e-05 kg/s
T/W	4.00e-03
Specific Power	3 kg/MW
All
Exhaust Velocity	15,000,000 m/s
Specific Impulse	1,529,052 s
Total Engine Mass	9,000 kg
Fuel	Fission: Uranium 235
Reactor	Gas Core MHD Choke
Remass	Reaction Products
Remass Accel	Fission-Fragment
Thrust Director	Magnetic Nozzle

Rodney Clark and Robert Sheldon solve the problem with their Dusty plasma bed reactor (report).

You take the fission fuel and grind it into dust grains with an average size of 100 nanometers (that is, about 1/20th the thickness of the fuel coating in dr. Chapline's design). This does two things [A] most of the fragments escape and [B] the dust particles have such a high surface to volume ratio that heat (caused by fragments which fail to escape) readily dissipates, preventing the dust particles from melting.

The dust is suspended in the center of a reaction chamber whose walls are composed of a nuclear moderator. Power reactors will use beryllium oxide (BeO) as a moderator, but that is a bit massive for a spacecraft. The ship will probably use lithium hydride (LiH) for a moderator instead, since is only has one-quarter the mass. Probably about six metric tons worth. The dust is suspended electrostatically or magnetically by a containment field generator. The dust is heated up by radio frequency (RF) induction coils. The containment field generator will require superconductors, which will probably require a coolant system of its own.

The dust particles are slow and are relatively massive, while the fission fragments are fast and not very massive at all. So the magnetic field can be tailored so it holds the dust but allows the fission fragments to escape. Magnetic mirrors ensure that fragments headed the wrong way are re-directed to the exhaust port.

One valuable trick is that you can use the same unit for thrust or to generate electricity. Configure the magnetic field so that the fragments escape "downward" through the exhaust port and you have thrust. Flip a switch to change the magnetic field so that the fragments escape upward into deceleration and ion collection electrodes and you generate electricity. As a matter of fact, it is go efficient at generrating electricity that researchers are busy trying to adapt this for ground based power plants. But I digress.

The dust is only sufficient for a short period of critical nuclear reaction so it must be continuously replenished. The thermal energy released by fission events plus heat from collisions between fission fragments and dust grains create intense heat within the dust cloud. Since there is no core cooling flow, the reactor power is limited to the temperature at which the dust can radiatively cool itself without vaporizing. The interior of the reaction chamber walls will protected by a mirrored (95% reflection) heat shield attached to a heat radiator. The outer moderator layer will have its own heat shield.

Clark and Sheldon roughed out a propulsion system. It had six tons for the moderator, 2 tons for radiators and liquid metal cooling, 1 ton for magnets, power recovery, and coils, for a grand total of 9 tons. The reaction chamber will be about 1 meter in diameter and 10 meters long. The moderator blanket around the chamber will be about 40 centimeters thick. The thrust is a function the size of the cloud of fissioning dust, and is directly related to the power level of the reactor. There is a limit to the maximum allowed power level, set by the coolant system of the reaction chamber. Clark and Sheldon estimate that only about 46% of the fission fragments provide thrust while the rest are wasted. See the report for details.

In the table, the 550AU engine is for a ten year journey to the Solar gravitational lensing point at 550 astronomical units (so you can use the sun as a giant telescope lens). The 0.5LY engine is for a thirty year trip to the Oort cloud of comets. These are constant acceleration brachistochrone trajectories, the 550AU mission will need a reactor power level of 350 MW and the 0.5LY mission will need 5.6 GW. Don't forget that the engine power is only 46% efficient, that's why the table thrust values are lower.

Dusty plasma bed reactor by Rodney Clark and Robert Sheldon
1. fission fragments ejected for propulsion
2. reactor
3. fission fragments decelerated for power generation
1. moderator (BeO or LiH)
2. containment field generator
3. RF induction coil
Dusty Plasma Terawatt Thruster patent card from the game High Frontier (Colonization Expansion).

Werka FFRE
First Generation
Exhaust Velocity	5,170,000 m/s
Specific Impulse	527,013 s
Thrust	43 N
Thrust Power	0.1 GW
Mass Flow	8.00e-06 kg/s
Total Engine Mass	113,400 kg
T/W	3.90e-05
Fuel	Fission: Plutonium 239
Reactor	Gas Core MHD Choke
Remass	Reaction Products
Remass Accel	Fission-Fragment
Thrust Director	Magnetic Nozzle
Specific Power	1,020 kg/MW
HOPE FFRE
Propulsion System	Werka FFRE
Wet Mass	303,000 kg
Dry Mass	295,000 kg
Mass Ratio	1.03 m/s
ΔV	138,336 m/s

Robert Werka has a more modest and realistic design for his fission fragment rocket engine (FFRE). He figures that a practical design will have an exhaust velocity of about 5,200,000 m/s instead of his estimated theoretical maximum of 15,000,000 m/s. His lower estimate is still around 1.7% the speed of light so we are still talking about sub 2.0 mass ratios. Collisions between fission fragments and the dust particles is responsible for the reduction in exhaust velocity.

Incidentally the near relativistic exhaust velocity reduces radioactive contamination of the solar system. The particles are traveling well above the solar escape velocity (actually they are even faster than the galactic escape velocity) so all the radioactive exhaust goes shooting out of the solar system at 0.017c.

The dusty fuel is nanometer sized particles of slightly critical plutonium carbide, suspended and contained in an electric field. A moderator of deuterated polyethylene reflects enough neutrons to keep the plutonium critical, while control rods adjust the reaction levels. The moderator is protected from reaction chamber heat by a heat shield, an inner layer composed of carbon-carbon to reflect infrared radiation back into the core. The heat shield coolant passes through a Brayton cycle power generator to create some electricty, then the coolant is sent to the heat radiator.

The details of Werka's initial generation FFRE can be found in the diagram below. The reaction chamber is about 5.4 meters in diameter by 2.8 meters long. The magnetic nozzle brings the length to 11.5 meters. The fuel is uranium dioxide dust which melts at 3000 K, allowing a reactor power of 1.0 GW. It consume about 29 grams of uranium dioxide dust per hour (not per second). Of the 1.0 GW of reactor power, about 0.7 GW of that is dumped as waste heat through the very large radiators required.

The second most massive component is the magnetic mirror at the "top" of the reaction chamber. Its purpose is to reflect the fission fragments going the wrong way so they turn around and travel out the exhaust nozzle. Surrounding the "sides" of the reaction chamber is the collimating magnet which directs any remaining wrong-way fragments towards the exhaust nozzle. The exhaust beam would cause near-instantaneous erosion of any material object (since it is electrically charged, relativistic, radioactive grit). It is kept in bounds and electrically neutralized by the magnetic nozzle cage.

Werka Initial Generation FFRE Design

Fission Sail

1. plastic layer
2. radionuclides layer
3. stopped α particle
4. escaping α particle
5. resulting mean motion
6. neutralizer electron beam

Antimatter-Driven Sail

The sail is made of graphite and carbon-carbon fiber, infused with a tiny amount of uranium. It is subjected to a misting of antiprotons. These induce uranium atoms to fission, with the recoil pushing the sail. Since this is nuclear powered, the sail does not have to be kilometers in diameter, five meters will do. 30 miligrams of antiprotons could push the sail to the Kuiper Belt.

Art: Hbar Technologies, LLC/Elizabeth Lagana
Antiproton Sail and Harvestor Freighter Fleet card from the game High Frontier (Colonization Expansion).

Pulse

Orion

Artwork by Rhys Taylor

Fission Orion
Exhaust Velocity	43,000 m/s
Specific Impulse	4,383 s
Thrust	263,000 N
Thrust Power	5.7 GW
Mass Flow	6 kg/s
Total Engine Mass	200,000 kg
T/W	0.13
Fuel	Fission: Uranium 235
Reactor	Pulse Unit
Remass	Tungsten
Remass Accel	Thermal Accel: Reaction Heat
Thrust Director	Pusher Plate
Specific Power	35 kg/MW
Fusion Orion
Exhaust Velocity	73,000 m/s
Specific Impulse	7,441 s
Thrust	292,000 N
Thrust Power	10.7 GW
Mass Flow	4 kg/s
Total Engine Mass	200,000 kg
T/W	0.15
Fuel	Deuterium-Deuterium Fusion
Specific Power	19 kg/MW
1959 Orion 1^st Gen
Thrust Power	1,600 GW
Exhaust velocity	39,000 m/s
Thrust	80,000,000 n
Engine mass	1,700 tonne
T/W >1.0	yes
1959 Orion 2^nd Gen
Thrust Power	24,000 GW
Exhaust velocity	120,000 m/s
Thrust	400,000,000 n
Engine mass	3,250 tonne
T/W >1.0	yes
ORION USAF 10m
Exhaust Velocity	32,900 m/s
Specific Impulse	3,354 s
Thrust	2,000,000 N
Thrust Power	32.9 GW
Mass Flow	61 kg/s
Total Engine Mass	107,900 kg
T/W	2
Wet Mass	475,235 kg
Dry Mass	180,975 kg
Mass Ratio	2.63 m/s
ΔV	31,763 m/s
Specific Power	3 kg/MW
ORION 4K ton battleship
Exhaust Velocity	39,000 m/s
Specific Impulse	3,976 s
Thrust	80,000,000 N
Thrust Power	1.6 TW
Mass Flow	2,051 kg/s
Total Engine Mass	1,700,000 kg
T/W	4.80
Specific Power	1.09 kg/MW
ΔV 10 km/s
Wet Mass	4,000,000 kg
Dry Mass	3,100,000 kg
Mass Ratio	1.29 m/s
ΔV	9,941 m/s
ΔV 21 km/s
Wet Mass	4,000,000 kg
Dry Mass	2,353,000 kg
Mass Ratio	1.70 m/s
ΔV	20,694 m/s
ΔV 30 km/s
Wet Mass	4,000,000 kg
Dry Mass	1,852,000 kg
Mass Ratio	2.16 m/s
ΔV	30,031 m/s
ORION 10k ton adv
Exhaust Velocity	120,000 m/s
Specific Impulse	12,232 s
Thrust	400,000,000 N
Thrust Power	24.0 TW
Mass Flow	3,333 kg/s
Total Engine Mass	3,250,000 kg
T/W	13
Specific Power	0.14 kg/MW
ΔV 10 km/s
Wet Mass	10,000,000 kg
Dry Mass	9,199,000 kg
Mass Ratio	1.09 m/s
ΔV	10,019 m/s
ΔV 15.5 km/s
Wet Mass	10,000,000 kg
Dry Mass	8,772,000 kg
Mass Ratio	1.14 m/s
ΔV	15,722 m/s
ΔV 20 km/s
Wet Mass	10,000,000 kg
Dry Mass	8,403,000 kg
Mass Ratio	1.19 m/s
ΔV	20,880 m/s
ΔV 30 km/s
Wet Mass	10,000,000 kg
Dry Mass	7,813,000 kg
Mass Ratio	1.28 m/s
ΔV	29,616 m/s
ΔV 100 km/s
Wet Mass	10,000,000 kg
Dry Mass	4,348,000 kg
Mass Ratio	2.30 m/s
ΔV	99,944 m/s
Orion MAX
Exhaust Velocity	9,800,000 m/s
Specific Impulse	998,981 s
Thrust	8,000,000 N
Thrust Power	39.2 TW
Mass Flow	0.82 kg/s
Total Engine Mass	8,000 kg
T/W	102
Fuel	Proton-Proton Fusion
Remass	Tungsten
Specific Power	2.04e-04 kg/MW

Orion AKA "old Boom-boom" is the ultimate consumable nuclear thermal rocket, based on the "firecracker under a tin can" principle. Except the tin can is a spacecraft and the firecracker is a nuclear warhead.

This concept has the spacecraft mounted with shock absorbers on an armored "pusher plate". A stream of small (5 to 15 kiloton) fission or fusion explosives are detonated under the plate to provide thrust. While you might find it difficult to believe that the spacecraft can survive this, you will admit that this will give lots of thrust to the spacecraft (or its fragments). On the plus side, a pusher plate that can protect the spacecraft from the near detonation of nuclear explosives will also provide dandy protection from any incoming weapons fire. On the minus side I can hear the environmentalists howling already. It will quite thoroughly devastate the lift-off site, and give all the crew bad backs and fallen arches. And they had better have extra-strength brassieres and athletic supporters.

Mathematician Richard Courant viewed an Orion test and said "Zis is not nuts, zis is super-nuts."

This section is about the Orion propulsion system. If you want all the hot and juicy details about various versions of Orion spacecraft go here.

Please note that Orion drive is pretty close to being a torchship, and is not subject to the Every gram counts rule. It is probably the only torchship we have the technology to actually build today.

If you want the real inside details of the original Orion design, run, do not walk, and get a copies the following issues of of Aerospace Projects Review: Volume 1, Number 4, Volume 1, Number 5, and Volume 2, Number 2. They have blueprints, tables, and lots of never before seen details.

If you want your data raw, piled high and dry, here is a copy of report GA-5009 vol III "Nuclear Pulse Space Vehicle Study - Conceptual Vehicle Design" by General Atomics (1964). Lots of charts, lots of graphs, some very useful diagrams, almost worth skimming through it just to admire the diagrams.

The sad little secret about Orion is that the mission it is best suited for is boosting heavy payloads into orbit. Which is exactly the mission that the enviromentalist and the nuclear test ban treaty will prevent. Orion has excellent thrust, which is what you need for lift-off and landing. Unfortunately its exhaust velocity is pretty average, which is what you need for efficient orbit-to-orbit maneuvers.

Having said that, there is another situation where high thrust is desirable: a warship jinking to make itself harder to be hit by enemy weapons fire. It is also interesting to note that the Orion propulsion system works very well with the bomb-pumped laser weapons system.

Each pulse unit is a tiny nuclear bomb, encased in a "radiation case" that has a hole in the top. A nuclear blasts is initially mostly x-rays. The radiation case is composed of a material that his opaque to x-rays (depleted uranium). The top hole thus "channels" the flood of x-rays in an upwards direction (at least in the few milliseconds before the bomb vaporizes the radiation case).

The channeled x-rays then strike the "channel filler" (beryllium oxide). The channel filler transforms the atomic fury of x-rays into an atomic fury of heat.

Lying on top of the channel filler is the disc of propellant (tungsten). The atomic fury of heat flashes the tungsten into a jet of ionized tungsten plasma, traveling at high velocity (in excess of 1.5 × 10⁵ meters per second). This crashes into the pusher plate, accelerating the spacecraft. It crashes hard. You will note that there are two stages of shock absorbers between the pusher plate and the spacecraft, preventing instant crew death.

The ratio of beryllium oxide to tungsten is 4:1.

The thickness of the beryllium oxide and tungsten should be such to serve as a shield to protect the engine and upper vehicle from the neutron and high-energy gamma radiation produced by the nuclear explosion. This sets a lower limit on the thickness of the propellant and channel filler for a particular design.

The jet is confined to a cone about 22.5 degrees (instead of in all directions). The detonation point is positioned such that the 22.5 cone exactly covers the diameter of the pusher plate. The idea is that the wider the area of the cone, the more spread out the impulse will be, and the larger the chance that the pusher plate will not be utterly destroyed by the impulse.

It is estimated that 85% of the energy of the nuclear explosion can be directed in the desired direction. The pulse units are popped off at a rate of about one per second. A 5 kiloton charge is about 1,152 kg. The pulses are so brief that there is no appreciable "neutron activation", that is, the neutron from the detonations do not transmute parts of the spacecraft's structure into radioactive elements. This means astronauts can exit the spacecraft and do maintenance work shortly after the pulse units stop detonating.

The device is basically a nuclear shaped charge. A pulse unit that was not a shaped charge would of course waste most of the energy of the explosion. Figure that 1% at best of the energy of a non-shaped-charge explosion would actually hit the pusher plate, what a waste of perfectly good plutonium.

Each charge accelerates the spacecraft by roughly 12 m/s. A 4,000 ton spacecraft would use 5 kiloton charges, and a 10,000 ton spacecraft would use 15 kiloton charges. For blast-off, smaller charges of 0.15 kt and 0.35 kt respectively would be used while within the Terra's atmosphere. The air between the charge and the pusher plate amplifies the impulse delivered (it is extra propellant), so if you are not in airless space you can get away with a smaller kt yield.

How much weapons-grade plutonium will each charge require? As with most details about nuclear explosives, specifics are hard to come by. According to GA-5009 vol III , pulse units with 2.0×10⁶ newtons to 4.0×10⁷ newtons all require approximately 2 kilograms per pulse unit, with 1964 technology. It goes on to say that advances in the state of the art could reduce the required amount of plutonium by a factor 2 to 4, especially for lower thrust units. 2.0×10⁶ n is 1 kiloton, I'm not sure what 4.0×10⁷ n corresponds to, from the document I'd estimate it was about 15 kt. Presumably the 2 kg plutonium lower limit is due to problems with making a critical mass, you need a minimum amount to make it explode at all.

According to Scott Lowther, the smallest pulse units were meant to propel a small ten-meter diameter Orion craft for the USAF and NASA. The units had a yield ranging from one-half to one kiloton. The USAF device was one kiloton, diameter 36 centimeters, mass of 86 kilograms, tungsten propellant mass of 34.3 kilograms, jet of tungsten plasma travels at 150,000 meters per second. One unit would deliver to the pusher plate a total impulse of 2,100,000 newton-seconds. Given the mass of the ten-meter Orion, detonating one pulse unit per second would give an acceleration well over one gee. According to my slide rule, this implies that the mass of the ten-meter Orion is a bit under 210 metric tons.

Pulse Unit	Yield	Mass	Dia.	Height	Propellant (percent)	Det. Interval	Propellant Velocity	Effective Exhaust Velocity (I_sp)	Thrust per unit	Effective Thrust
NASA 10m Orion (vacuum)		141 kg				0.86 s		18,200 m/s (1,850 s)	3.0×10⁶ N	3.5×10⁶ N
USAF 10m Orion (vacuum)	1 kg	79 kg (86 kg?)	0.33 m	0.61 m	34.3 kg (40%)	1 s	1.5×10⁵ m/s	25,800 m/s (2,630 s)	2.0×10⁶ N	2.0×10⁶ N
20m Orion (vacuum)		450 kg				0.87 s		30,900 m/s (3,150 s)	1.4×10⁷ N	1.6×10⁷ N
4000T Orion (atmo)	0.15 kt	1,152 kg	0.81 m	0.86 m		1.1 s	1.17×10⁵ m/s	42,120 m/s (4,300 s)	8.8×10⁷ N	8.0×10⁷ N
4000T Orion (vacuum)	5 kt	1,152 kg	0.81 m	0.86 m	415 kg (36%)	1.1 s	1.17×10⁵ m/s	42,120 m/s (4,300 s)	8.8×10⁷ N	8.0×10⁷ N
10,000T Orion (atmo)	0.35 kt							118,000 m/s (12,000 s)		4.0×10⁸
10,000T Orion (vacuum)	15 kt							118,000 m/s (12,000 s)		4.0×10⁸
20,000T Orion (vacuum)	29 kt	1,150 kg	0.8 m

Pulse Unit: The type of Orion spacecraft that uses this unit, and whether it is an atmospheric or vacuum type.
Yield: Nuclear explosive yield (kilotons)
Mass: Mass of the pulse unit
Dia.: Diameter of pulse unit
Height: Height of pulse unit
Propellant (percent): Mass of tungsten propellant in kilograms, as percentage of pulse unit mass in parenthesis.
Det. Interval: Time delay interval between pulse unit detonations.
Propellant Velocity: The velocity the tungsten propellant plasma travels at. Do not use this for delta V calculations.
Effective Exhaust Velocity (Isp): A value for exhaust velocity suitable for delta V calculations. Specific impulse in parenthesis.
Thrust per unit: Amount of thrust produced by detonating one pulse unit.
Effective Thrust: Thrust per second. Calculated by taking Thrust per unit and dividing by Det. Interval.

Tungsten has an atomic number (Z) of 74. When the tungsten plate is vaporized, the resulting plasma jet has a relatively low velocity and diverges at a wide angle (22.5 degrees). Now, if you replace the tungsten with a material with a low Z, the plasma jet will instead have a high velocity at a narrow angle. The jet angle also grows narrower as the thickness of the plate is reduced. This makes it a poor propulsion system, but an effective weapon. Instead of a wall of gas hitting the pusher plate, it is more like a directed energy weapon. The military found this to be fascinating, who needs cannons when you can shoot spears of pure nuclear flame? The process was examined in a Strategic Defense Initiative project called "Casaba-Howitzer", which apparently is still classified. Which is not surprising but frustrating if one is trying to write a science fiction novel or spacecraft combat game.

NASA has been quietly re-examining ORION, under the new name of "External Pulsed Plasma Propulsion". As George Dyson observed, the new name removes most references to "Nuclear", and all references to "Bombs."

For details about spacecraft using Orion propulsion, go here.

Oh, and another thing. ORION is fantastic for boosting unreasonably huge payloads into orbit and it is pretty great for orbit to orbit propulsion. But trying to use it to land is not a very good idea. At least not on a planet with an atmosphere.

Artwork by Master Artist William Black. Click for larger image

The letter that terminated Project Orion

Orion Thrust and Isp

Even though only a fraction of the pulse unit's mass is officially tungsten propellant, you have to count the entire mass of the pulse unit when figuring the mass ratio. The mass of the Orion spacecraft with a full load of pulse units is the wet mass, and the mass with zero pulse units is the dry mass.

The thrust is not applied constantly, it is in the form of pulses separated by a fixed detonation interval. Generally the interval is from about half a second to 1.5 seconds. This means to figure the "effective" thrust you take the thrust-per-pulse-unit and divide it by the detonation interval in seconds. So if each pulse unit gives 2×10⁶ Newtons, and they are detonated at 0.8 second intervals, the effective thrust is 2×10⁶ / 0.8 = 2.5×10⁶ Newtons

Obviously the converse is if you have the effective thrust, you multiply it by the detonation interval to find the thrust-per-pulse-unit. So if the effective thrust is 3.5×10⁶ N and the units are detonated at 0.86 second intervals, the thrust-per-pulse-unit is 3.5×10⁶ N * 0.86 = 3.01×10⁶ Newtons

There are some interesting equations in GA-5009 vol III on pages 25 and 26 on the subject of nuclear pulse units. These were developed in the study for the 10 and 20 meter NASA Orion spacecraft, and they heavily rely upon a number of simplifying assumptions. These were for first generation pulse units, with the assumption that second generation units would have better performance. So take these with a grain of salt.

These equations are only considered valid over the range 3×10⁶ < F_E < 2×10⁸

You are given the amount of thrust you want to get out of the propulsion system: F_E and the detonation interval time D_p. From those you calculate the amount of thrust each pulse unit has to deliver F_p:

F_p = F_E / D_p

From this the specific impulse, nuclear yield, and the mass of the Orion propulsion module.

I_sp = 1 / ((5.30×10² / (F_p * (1 + (2.83×10^-3 * F_p^1/3)))) + ((4.32×10^-2 * (1 + (2.83×10^-3 * F_p^1/3))) / F_p^1/3))

V_e = I_sp * g₀

Y = 9.30×10^-10 * F_p^4/3

M_E = F_p / (3.6 * g₀)

where

F_E = effective thrust (newtons)
D_p = delay between pulses (seconds)
F_p = thrust per pulse (newtons)
I_sp = effective specific impulse (seconds)
V_e = exhaust velocity (m/s)
Y = size of nuclear yield in pulse unit (kilotons)
M_E = mass of Orion propulsion module (kg)
g₀ = acceleration due to gravity = 9.81 m/s²
x^1/3 = 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 Thrust	3.5×10⁶ N
Given Detonation Delay	0.86 s
Parameter	Document Value	Equation Value
Specific Impulse	1,850 s	1,830 s
Yield	1 kt	0.4 kt
Propulsion module mass	90,946 kg	85,245 kg
NASA 20-meter Orion
Given Effective Thrust	1.6×10⁷ N
Given Detonation Delay	0.87 s
Parameter	Document Value	Calculated Value
Specific Impulse	3,150 s	3,082 s
Yield	5 kt	3.1 kt
Propulsion module mass	358,000 kg	394,223 kg

For more in depth calculations of an Orion rocket's specific impulse, read page 1 and page 2. But be prepared for some heavy math.

Orion Environmental Impact

Naturally, some people freak out when you tell them about a rocket that rises into orbit by detonating Two! Hundred! Atom! Bombs!. But it actually isn't quite as bad as it sounds.

First off, these are teeny-tiny atom bombs, honest. The nuclear pulse units used in space will be about one kiloton each, while the Nagasaki device was more like 20 kt. And in any event, the nuclear pulse units used in the atmosphere are only 0.15 kt ( about 1/130th the size of the Nagasaki device). This is because the atmosphere converts the explosion x-rays into "blast", increasing the effectiveness of the pulse unit so you can lower the kilotonnage.

So we are not talking about zillions of 25 megaton city-killer nukes scorching the planet and causing nuclear winter.

Some environmentalists howl that Orion should never be used for surface-to-orbit boosts, due to the danger of DUNT-dunt-Dunnnnnnnn Deadly Radioactive Fallout. However, there is a recent report that suggests ways of minimizing the fallout from an ORION doing a ground lift-off (or a, wait for it, "blast-off" {rimshot}). Apparently if the launch pad is a large piece of armor plate with a coating of graphite there is little or no fallout.

By which they mean, little or no ground dirt irradiated by neutrons and transformed into deadly fallout and spread the the four winds.

There is another problem, though, ironically because the pulse units use small low-yield nuclear devices.

Large devices can be made very efficient, pretty much 100% of the uranium or plutonium is consumed in the nuclear reaction. It is much more difficult with low-yield devices, especially sub-kiloton devices. Some of the plutonium is not consumed, it is merely vaporized and sprayed into the atmosphere. Fallout, in other words. You will need to develop low-yield devices with 100% plutonium burn-up, or use fusion devices (with 100% burn-up fission triggers or with laser inertial confinement fusion triggers).

The alternative is boosting the Orion about 90 kilometers up using a non-fallout chemical rocket. Which more or less defeats the purpose of using an Orion engine in the first place. Remember that Orions are best at boosting massive payloads into orbit.

Most of the fallout will fall within 80 kilometers of the launch site. You can also reduce the fallout by a factor of 10 if you launch from near the Magnetic Pole.

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.

Eyeburn
From Aerospace Projects Review Volume 1, Number 4

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.

Artificial Radiation Belt Lifetime
From Aerospace Projects Review Volume 1, Number 4
Artificial Radiation Belt
Do not launch Orion from anywhere within the "Trapping Region"
From Aerospace Projects Review Volume 1, Number 4

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.

Pulse unit failure modes
From Aerospace Projects Review Volume 1, Number 4
Failure Mode Class I
From Aerospace Projects Review Volume 1, Number 4

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.

From Aerospace Projects Review Volume 1, Number 4
From Aerospace Projects Review Volume 1, Number 4
From Aerospace Projects Review Volume 1, Number 4

By about 1963 General Atomic had given up on designing an Orion to lift off from Terra's surface under nuclear power. They put together three plans for using chemical rocket boosters to get the Orion into orbit. Again this is throwing away the big advantage of the Orion, its ability to boost massive payloads.

Mode I

A fully loaded and fully fueled Orion is boosted to an altitude of 90 kilometers and 900 m/s by a chemical rocket. There it stages, and the Orion proceeds into orbit or into mission trajectory under nuclear power. The disadvantage is it requires a subobital start-up of the Orion engine. The Orion engine will need a thrust greater than the mass of the spacecraft, the standard was T/W of 1.25. But high thrust is never a problem with Orion.

Mode II

An empty Orion is loaded with just enough pulse units. It is boosted to an altitude of 90 kilometers and 900 m/s by a chemical rocket. There it stages, and the Orion proceeds into orbit. A second chemical booster rendezvous with the Orion to deliver the payload and a full load of pulse units.
This was the worst plan. It combines the disadvantage of Mode I (by requiring suborbital start-up of the Orion engine) with the disadvantage of Mode III (by requiring orbital assembly).

Mode III

The Orion is boosted into orbit piecemeal as payload on a series of chemical boosters. The Orion is assembled in orbit, then departs on its mission under nuclear power. The main advantage is it avoids the possibility of the entire Orion spacecraft crashing to Terra in the event of a propulsion failure. The second advantage is it allowed a lower thrust Orion unit to be used, but with Orion thrust is never a problem. The main disadvantage is that orbital assembly is time consuming and difficult.

Zeta-Pinch

Zeta pinch is a type of plasma confinement system that uses an electrical current in the plasma to generate a magnetic field that compresses it. The compression is due to the Lorentz force.

Zeta-Pinch Fission

Mini-Mag Orion

Mini-Mag Orion
Exhaust Velocity	157,000 m/s
Specific Impulse	16,004 s
Thrust	1,870,000 N
Thrust Power	0.1 TW
Mass Flow	12 kg/s
Total Engine Mass	199,600 kg
T/W	0.95
Fuel	Fission: Curium 245
Specific Power	1 kg/MW
Fuel	Fission: Curium 245
Reactor	Zeta-Pinch
Remass	Reaction Products
Remass Accel	Thermal Accel: Reaction Heat
Thrust Director	Magnetic Nozzle
Mini-Mag Orion (DRM-1)
Exhaust Velocity	93,164 m/s
Specific Impulse	9,497 s
Thrust	642,000 N
Thrust Power	29.9 GW
Mass Flow	7 kg/s
Total Engine Mass	119,046 kg
T/W	0.55
Wet Mass	731,924 kg
Dry Mass	250,300 kg
Mass Ratio	2.92 m/s
ΔV	99,967 m/s
Specific Power	4 kg/MW
Mini-Mag Orion (DRM-3)
Exhaust Velocity	93,000 m/s
Specific Impulse	9,480 s
Thrust	642,000 N
Thrust Power	29.9 GW
Mass Flow	7 kg/s
Total Engine Mass	199,600 kg
T/W	0.33
Wet Mass	788,686 kg
Dry Mass	157,723 kg
Mass Ratio	5.00 m/s
ΔV	149,686 m/s
Specific Power	7 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.

Mini-Mag Orion Z-Pinch Fission Gigawatt Thruster patent card from the game High Frontier (Colonization Expansion).

Z-pinch Microfission

n-Li6 Microfission

Zeta-Pinch Fusion

HOPE Z-Pinch
Propulsion System	Z-Pinch Fusion
Exhaust Velocity	189,780 m/s
Specific Impulse	19,346 s
Thrust	38,120 N
Thrust Power	3.6 GW
Mass Flow	0.20 kg/s
Total Engine Mass	95,138 kg
T/W	0.04
Fuel	Deuterium-Tritium fusion + Lithium6 fission
Reactor	Zeta-Pinch
Remass	Reaction Products
Remass Accel	Thermal Accel: Reaction Heat
Thrust Director	Magnetic Nozzle
Wet Mass	888,720 kg
Dry Mass	552,000 kg
Mass Ratio	1.61 m/s
ΔV	90,380 m/s
Specific Power	26 kg/MW
Firefly Starship 2013 design
ΔV	2.698×10⁷ 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	1.289×10⁷ m/s
Thrust	1.9×10⁶ N
Acceleration	0.11 m/s (0.01 g)
Accel time	4 years
Coast time	93 years
Decel time	1 years

Firefly Starship, 2013 design

Firefly Starship, 2013 design

Medusa

Medusa
Exhaust velocity	490,000 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.

1. the payload capsule
2. the winch mechanism
3. the main tether cable
4. riser tethers
5. the parachute mechanism
1. Starting at moment of bomb / pulse unit firing
2. As the bomb's explosion pulse reaches the parachute canopy
3. Pushes the canopy, accelerating it away from the bomb explosion as the spacecraft plays out the main tether with the winch, braking as it extends, starting to accelerate the spacecraft
4. And finally winches the tether back in.
Solem Medusa Tugged Orion Terawatt Thruster patent card from the game High Frontier (Colonization Expansion).

Video explaining Medusa, by Nick Stevens

Inertial Confinement

IC-Fusion
Exhaust Velocity	10,000,000 m/s
Specific Impulse	1,019,368 s
Thrust	100,000,000 N
Thrust Power	500.0 TW
Mass Flow	10 kg/s
Total Engine Mass	1,000,000 kg
T/W	10
Fuel	Proton-Proton Fusion
Specific Power	2.00e-03 kg/MW

A pellet of fusion fuel is bombarded on all sides by strong pulses from laser or particle accelerators. The inertia of the fuel holds it together long enough for most of it to undergo fusion.

VISTA
Propulsion System	IC Fusion
Exhaust Velocity	170,000 m/s
Specific Impulse	17,329 s
Thrust	240,000 N
Thrust Power	20.4 GW
Mass Flow	1 kg/s
Fuel	Deuterium-Tritium Fusion
Reactor	Inertial Confinement Laser
Remass	Reaction Products
Remass Accel	Thermal Accel: Reaction Heat
Thrust Director	Magnetic Nozzle
Wet Mass	6,000,000 kg
Dry Mass	1,835,000 kg
Mass Ratio	3.27 m/s
Width	170 m
Height	100 m

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

Magneto Inertial Fusion

Magneto Inertial Fusion
Both
Exhaust Velocity	50,420 m/s
Specific Impulse	5,140 s
Fuel	Deuterium-Deuterium Fusion
Reactor	Magneto-Inertial Confinement
Remass	Lithium
Remass Accel	Thermal Accel: Reaction Heat
Low Gear
Thrust	103 N
Thrust Power	2.6 MW
Mass Flow	2.00×10^-03 kg/s
Delay between Fusion Pulses	180 seconds
High Gear
Thrust	13,800 N
Thrust Power	0.3 GW
Mass Flow	0.27 kg/s
Delay between Fusion Pulses	14 seconds

There are two main approaches to utilizing nuclear fusion, magnetic confinement and inertial confinement. Magnetic confinement uses titanic magnetic fields, inertial confinement is how fusion bombs explode (a third way would be stars shining by gravitational confinement, but we don't know how to generate artificial gravitational fields). As propulsion systems, both have major drawbacks.

Problem 1

Magnetic confinement requires huge (read: massive) electromagnets. The technique also has the problem of plasma instabilities (read: fusion plasma has thousands of different ways to wiggle out of the magnetic cage) which so far have defied any solution. Meaning that every time fusion researchers have devised a new magnetic cage, the blasted plasma finds two new ways of wiggling out.

Inertial confinement works well in bombs, but trying to do it in a small controlled fashion (read: so the fusion reaction does not vaporize everything in a one kilometer radius) has also defied any solution. The compressing laser or particle beams have such low efficiencies that tons of excess power is required. Timing all the beams so they strike at the same instant is a challenge.

Problem 2

Both approaches have a problem with getting the fusion reaction energy to heat the propellant. Magnetic confinement tries to use the actual fusion plasma as propellant, resulting in a ridiculously small mass flow and thus a tiny thrust.

Problem 3

Also, there is nothing in between the fusion reaction and the chamber walls, leading to severe damage to the walls. The escaping radiation harms the crew as well.

Magneto Inertial Fusion

Dr. John Slough and his associates have come up with a new technique that sort of combines the two conventional approaches: magneto inertial fusion (MIF). You can find their published papers on the subject here

A blob of FRC (field reversed configuration) plasma is created and injected axially into the chamber.

Simultaneously injected into the chamber is a "liner". The liner is a foil ring composed of lithium, about 0.2 meters in radius. Each liner will have a mass of 0.28 kg (minimum) to 0.41 kg.

As the liner travels axially down the chamber, electromagnets crush it down into a solid cylinder (the crush speed is about 3 kilometers per second, the cylinder will have a radius of 5 centimeters). This is timed so that the plasma blob (plasmoid) is in the center of the cylinder. The liner compresses the plasmoid and ignites the fusion reaction.

The fusion reaction vaporizes the lithium liner. The ionized lithium (plus the burnt fusion fuel) exits through a magnetic nozzle, providing thrust.

Liner compression is a heck of a lot more efficent than using huge magnetic fields or batteries of laser beams. Translation: it uses way less power and the equipment has a far smaller mass cost. Problem 1 solved.

The lithium is also the propellant. Since it is tightly wrapped around the reaction, it is very efficient at getting the fusion reaction energy to heat the propellant. Problem 2 solved.

The lithium stands in between the reaction and the chamber walls, protecting the walls. It also absorbs much of the radiation, protecting the crew. Problem 3 solved.

So magneto inertial fusion solves the fusion ignition problem, the fusion heating the propellant problem, and the reaction damaging the chamber problem which are endemic to magnetic and inertial confinement fusion. And the engine has a far lower mass.

Since this is an open-cycle system, the exhaust acts as the heat radiator, so the spacecraft can get by with only a tiny radiator. The energy to run the magnets can be supplied by solar cell arrays. Since the compression is so efficient, this will work with several types of fusion fuel: D-T, D-D, and D-³He. D-D is probably preferred, since tritium is radioactive with a short half-life, and ³He is rare.

Please note that if you replace the magnetic nozzle with a magnetohydrodynamic (MHD) generator, the propulsion system is transformed into an electrical power generator. This could be used for ground based fusion power generators.

Dr. Slough et al worked up two spacecraft for a Mars mission. The first was optimized to have a high payload mass fraction. The second was optimized to have the fastest transit time. Both were capable of a direct abort and return. The "Low Gear" engine is the study author's opinion of an engine easily achievable with current technology (that is, achievable fusion yields). The "High Gear" engine is a bit more speculative, but requiring only modest incremental improvements in technology.

Fusion Drive Rockets (FDR)
High Mass Fraction
Engine	Low Gear
Transit Time	90 days
Initial Mass	90 mT
Payload Mass Fraction	65%
Specific Mass	4.3 kg/kW
Shortest Transit Time
Engine	High Gear
Transit Time	30 days
Initial Mass	153 mT
Payload Mass Fraction	36%
Specific Mass	0.38 kg/kW

Antimatter Bottle

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 Velocity	598,000 m/s
Specific Impulse	60,958 s
Thrust	55 N
Thrust Power	16.4 MW
Mass Flow	1.00e-04 kg/s
Fuel	Helium3-Deuterium Fusion
Reactor	Antimatter Catalyzed
Remass	Reaction Products
Remass Accel	Thermal Accel: Reaction Heat
Thrust Director	Magnetic Nozzle

Antiproton-initiated Microfusion. Inertial Confinement Fusion. See here.

ACMF

ICAN-II
Propulsion System	ACMF
Exhaust Velocity	132,435 m/s
Specific Impulse	13,500 s
Thrust	180,000 N
Thrust Power	11.9 GW
Mass Flow	1 kg/s
Total Engine Mass	27,000 kg
T/W	0.68
Fuel	Fission: Uranium 235
Reactor	Antimatter Catalyzed
Remass	Silicon Carbide
Remass Accel	Thermal Accel: Reaction Heat
Thrust Director	Ablative Nozzle
Wet Mass	707,000 kg
Dry Mass	345,000 kg
Mass Ratio	2.05 m/s
ΔV	95,020 m/s
Specific Power	2 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.

Artwork Pennsylvania State University
Artwork Pennsylvania State University
Artwork Pennsylvania State University
Antimatter-catalyzed fission-fusion Gigawatt Thruster patent card from the game High Frontier (Colonization expansion).

Sail

Sail propulsion does not carry onboard reaction mass or does not use reaction mass. They are powered by a remote source, either the Sun or a satellite installation with a huge power supply and an equally huge laser/plasma beam.

Electric Sail

An E-Sail is a sail powered by solar wind.

Magnetic Sail

Magnetic Sail
Thrust per sail area	0.001 N/km²
Thrust by Sol dist	1/R²

A MagSail is a sail powered by the solar magnetic field.

M2P2

M2P2
Thrust per sail area	0.001 N/km²
Thrust by Sol dist	Constant Disk Inflates as 1/R²
Plasma use	0.25 kg/Day per N Thrust I_sp = 35,000

A Mini-magnetospheric plasma sail (M2P2) is a MagSail inflated by an injection of plasma, powered by the solar wind.

MagBeam

A MagBeam is Mini-magnetospheric plasma sail beam-powered by a remote helicon plasma beam installation. Report here. Alternatively the spacecraft can use a plasma magnet instead of a M2P2 to intercept the beam. With the current design, the spacecraft mass cannot be larger than about 10,000 kg (10 metric tons).

The installation is called a High Power Platform (HPP). The HPP does not have much range, so the spacecraft will require a second HPP at the destination in order to slow down. For a Mars mission the HPP fires for about four hours before the spacecraft is out of range. By that time the spacecraft is travelling at about 20,000 m/s, which is fast enough to get to Mars in 50 days flat. The range is about 1×10⁷ meters (ten thousand kilometers).

After boosting a spacecraft, the HPP rotates the MagBeam in the opposite direction and uses it as an ion drive to move back into position. Newton's laws still hold, the recoil from the MagBeam is going to push the HPP way off base.

And I'm quite sure that at short ranges the MagBeam can be used as a weapon. Please note that when I say "short range", I mean "less than 50 meters or so."

It would also be a nifity thing for a warship to mount, so it can use it to boost missiles to ferocious velocities.

The main advantages seem to be increased acceleration levels on the spacecraft, and that one HPP propulsion unit can service multiple spacecraft. There are certain maneuvers that are impossible for low acceleration spacecraft, such as sub-orbital to orbital transfers, LEO to GEO transfers, LEO to escape velocity, and fast planetary missions.

Plasma beams as a general rule have short ranges. However, the system can take advantage of the fact that both the HPP and the spacecraft have magnetic fields. The MagBeam uses magnetic fields to focus the beam and the spacecraft has a MagSail to catch the beam. If they start off close enough to each other, the two magnetic field merge ("magnetic reconnection"), and gradually stretch as the spacecraft moves. This creates a long magnetic tunnel to confine the plasma stream, making the stream self-focusing.

This will be a problem when the HPP is faced with the task of slowing down an incoming spacecraft, since initially there will be no magnetic link. The spacecraft will have to temporarily inflate its MagSail, which can be done because it is an M2P2. Once the magnetic connection is made the M2P2 can be deflated to normal size.

Plasma will probably be argon or nitrogen. The beam range will a few thousand kilometers if the HPP or the beam passes through the ionosphere, tens of thousands of kilometers if in the magnetosphere. This is because of the ambient plasma and magnetic fields in the ionosphere.

Since the spacecraft does not carry its propellant, the standard rocket equation does not apply. Instead:

HPP_e = (0.25 * M * deltaV * V_e ) / HPP_eff

where:

HPP_e = electrical energy expended by HPP (joules)
M = mass of spacecraft (kg)
deltaV = delta V applied to spacecraft (m/s)
HPP_eff = efficiency of HPP at converting electricity into plasma energy (100% = 1.0, currently 0.6)

M_pb = HPP_e / (0.5 * V_e²)

where:

M_pb = mass of propellant expended in HPP beam (kg)
HPP_e = electrical energy expended by HPP (joules)
V_e = velocity of HPP beam (m/s)

HPP_power = HPP_e / T_accel

where:

HPP_power = miminum power level of HPP power plant (watts)
HPP_e = electrical energy expended by HPP (joules)
T_accel = duration of HPP beam usage (sec)

So if a HPP had to boost a 10,000 kg (10 metric ton) spacecraft to a deltaV of 3,000 m/s (3 km/s) using a plasma beam with a velocity of 19,600 m/s (2000 s) had only 300 seconds (5 minutes) to do so and had an efficiency of 0.6 (60%), then the electrical power used would be 2.5×10¹⁰ joules, the power plant would need a level of 82,000,000 watts (82 megawatts), and 127 kilograms of propellant would be expended.

MagBeam. Image credit: U. of Washington/Robert Winglee.
MagBeam. Image credit: U. of Washington/Robert Winglee.
MagBeam mothership launches a few Jupiter Probes. Image credit: U. of Washington/Robert Winglee

Photon Sail

Photon Sail
Thrust per sail area	9 N/km²
Thrust by Sol dist	1/R²

A Photon Sail is a sail powered by solar photons. Commonly called a "solar sail", but that term does not make it clear if the sail is powered by solar photons, solar magnetic field, or solar wind.

Artwork by Frank Tinsley. Note spining habitat in center of sail. Click for larger image.
Artwork by Philippe “Manchu” Bouchet for a French edition of The Instrumentality of Mankind by Cordwainer Smith. Click for larger image.
Click for larger image.
Click for larger image.
Illustration for Arthur C. Clarke's "Sunjammer", aka "The Wind From The Sun"
Illustration for Arthur C. Clarke's "Sunjammer", aka "The Wind From The Sun"
Real world photon sail. Ikaros solar sail built by the Japan Aerospace Exploration Agency.

Plasma Magnet

An plasma Magnet is a type of E-sail powered by solar wind.

Other

( Beer )

Artwork by Ed Emshwiller
Artwork by Ed Emshwiller

Beer
Thrust Power	8 × 10^-8 GW
Exhaust velocity	83 m/s
Thrust	84 n
T/W >1.0	no

In The Makeshift Rocket (also known as A Bicycle Built for Brew), the old geezer cobbles together a crude rocket out of hogs-heads of pressurized beer in order to escape to an adjacent asteroid.

Mass Driver

Mass Driver
Exhaust Velocity	30,000 m/s
Specific Impulse	3,058 s
Thrust	20,000 N
Thrust Power	0.3 GW
Mass Flow	0.67 kg/s
Total Engine Mass	150,000 kg
T/W	0.01
Thermal eff.	90%
Total eff.	90%
Fuel	800MWe input
Remass	Regolith
Remass Accel	Electromagnetic Acceleration
Specific Power	500 kg/MW

Mass drivers: magnetic buckets filled with packed rock dust are accelerated electmagnetically. Buckets are recovered for re-use. Propellant is rock dust or anything else you can stuff into the bucket. Popular with asteroid miners who want to nudge their claims into different orbits. However, their existence may prompt the creation of an Orbital Guard.

In Gerard O'Neill's plan for L5 colonies, mass drivers were used to deliver raw materials mined on Luna into orbit for colony construction. But instead of the mass driver being mounted on a cargo rocket, it was instead a ground installation near the lunar mine. The buckets were filled not with rock propellant, but instead with cargo cannisters of raw materials. The mass driver shot the cannisters into orbit. The cannisters were intercepted by a "catcher" at the colony site. So instead of needing a fleet of cargo rockets, you just needed a mass driver launcher and a catcher.

A mass driver is an electromagnetic mass accelerator that is optimized for propulsion. If you optimize it as a weapon instead, you have a coil-gun or rail gun. The weapons still have recoil and can be used as a crude propulsion system.

O'Neill's lunar mass driver

From Indistinguishable From Breakup by Alistair Young (2014)

Photon

Photon
Exhaust Velocity	299,792,458 m/s
Specific Impulse	30,559,884 s
Fuel	1.1TWe input
Remass	Photons
Remass Accel	Electromagnetic Acceleration

The exhaust is not a stream of matter. Instead it is a beam of Electromagnetic radiation, basically a large laser. The advantage is that it has the maximum possible exhaust velocity and thus the highest specific impulse. The disadvantage is the ludicrously high power requirements.

The momentum of a photon is p = E/c, where E is the energy of the photon. So the thrust delivered by a stream of photons is ∂p/∂t = ∂E/∂t/c. This boils down to:

F = P/c

P = F * c

where:

F = thrust in Newtons
P = power in watts
c = speed of light in a vacuum (3e8 m/s)

In other words, one lousy Newton of thrust takes three hundred freaking megawatts!!

From Boeing's "Program for Astronomical Research and Scientific Experiments Concerning Space" (1960)
Art by Frank Tinsley

Watch the Heat

Chart from "The Atomic Rocket" by L. R. Shepherd, Ph.D., B.Sc., A.Inst.P., & A. V. Cleaver, F.R.Ae.S., 1948. Collected in Realities of Space Travel
Magnetic Nozzle

Painting by Vincent Di Fate for the novel Starfire by Paul Preuss

From my limited understanding, the basic problem is how to keep the engine from vaporizing.

F_p = (F * V_e ) / 2

where

F_p = thrust power (watts)
F = thrust (newtons)
V_e = exhaust velocity (m/s)

The problem is that at high enough values for exhaust velocity and thrust, the amount of watts in the jet is too much. "Too much" is defined as: if only a fractional percentage of those watts are lost as waste heat, the spacecraft glows blue-white and evaporates. The size of the dangerous fractional percent depends on heat protection technology. There is a limit to how much heat that current technology can deal with, without a technological break-through.

Jerry Pournelle says (in his classic A STEP FARTHER OUT) that an exhaust velocity of 288,000 m/s corresponds to a temperature of 5 million Kelvin.

As an exceedingly rough approximation:

A_e = (0.5 * A_m * A_v²) / B

where

A_e = particle energy (Kelvin)
A_m = mass of particle (g) (1.6733e-24 grams for monatomic hydrogen)
A_v = exhaust velocity (cm/s)
B = Boltzmann's constant: 1.38e-16 (erg K^-1)
x²: square of x, that is x * x

(note that the above equation is using centimeters per second, not meters per second)

A slightly less rough approximation:

Q_e = (V_e / (Z * 129))² * P_w

where

Q_e = engine reaction chamber temperature (Kelvin)
V_e = exhaust velocity (m/s)
Z = heat-pressure factor, varies by engine design, roughly from 1.4 to 2.4 or so.
P_w = mean molecular weight of propellant, 1 for atomic hydrogen, 2 for molecular hydrogen

The interiors of stars are 5 million Kelvin, but few other things are. How do you contain temperatures of that magnitude? If the gadget is something that can be mounted on a ship smaller than the Queen Mary, it has other implications. It is an obvious defense against hydrogen bombs, for starters.

Larry Niven postulates something like this in his "Known Space" series, the crystal-zinc tube makes a science-fictional force field which reflects all energy. Niven does not explore the implications of this. However, Niven and Pournelle do explore the implications in THE MOTE IN GOD'S EYE. The Langson Field is used in the ship's drive, and as a force screen defense. The Langson field absorbs energy, and can re-radiate it. As a defense it sucks up hostile laser beams and nuclear detonations. As a drive, it sucks up and contains the energy of a fusion reaction, and re-radiates the energy as the equivalent of a photon drive exhaust.

(And please remember the difference between "temperature" and "heat". A spark from the fire has a much higher temperature than a pot of boiling water, yet a spark won't hurt your hand at all while the boiling water can give you second degree burns. The spark has less heat, which in this context is the thrust power in watts.)

Reaction Chamber Size

If one has no science-fictional force fields, as a rule of thumb the maximum heat load allowed on the drive assembly is around 5 MW/m². This is the theoretical ultimate, for an actual propulsion system it will probably be quite a bit less. For a back of the envelope calculation:

A_f = sqrt[(1/E_l) * (1 / (4 * π))]

R_c = sqrt[H] * A_f

where

A_f = Attunation factor. Anthony Jackson says 0.126, Luke Campbell says 0.133
E_l = Maximum heat load (MW/m²). Anthony Jackson says 5.0, Luke Campbell says 4.5
π = pi = 3.141592...
H = reaction chamber waste heat (megawatts)
R_c = reaction chamber radius (meters)
sqrt[x] = square root of x

As a first approximation, for most propulsion systems one can get away with using the thrust power for H. But see magnetic nozzle waste heat below.

Science-fictional technologies can cut the value of H to a percentage of thrust power by somehow preventing the waste heat from getting to the chamber walls (e.g., Larry Niven's technobabble crystal-zinc tubes lined with magic force fields).

Only use this equation if H is above 4,000 MW (4 GW) or so, and if the propulsion system is a thermal type (i.e., fission, fusion, or antimatter). It does not work on electrostatic or electromagnetic propulsion systems.

(this equation courtesy of Anthony Jackson and Luke Campbell)

Playing with these figures will show that enclosing a thermal torch drive inside a reaction chamber made of matter appears to be a dead end. Unless you think a drive chamber a half mile in diameter is reasonable.

Therefore, the main strategy is to try and direct the drive energy with magnetic fields instead of metal walls. The magnetic field is created by an open metal framework ("magnetic nozzle"). The metal framework lets the heat escape instead of trying to stop the heat to the detriment of the metal reaction chamber. The magnetic field cannot be vaporized since it is composed of energy instead of matter. Note this is different from an ion drive, where the exhaust is being accelerated by electromagnetic or electrostatic fields. In this case, the exhaust is being accelerated by thermal, fusion, or antimatter reactions; the magnetic fields are being used to contain and direct the exhaust.

Magnetic nozzles are used in some fusion and antimatter propulsion systems.

With these propulsion systems, H is not equal to thrust power. It is instead equal to the fraction of thrust power that is being wasted. In other words the reaction energy that cannot be contained and directed by the magnetic nozzle. Which usually boils down to neutrons, x-rays, and any other reaction products that are not charged particles.

For instance, D-T (deuterium-tritium) fusion produces 80% of its energy in the form of uncharged neutrons and 20% in the form of charged particles. The charged particles are directed as thrust by the magnetic nozzle, so they are not counted as wasted energy. The pesky neutrons cannot be so directed, so they do count as wasted energy. Therefore in this case H is equal to 0.8 * thrust power.

Magnetic nozzles are gone into with more detail here in the Torchship section.

And don't forget the Kzinti Lesson.

*Chart from **"To The Stars"** by Gordon Woodcock, (1983). Collected in **Islands In The Sky**, edited by Stanley Schmidt and Robert Zubrin (1996). Most of the engines on this chart are torchships.*

Popular Conceptions

These illustrations are from a 1963 Russian magazine called "Техника молодежи" magazine ("Technology Youth"), as shown in Pavel Popelskii's Science Illustration blog. They are more a popularization for children than they are a rigorous technical document, but they are interesting. I do not speak or read Russian, but I discovered that Google Translate is my friend. Any awkward phrasing is the fault of Google translate.

The radioactive isotope - a source of alpha particles
Absorber of alpha particles, which protects the equipment from the particles emitted in a random direction
Alpha particles.
Reactor
Vacuum diode - a source of electrical current, working on the principle of thermionic emission
Neutron reflector to their concentration in the reaction zone
Solenoid to produce a magnetic field
Capacitor divider that separates the uranium from the hydrogen
Hydrogen plasma, fed into accelerators
Electrodes for the removal of the electric current created by the movement of plasma through a magnetic field
The direction of electric current
Zone of fission
Nozzle
Uranium-graphite reactor core
Openings for supply of hydrogen in the tangential and the walls of the cylindrical chamber
Molten uranium carbide
Porous wall through which the hydrogen leak
Heat exchanger, where sodium, heated in the reactor, transfers its heat to mercury
Radiator cooler for removal of excess heat and condensation of mercury vapor
Turbogenerator to generate electricity

*"Isotopic motor" (a.k.a. fission sail.)*
1. *The radioactive isotope - a source of alpha particles.*
2. *Absorber of alpha particles, which protects the equipment from the particles emitted in a random direction.*
3. *Alpha particles.*

*"Reactor", possibly a radioisotope thermoelectric generator.*
4. *Reactor.*
5. *Vacuum diode - a source of electrical current, working on the principle of thermionic emission.*
6. *Neutron reflector to their concentration in the reaction zone.*

*Fission reactor and magnetohydrodynamic generator.*
6. *Neutron reflector to their concentration in the reaction zone.*
7. *Solenoid to produce a magnetic field.*
8. *Capacitor divider that separates the uranium from the hydrogen.*
9. *Hydrogen plasma, fed into accelerators.*
10. *Electrodes for the removal of the electric current created by the movement of plasma through a magnetic field.*
11. *The direction of electric current.*
12. *Zone of fission.*

These are the atomic rockets, as tipped off by the Russian word for "uranium". All of these are nuclear thermal rockets or NTR. As near as I can figure:

13. *Nozzle.*
14. *Uranium-graphite reactor core.*

6. *Neutron reflector to their concentration in the reaction zone.*
12. *Zone of fission.*

6. *Neutron reflector to their concentration in the reaction zone.*
12. *Zone of fission.*
15. *Openings for supply of hydrogen in the tangential and the walls of the cylindrical chamber.*

6. *Neutron reflector to their concentration in the reaction zone.*
8. *Capacitor divider that separates the uranium from the hydrogen.*
12. *Zone of fission.*

6. *Neutron reflector to their concentration in the reaction zone.*
16. *Molten uranium carbide.*
17. *Porous wall through which the hydrogen leak.*

This is from a 1960 issue of Technology Youth magazine.

Solid-core NTR
Gas-core Open-Cycle NTR (note lead shielding around exhaust nozzle)
Nuclear Electric Ion Drive
Shock Tubes (first time I ever heard of this, outside of a V-1 Buzz Bomb)
ArcJet

Nuclear Power Reactor
Propellant Tank
Exhaust Nozzle
Uranium Tank
Pump
Steam Turbine
Electric Generator
Heat Radiator
Ion Acceleration Grids
High-pressure tank for accumulation of reactor-heated propellant
Shock tube injector
Valve exhaust
Valves of the cooling system
Exhaust pipe
Anode Arc
Stabilizer
Ring electrode (the cathode of the arc)

NUCLEAR ROCKET by M. Viskova. Technology Youth magazine Jan. 1960

The rocket marked IV appears to be using a system of 'shock tubes', heating a working fluid then pulsing it out underpressure. However, this seems like it would be less efficient then simply operating the engine directly as an NTR, so i have my doubts. As Rob Davidoff pointed out, there is no addition of further "work" after the propellant is heated in the reactor.

Engines: Torchships▶

◀Engines: Multi-stage

Engines: Torchships▶

◀Engines: Multi-stage

Table 1: Metal/Oxygen Combustion Properties
Metal	Specific Enthalpy (joules/kg)	Isp (seconds)
hydrogen	1.39×10⁷	457
aluminum	1.63×10⁷	270
calcium	1.41×10⁷	213
iron	4.7×10⁶	184
magnesium	1.83×10⁷	260
silicon	1.58×10⁷	272
titanium	1.17×10⁷	255

³He-D Mirror Cell
Exhaust Velocity	313,920 m/s
Specific Impulse	32,000 s
Thrust	10,600 N
Thrust Power	1.7 GW
Mass Flow	0.03 kg/s
Total Engine Mass	106,667 kg
T/W	0.01
Frozen Flow eff.	92%
Thermal eff.	90%
Total eff.	83%
Fuel	Helium3-Deuterium Fusion
Reactor	Magnetic Confinement Linear
Remass	Reaction Products
Remass Accel	Thermal Accel: Reaction Heat
Thrust Director	Magnetic Nozzle
Specific Power	64 kg/MW

Discovery II
Propulsion	Helium³-Deuterium MC Fusion
Exhaust Velocity	347,000 m/s
Specific Impulse	35,372 s
Thrust	18,000 N
Thrust Power	3.1 GW
Mass Flow	0.05 kg/s
Fuel	Helium3-Deuterium Fusion
Reactor	Magnetic Confinement Toroidal
Remass	Liquid Hydrogen
Remass Accel	Thermal Accel: Reaction Heat
Thrust Director	Magnetic Nozzle
Wet Mass	1,690,000 kg
Dry Mass	883,000 kg
Mass Ratio	1.91 m/s
ΔV	225,258 m/s
Specific Power	3.5 kW/kg (3,540 W/kg)
Initial Acceleration	1.68 milli-g
Payload	172,000 kg
Length	240 m
Diameter	60 m wide

D-T Fusion Tokamak
Exhaust Velocity	66,800 m/s
Specific Impulse	6,809 s
Thrust	66,800 N
Thrust Power	2.2 GW
Mass Flow	1 kg/s
Total Engine Mass	197,000 kg
T/W	0.04
Frozen Flow eff.	77%
Thermal eff.	85%
Total eff.	65%
Fuel	Deuterium-Tritium Fusion
Reactor	Magnetic Confinement Toroidal
Remass	Reaction Products
Remass Accel	Thermal Accel: Reaction Heat
Thrust Director	Magnetic Nozzle
Specific Power	88 kg/MW

Thrust power	1,650 MW
Exhaust velocity	9,420 m/s
Specific impulse	960 s
Thrust	330,000 N
Engine mass	5,260 kg
T/W	6.4

Table 4
Characteristics of 5000 s Porous Wall Gas Core Rocket Engines
Thrust F(kN)	Engine Power P_rx(MW)	Radiator Power P_rad(MW)^a	Engine Weight M_w(mT)	Pressure Vessel Weight M_pv(mT)^b	Radiator Weight M_rad(mT)^c	Moderator Weight M_mod(mT)^d	Alpha α_p(kW/kg)	Thrust to Weight F/M_w
22	750	43.5	52.3	10	6.3	36	10.3	4.3×10^-2
44	1500	87	61.6	13	12.6	36	17.5	7.3×10^-2
110	3750	218	86	18	32	36	31.3	0.13
220	7500	435	123	24	63	36	43.8	0.18
440	15,000	870	193	31	126	36	55.9	0.23

Z-pinch Microfission
Exhaust Velocity	156,960 m/s
Specific Impulse	16,000 s
Thrust	8,500 N
Thrust Power	0.7 GW
Mass Flow	0.05 kg/s
Total Engine Mass	193,333 kg
T/W	4.00e-03
Frozen Flow eff.	74%
Thermal eff.	90%
Total eff.	67%
Fuel	Fission: Curium 245
Reactor	Zeta-Pinch
Remass	Reaction Products
Remass Accel	Thermal Accel: Reaction Heat
Thrust Director	Magnetic Nozzle
Specific Power	290 kg/MW

Electric Sail
Thrust per tether	0.01 N @ 1 AU
Number tethers	30,000
Total Thrust	300 N @ 1 AU
Mass per tether	1 kg
Total Mass	30,000 kg