So, an extended BFR spacecraft that consists of a 150 tonne payload and 170 tonne structure (twice the 85 tonne structure weight of a standard BFR starship) which includes a hydrogen tank that carries 500 tonnes of liquid hydrogen in a long duration zero boil off tank, as well as 600 tonnes of LOX, along with large inflatable concentrators.

A laser beam is focused on the ship and the receiver optics focus the laser beam into the engine where it heats liquid hydrogen to 40 km/sec (exhaust velocity of 40,000 m/s, specific impulse of 4,000 sec). The other 700 tonnes of propellant is used in a hydrogen/oxygen rocket through the same nozzle which has a 4.5 km/sec exhaust speed (I_sp of 450 sec). This permits the ship to carry out maneuvers without being illuminated by the laser beam. This also is used as an energy storage medium to take water carried aboard ship, along with water ice found in situ — and produce hydrogen and oxygen with it using laser energy received from Earth.

This makes use of a solar pumped laser power satellite that is developed to be deployed by the BFR system — and operate to generate energy for use on Earth and other inhabited worlds.

In this case the 9 GW solar pumped laser is used with a large projector system launched by a second BFR to beam energy from Earth orbit to the vicinity of Jupiter. This laser beam is used to heat hydrogen in a laser theraml rocket described above. It may also be used to use high temperature electrolysis to break down water into hydrogen and oxygen. In this way the ship is capable of extended duration missions and refueling using water ices found in the outer solar system.

Now during launch the ‘Jupiter Stage’ is equipped with 600 tonnes of LOX and 100 tonnes of LH₂. It masses 170 tonnes empty and can carry 46 tonnes during launch burning through the 700 tonnes of propellant.

After in orbit, another 104 tonnes of equipment is added with a ferry flight, along with another 1,100 tonnes of propellant. 600 tonnes of LOX, 500 tonnes of LH₂. This requires another 8 flights of specially constructed tanker and ferry stage.

The 400 tonnes of LOX combined with 50 tonnes of LH₂ produce 450,000 liters of water along with 6.005 trillion joules. A lot of energy. It could supply 1 MW for nearly 10 weeks nonstop.

Used as propellant the 700 tonnes of LOX/LH₂ can impart 3.05 km/sec to the ship carrying its payload and 400 tonnes of LH₂. Without is LH₂ tank (and associated engine and optics) it can impart 6.21 km/sec to the ship — used as a separate landing craft.

The 400 tonnes of LH₂ when energised by the 9 GW laser imparts another 13.23 km/sec to the system.

• LOX/LH₂ — 4.5 km/sec — 3.05 km/sec delta v
• 100 tonnes — LH₂ — 0.083 t/m3 — 1204.82 m3
• 600 tonnes — LOX — 1.14 t/m3 — 536.32 m3
• Laser/LH₂ — 40.0 km/sec — 13.23 km/sec delta v.
• 400 tonnes — LH₂ — 0.083 t/m3 — 4,819.28 m3
• Total (without refueling) — 16.28 km/sec delta v.

At peak velocity the 9 GW laser can energise 11.25 kg/sec of liquid hydrogen. This produces 450 kN thrust (101,160 lbf). This produces 0.3169 m/s2 or 1/5th the acceleration on the surface of the Moon.

A 12 meter diameter spherical tank stores the required LOX.

The smaller LH₂ tank has an 10.7 meter long cylinder attached to the sphere with a 12 meter wide and 6 meter tall hemispherical end cap.

The larger LH₂ tank has a 42.6 meter long cylinder attached to the other side of the LOX sphere with a 12 meter wide and 6 meter tall hemispherical end cap — which is detachable from the LOX tank along their common bulkhead.

Around the common bulkhead is a ring of LOX/LH₂ engines and separate landing gear.

Around the end of the large LH₂ tank is the laser receiver optics and the laser engine.

Assembled the tank system is 12 meters in diameter and 65.3 meters long including the hemispherical end caps. With 22.3 meters nose section atop the short liquid hydrogen tank the entire upper stage is 55 m long without the larger LH₂ tank. And is 87.6 meters long with the larger liquid hydrogen tank.

So, the upper stage would look like the BFR at launch with a half height Heavy Booster attached on Orbit.

The inflatable solar collector that powers the laser is 3.6 km in diameter. A similar sized inflatable projector beams the 1000 nm wavelength light (longest wavelength) up to 6.203 AU from the Earth. This creates a receiver size 315 meters in diameter. At 4.203 AU and 850 nm wavelength 185 meters is sufficient.

The larger reflector masses 2.15 metric tons!

To boost to Jupiter requires a hyperbolic excess velocity of 12.34 km/sec which requires 9.00 km/sec delta v from LEO. It takes 7 hours 54 minutes to boost to this speed using the laser rocket.

It then takes 2.731 years to get to Jupiter.

At Jupiter the ship is moving 7.418 km/sec. Jupiter is moving at 13.064 km/sec a difference of 5.646 km/sec.

Jupiter has an escape velocity of 60.2 km/sec. So, aerobraking at the surface of Jupiter to slow into orbit around the planet, the ship arrives with this hyperbolic excess, so arrives at Jupiter’s cloud tops at 60.465 km/sec and must be slowed by 17.710 km/sec to enter low orbit. Less if the ship is to enter an elliptical orbit taking it to one of the Moons.

Ganymede is an interesting moon to visit — and base exploration from.

So, going from one Jovian radius to 15.311 Jovian radii away — means that we must go from

sqrt(2/1–1/8.1555) = 1.37018 times Jupiter orbital velocity.

60.2 km/sec — Jupiter escape velocity

So, 58.616 km/sec is the speed that gets you to Ganymede from Jupiter’s cloud tops to you subtract off only 1.849 km/sec as you Swing by Jupiter.

If you wanted to avoid the deep dive into Jupiter’s cloud tops, you could drop into Ganymede directly and fire your rockets to enter orbit. There is sufficient delta v to do that. As well as sufficient delta v to get back from Ganymede orbit.

Average orbital speed is 10.88 km/sec for Ganymede. Escape velocity from that radius (1.07 million km) is 15.39 km/sec.

So arriving at Ganymede with a perijovian distnace of 1.07 million km it will have an excess speed of 16.406 km/sec. A delta v of 5.526 km/sec to come to a dead top relative to Ganymede.

Of course Ganymede has an escape velocity of its own. 2.741 km/sec. So, an object would hit Ganymede with a speed of 6.169 km/sec — and to come to rest on Ganymede requires that much speed be cancelled. Of course if you enter orbit around Ganymede you need only cancel 4.231 km/sec.

Which lets you arrive empty hydrogen tank at the Moon.

1.938 km/sec lands you from Ganymede orbit to Ganymede surface — this uses your LOX/LH₂ rockets. You land with your laser receiver and empty hydrogen tank — and begin using laser energy to process water ice into propellant. You also use unusued LOX/LH₂ to power fuel cells aboard the ship for times when the ship is not in direct line of sight of Earth’s laser.

Of course you modulate the laser, and use a counter propagating beam to steer your laser and provide two way broadband.

Every 1.092 years the Earth is in a position to fly from Jupiter to Earth along a minimum energy trajctory. The first return window is 200 days after arrival, and then every 400 days.

Now 500 tonnes of LH₂ requires the decomopsition of 4500 tonnes of water ice on Ganymede. A ball of water 20.48 meters in diameter (67.2 ft) Not particularly large.

At 9 GW it takes only 2 hours 11 minutes 19 seconds to process this much water at 100% efficiency. With 70 days of illumination by laser over the 200 days on the surface only 18 MW of laser energy is required with a 65% efficient electrolysis unit.

LOX/LH₂ is used as propellant to power Flyboards used by the explorers to travel and visit all parts of the moon. A small satellite array is released upon descent, to form a GPS/StarLink/Mapping network to guide the explorers and help them move around the surface.

If there is an okay to stay another Synodic period, another moon can be explored after refuelling on Ganymede. In this way the major satellites may be visited.

Dr. Mark Roth says that suspended animation is within our grasp. This is something to consider for the Jupiter expedtion. Putting robots and AI in charge of the ship for over two years and putting humans in suspended animation during long transit saves resources improves safety increases crew size and flexibility, and eases psychological burdens of long duration flight whilst proving systems that will be used in longer duration insterstellar voyages.

The entire trip takes 7 years to complete 2.75 years outbound, 1.50 years in the Jovian system, and 2.75 years inbound.

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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

A rocket can be driven by high-energy, short-duration (<10^-10 sec) laser pulses, focused on a solid propellant.

A double-pulse system is used: the first pulse ablates material and the second further heats the ablated gas. A low Z propellant, such as graphite, obtains the best specific impulse (4 ksec). Unfortunately, ice is not a suitable medium due to melting and “dribbling” losses.

Primary and secondary mirrors focus the pulses at irradiances of 3 × 10¹³ W/cm². The mass-removal rate is 3 μg per laser pulse. Powered with a 60 MW beam, an ablative laser thruster has a thrust of 2.4 kN and, with a fuel tuned to the firing sequences and an efficient double-pulsed shape, the overall efficiency is 80%.

“Specific impulse and other characteristics of elementary propellants for ablative laser propulsion”, Dr. Andrew V. Pakhomov, Associate Professor at the Department of Physics, UAH, 2002.

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Mirror Steamer
Exhaust Velocity	9,810 m/s
Specific Impulse	1,000 s
Thrust	2,600 N
Thrust Power	12.8 MW
Mass Flow	0.27 kg/s
Total Engine Mass	20,977 kg
T/W	0.01
Frozen Flow Efficency	97%
Thermal Efficency	90%
Total Efficency (Bε)	87%
Fuel	Solar Photons
Reactor	Collector Mirror
Remass	Liquid Hydrogen
Remass Acceleration	Thermal Acceleration: Collector Mirror
Thrust Director	Nozzle
Specific Power	1,645 kg/MW

Water is an attractive volumetric absorber for infrared laser propulsion. Diatomic species formed from the disassociation of water such as OH are present at temperatures as high as 5000 K, and can be rotationally excited by a free electron laser operating in the far infrared. The OH molecules then transfer their energy to a stream of hydrogen propellant in a thermodynamic rocket nozzle by relaxation collisions.

Beamed heat can also be added by a blackbody cavity absorber. This heat exchanger is a series of concentric cylinders, made of hafnium carbide (HfC). Focused sunlight or lasers passes through the outermost porous disk, and is absorbed in the cavity. Heat is transferred to the propellant by the hot HfC without the need for propellant seeding. The specific impulse is materials-limited to 1 ks.

“Solar Rocket System Concept Analysis”, F.G. Etheridge, Rockwell Space Systems Group. (I resized the Rockwell “Solar Moth” design for 3 kN thrust).

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It would consist of a huge bubble of transparent polyester plastic. The bubble could be some 300 feet (90 m) in diameter with a skin only a thousandth of an inch (0.0254 mm) thick. It would be slightly ressurized to give it a spherical shape. Half the inside surface would he silvered to create a hemispherical mirror that would concentrate the sun's rays on a heating element. In this element the hydrogen would be vaporized.

Piped to directable nozzles, one at each side of the sphere, the gas would provide thrust for acceleration, braking and maneuvering. The crew's gondola and associated equipment including solar battery for auxiliary power would he supported by a framework in the center of the big sphere.

It should he remembered that a space ship uses power only during its initial acceleration. The vehicle coasts the rest of the trip. Nevertheless it should carry large reserves of propellant.

Here the solar drive has real advantage. Its heat-collecting device, the hemispherical mirror, weighs possibly 1000 pounds (450 kg) as compared to a much greater weight of oxidizer that would need to be carried in a comparable chemical rocket. This saving in weight permits additional hydrogen to be carried.

Solar drive provides low thrust as compared to the very high thrust of a chemical rocket. This is a good thing, for the fragile plastic bubble will tolerate only low accelerations. It will be necessary to remain under power for hours to achieve the acceleration obtained in minutes by a chemical power plant.

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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

Impulsive electric rockets can accelerate propellant using magnetoplasmadynamic traveling waves (MPD T-waves).

In the design shown, superfluid magnetic helium-3 is accelerated using a megahertz pulsed system, in which a few hundred kiloamps of currents briefly develop extremely high electromagnetic forces. The accelerator sequentially trips a column of distributed superconducting L-C circuits that shoves out the fluid with a magnetic piston.

The propellant is micrograms of regolith dust entrained by the superfluid helium. The dust and helium are kept from the walls by the inward radial Lorentz force, with an efficiency of 81%.

Each 125 J pulse requires a millifarad of total capacitance at a few hundred volts. Compared to ion drives, MPDs have good thrust densities and have no need for charge neutralization. However, they run hot and have electrodes that will erode over time. Moreover, small amounts of an expensive superfluid medium are continually required.

• 

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
Thrust Director	Magnetic Nozzle
Specific Power	1,937 kg/MW

A plasmoid is a coherent torus-shaped structure of plasma and magnetic fields.

An example from nature is “Kugelblitz” (ball lightning). (One of my mentors, Dr. Roger C. Jones of the University of Arizona, has worked out the physics of this.)

A plasmoid rocket creates a torus of ball lightning by directing a mega-amp of current onto the propellant. Almost any sort of propellant will work. The plasmoid is expanded down a diverging electrically conducting nozzle. Magnetic and thermal energies are converted to directed kinetic energy by the interaction of the plasmoid with the image currents it generates in the nozzle. Ionization losses are a small fraction of the total energy; the frozen flow efficiency is 90%.

Unlike other electric rockets, a plasmoid thruster requires no electrodes (which are susceptible to erosion) and its power can be scaled up simply by increasing the pulse rate.

The design illustrated has a 50-meter diameter structure that does quadruple duty as a nozzle, laser focuser, high gain antenna, and radiator. Laser power (60 MW) (from a remote laser power station) is directed onto gap photovoltaics to charge the ultracapacitor bank used to generate the drive pulses.

R. Bourque, General Atomics, 1990.

• 

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

The variable-specific-impulse magnetoplasma rocket (VASIMR) has two unique features: the removal of the anode and cathode electrodes (which greatly increases its lifetime compared to other electric rockets) and the ability to throttle the engine, exchanging thrust for specific impulse. A VASIMR uses low gear to climb out of planetary orbit, and high gear for interplanetary cruise.

Other advantages include efficient resonance heating (80%), and a low current, high voltage power conditioner, which saves mass.

Propellant (typically hydrogen, although many other volatiles can be used) is first ionized by helicon waves and then transferred to a second magnetic chamber where it is accelerated to ten million degrees K by an oscillating electric and magnetic fields, also known as the ponderomotive force.

A hybrid two-stage magnetic nozzle converts the spiraling motion into axial thrust at 97% efficiency.

Franklin Chang-Diaz, et al., “The Physics and Engineering of the VASIMR Engine,” AIAA conference paper 2000-3756, 2000.

Central City and the other bases that had been established with such labor were islands of life in an immense wilderness, oases in a silent desert of blazing light or inky darkness. There had been many who had asked whether the effort needed to survive here was worthwhile, since the colonization of Mars and Venus offered much greater opportunities. But for all the problems it presented him, Man could not do without the Moon. It had been his first bridgehead in space, and was still the key to the planets.

The liners that plied from world to world obtained all their propellent mass here, filling their great tanks with the finely divided dust which the ionic rockets would spit out in electrified jets. By obtaining that dust from the Moon, and not having to lift it through the enormous gravity field of Earth, it had been possible to reduce the cost of spacetravel more than ten-fold. Indeed, without the Moon as a refueling base, economical space-flight could never have been achieved.

Xenon The Noble Gas

Xenon is one of heavier Noble Gases

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The noble gases are the orange column on the right of the periodic table. These are chemically inert. Which means they're not corrosive. This makes them easier to store or use.

Low Ionization Energy

Per this graph is from Wikipedia, Xenon has a lower ionization energy than the lighter noble gases.

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Ionization energy for xenon (Xe) is 1170.4 kJ/mol. Ionization for krypton (Kr) is 1350.8 kJ/mol. Looks like about a 15% difference, right?

But a mole of the most common isotope of xenon is 131.3 grams, while a mole of krypton is 82.8 grams. So it takes 181% or nearly twice as much juice to ionize a gram of krypton.

Likewise it takes nearly 4.5 times as much juice to ionize a gram of argon.

The reaction mass must be ionized before it can be pushed by a magnetic field. Xenon takes less juice to ionize. So more of an ion engine's power source can be devoted to imparting exhaust velocity to reaction mass.

Big Atoms, Molar Weight

Low molar weight makes for good ISP but poor thrust. And pathetic thrust is the Achilles heel of Hall Thrusters and other ion engines. The atomic weight of xenon is 131.29 (see  periodic table at the top of the page).

Tiny hydrogen molecules are notorious for leaking past the tightest seals. Big atoms have a harder time squeezing through tight seals. Big whopper atoms like xenon can be stored more easily.

Around 160 K, xenon is a liquid with a density of about 3 grams per cubic centimeter. In contrast, oxygen is liquid below 90 K and a density of 1.1. So xenon is a much milder cryogen than oxygen and more than double (almost triple) the density.

Abundance

Ordinary atmosphere is 1.2 kg/m³ while xenon is about 5.9 kg/m³ at the same pressure. Xenon has about 4.8 times the density of regular air.

By volume earth's atmosphere is .0000087% xenon. 4.8 * .000000087 = 4.2e-7. Earth's atmosphere is estimated to mass 5e18 kg. By my arithmetic there is about 2e12 kg xenon in earth's atmosphere. In other words, about 2 billion tonnes.

Page 29 of the Keck asteroid retrieval proposal calls for 12.9 tonnes of xenon. Naysayers were aghast: "13 tonnes is almost a third of global xenon production for year! It would cause a shortage." Well, production is determined by demand. With 2 billion tonnes in our atmosphere, 13 tonnes is a drop in the bucket. We throw away a lot of xenon when we liquify oxygen and nitrogen from the atmosphere.

In fact ramping up production of xenon would lead to economies of scale and likely cause prices to drop. TildalWave makes such an argument in this Space Stack Exchange answer to the question "How much does it cost to fill an ion thruster with xenon for a spacecraft propulsion system?" TildalWave argues ramped up production could result in a $250,000 per tonne price. That's about a four fold cut in the going market price of $1.2 million per tonne.

Radon

If you examined the periodic table and ionization tables above you might have noticed there's a heavier noble gas that has an even lower ionization energy: Radon a.k.a. Rn.  Radon is radioactive. Radon 222, the most stable isotope, has a half life of less than 4 days. If I count the zeros on the Radon page correctly, our atmosphere is about 1e-19% radon — what you'd expect for something with such a short half life. Besides being rare, it wouldn't last long in storage.

Where xenon excels

Great for moving between heliocentric orbits

Ion thrusters can get 10 to 80 km/s exhaust velocity, 30 km/s is a typical exhaust velocity. That's about 7 times as good as hydrogen/oxygen bipropellent which can do 4.4 km/s. But, as mentioned, ion thrust and acceleration are small. It takes a looong burn to get the delta V. To get good acceleration, an ion propelled vehicle needs good alpha. In my opinion, 1 millimeter/second² is doable with near future power sources.

If the vehicle's acceleration is a healthy fraction of local gravity field, the accelerations resemble the impulsive burns to enter or exit an elliptical transfer orbit. But if the acceleration is a tiny fraction of the local gravity field, the path is a slow spiral.

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Earth's distance from the sun, the sun's gravity is around 6 millimeters/second². At Mars, sun's gravity is about 2.5 mm/s² and in the asteroid belt 1 mm/s² or less. Ion engines are okay for moving between heliocentric orbits, especially as you get out as far as Mars and The Main Belt.

Sucks for climbing in and out of planetary gravity wells

At 300 km altitude, Earth's local gravity field is about 9000 millimeters/second². About 9 thousand times the 1 mm/s² acceleration a plausible ion vehicle can do. At the altitude of low Mars orbit, gravity is about 3400 millimeters/sec². So slow gradual spirals rather than elliptical transfer orbits. There's also no Oberth benefit.

At 1 mm/sec² acceleration, it would take around 7 million seconds (80 days) to climb in or out of earth's gravity well and about 3 million seconds (35 days) for the Mars well.

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The general rule of thumb for calculating the delta V needed for low thrust spirals: subtract speed of destination orbit from speed of departure orbit.

Speed of Low Earth Orbit (LEO) is about 7.7 km/s. But you don't have to go to C3 = 0, getting past earth's Hill Sphere suffices. So about 7 km/s to climb from LEO to the edge of earth's gravity well.

It takes about 5.6 km/s to get from earth's 1 A.U. heliocentric orbit to Mars' 1.52 A.U. heliocentric orbit.

Speed of Low Mars Orbit (LMO) is about 3.4 km/s. About 3 km/s from the edge of Mars' Hill Sphere to LMO.

7 + 5.6 + 3 = 15.6. A total of 15.6 km/s to get from LEO to LMO.

With the Oberth benefit it takes about 5.6 km/s to get from LEO to LMO. The Oberth savings is almost 10 km/s.

10 km/s is nothing to sneeze at, even if exhaust velocity is 30 km/s. Climbing all the way up and down planetary gravity wells wth ion engines costs substantial delta V as well as a lot of time.

Elevators and chemical for planet wells, ion for heliocentric

So in my daydreams I imagine infrastructure at the edge of planetary gravity wells. Ports where ion driven driven vehicles arrive and leave as they move about the solar system. Then transportation from the well's edge down the well would be accomplished by chemical as well as orbital elevators.

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Other possible sources of ion propellent

Another possible propellent for ion engines is argon. Also a noble gas. Ionization energy isn't as good as xenon, but not bad. Mars atmosphere is about 2% argon. Mars is next door to The Main Belt. I like to imagine Mars will supply much of the propellent for moving about the Main Belt.

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     Chris Wolfe said:
     Xenon's ionization energy is 1170 kJ/mol. Xenon's standard atomic mass is 131.29, yielding 131.29 g/mol or 7.62 mol/kg. That means you need 8915 kJ/kg for the atoms at first ionization. That might be easier to use as 8.9 J/mg given the low mass flows of electric engines.
     Argon's ionization energy is 1521 kJ/mol. Argon's standard atomic mass is 39.95, yielding 39.95 g/mol or 25.03 mol/kg. That means you need 38,071 kJ/kg for the atoms at first ionization. That might be easier to use as 38 J/mg given the low mass flows of electric engines.
     For the first stage of an ion thruster, argon requires about 4.3 times the power to ionize vs. xenon on a mass basis. On a molar basis argon requires 30% more power to ionize.
     Consider a 200 kW VASIMR thruster (link at end) pushing argon. This is a plasma thruster, so the doubly-ionized problem doesn't really apply. 28 kW is applied to producing 107mg/s of plasma; this power must be spent to produce a stable mass flow regardless of the power setting of the acceleration stage. The remaining 172 kW is spent on acceleration at maximum power output. This produces 5.8 N of thrust with an exhaust velocity of 48km/s (Isp of 4900). That's a beam power of 123 kW, an acceleration stage efficiency of 71.5% and an overall efficiency of 61.5%.
     Suppose the same device were to push xenon. The plasma stage would ionize 30% more propellant on a molar basis thanks to xenon's lower ionization energy. That plus xenon's higher molar mass means the engine processes 457 mg/s of plasma, around 4.3x the mass flow. Assuming the beam power remains the same (and by definition the efficiency), the exhaust velocity would be 23.2km/s (Isp 2365) and thrust would be 10.6 N.
     80% better thrust at the cost of four times the fuel consumption makes sense for certain use cases like GTO to GEO (where the opportunity cost of a commsat's unavailability during transit is high) or manned heliocentric transfers (where the reduction in supplies and required shielding due to fast transit might be a net benefit), but for cargo or really anything that isn't time sensitive the argon propellant is superior. I suspect NASA and others use xenon because their engine thrust levels are just barely adequate for their mission with all available power and every astrodynamics trick in the book; if there was more power available on the craft then a change in propellant could greatly increase total dV for the same mass and thrust. To paraphrase hop, we really need better alpha if we want to get serious about deep space.
     What if we cut the propellant flow in half? That would drop the ionization power to 14 kW. Argon exhaust velocity would be 67.8km/s (Isp 6912) and 3.6 N of thrust. Xenon exhaust velocity would be 32.8km/s (Isp 3345) and 7.5 N of thrust. Overall efficiency would rise to 66% in both cases, with a 41% increase in Isp and a 30-40% decrease in thrust (lower loss for xenon, higher for argon).
     The ionization stage efficiency is reportedly about 87%. Ionizing the amount of argon they describe should only require 4 kW of coupled power, so the ionization stage is pumping about six times that much energy into the plasma and contributing to the useful output power. That means my simplistic comparisons may not be completely accurate. 20 kW into 107mg of argon would be a v of 19.3km/s (Isp 1970) and thrust of 2 N, making the ionization stage a respectable plasma thruster in its own right. I must be missing something. Most likely it is that this is a plasma device, essentially using heat rather than electricity. The kinetic energy of individual atoms is increased to the point where they dissociate into a neutral plasma; powerful magnetic fields are used to direct the plasma to the next stage where they are further heated and accelerated through a magnetic nozzle. If so, xenon as a propellant would have a somewhat lower exhaust velocity (thus lower thrust and Isp) than presented above.
     source of VASIMR numbers: http://pepl.engin.umich.edu/pdf/AIAA-2012-3930.pdf

     Hollister David said:
     Chris, I had missed that chemical ionization energy is per mole. And a mole of Krypton is more than triple the mass a mole of Argon. So per kilogram, the ionization energy is a lot more dramatic than graphic I've published. There's a lot more to digest in your post. Am moving through it a little at a time. As usual, thanks for your input.

     Kenneth Ferland said:
     The in-between gas Krypton is likely to be brought into service before scaling up of Xenon production as it's already available as a similar byproduct of atmospheric separation plants and is available in 4-5 times the volume of Xenon.
     Also their are some concepts for thrusters that get around ionization energy, the Electrodeless Lorentz Force thruster (ELF) is intended to entrain neutral gas within a plasmoid which is ejected like a smoke ring. This would allow both higher thrust and efficiency from a propellant mixture of which only a fraction needs to be ionized.

     Hollister David said:
     I was enthusiastic about Martian argon until Chris Wolfe pointed out the ionization energy is per mole. So kilogram per kilogram, argon takes 4.5 times as much juice to ionize as xenon.
     I would imagine if we settle the Main Belt that fission nuclear power would be big. Even more so at the Trojans since solar falls with inverse square of distance from the sun. Do you have any idea how much xenon could be produced per watt?
     So in my daydreams I like to imagine nuclear power plants on Ceres or 624 Hektor cranking out xenon as well as watts.
     Also the space ships. As we get further from the sun, nuclear electric propulsion is more desirable than solar electric propulsion.

     Chris Wolfe said:
     Using internet numbers I see a uranium consumption of about 1200kg per GWe per year. (That's gigawatt, electric). Roughly 10^20 U235 fission events per second for a year. If 40% of those events result in Xenon then this reference reactor would produce 52,367 mol of Xe or about 6,875 kg with perfect recovery.
     Assume a moderate Isp of 2500 (since thrust is desired for this application, that seems to be a reasonable value). Also assume a 6km/s dV budget for a one-way Earth-Mars heliocentric transfer. Using the rocket equation I get a 'leverage*' of 3.6, so this amount of Xe could propel 24.8 tons of dry mass. Let's be generous and assume that the entire dry mass is useful cargo.
     I have trouble imagining a scenario where a colony using a gigawatt of electricity only needs 25 tons of supplies annually, or only produces 25 tons of exports. Such a colony could import highly-enriched U235 using only radiogenic xenon as propellant and still have surplus cargo capacity, but that seems like an arbitrary metric.
     Argon works and is quite efficient. The problem is finding an efficient power source to put it to work. Krypton is indeed a 'middle ground' in terms of mass, ionization energy, thrust and Isp for a given amount of electrical power and could be one of several electric propellant choices.
     * Leverage is similar to 'gear ratio', but in reverse. A chemical rocket is typically measured in tons of propellant per ton of cargo (gallons per mile). Electric rockets commonly deliver more than one ton of cargo per ton of propellant, so it makes sense to use the inverse value and express the number of tons of cargo per ton of propellant (miles per gallon) for a given route or mission.
     To get the figure of 3.6 I used Mf = 1 - e^-(dV/Ve) to get the propellant mass fraction and then took (1 / Mf) - 1 to get units of dry mass per unit of propellant.

     Matthew Hammer said:
     The ionization energy of the different noble gasses doesn't actually make that much difference. They look like big differences:

• Argon: 38.1 kJ/gram
• Krypton: 16.3 kJ/gram
• Xenon: 8.9 kJ/gram

     But, if the exhaust velocity is 30 km/s, then the Kinetic Energy is at least 450 kJ/gram (more, given exhaust spread). Which is 11, 28, and 51 times the ionization energy. So, you only get tiny improvements in thrust as you go up the periodic table. 5% improvement from Argon to Krypton, and 1.5% more from Krypton to Xenon. The real advantage is propellant density and more favorable melting point, since that can reduce structure mass and (at least at the moment) trumps the large price differences between the gasses.

One of the interesting things to consider about these types of thrusters, both the gridded ion and Hall effect thrusters, is propellant choice. Xenon is, as of today, the primary propellant used by all operational electrostatic thrusters (although some early thrusters used cesium and mercury for propellants), however, Xe is rare and reasonably expensive. In smaller Hall thruster designs, such as for telecommunications satellites in the 5-10 kWe thruster range, the propellant load (as of 1999) for many spacecraft is less than 100 kg – a significant but not exorbitant amount of propellant, and launch costs (and design considerations) make this a cost effective decision. For larger spacecraft, such as a Hall-powered spacecraft to Mars, the propellant mas could easily be in the 20-30 ton range (assuming 2500 s isp, and a 100 mg/s flow rate of Xe), which is a very different matter in terms of Xe availability and cost. Alternatives, then, become far more attractive if possible.

Argon is also an attractive option, and is often proposed as a propellant as well, being less rare. However, it’s also considerably lower mass, leading to higher specific impulses but lower levels of thrust. Depending on the mission, this could be a problem if large changes in delta-vee are needed in a shorter period of time, The higher ionization energy requirements also mean that either the propellant won’t be as completely ionized, leading to loss of efficiency, or more energy is required to ionize the propellant

The next most popular choice for propellant is krypton (Kr), the next lightest noble gas. The chemical advantages of Kr are basically identical, but there are a couple things that make this trade-off far from straightforward: first, tests with Kr in Hall effect thrusters often demonstrate an efficiency loss of 15-25% (although this may be able to be mitigated slightly by optimizing the thruster design for the use of Kr rather than Xe), and second the higher ionization energy of Kr compared to Xe means that more power is required to ionize the same amount of propellant (or with an SPT, a deeper ionization channel, with the associated increased erosion concerns). Sadly, several studies have shown that the higher specific impulse gained from the lower atomic mass of Kr aren’t sufficient to make up for the other challenges, including losses from Joule heating (which we briefly discussed during our discussion of MPD thrusters in the last post), radiation, increased ionization energy requirements, and even geometric beam divergence.

This has led some designers to propose a mixture of Xe and Kr propellants, to gain the advantages of lower ionization energy for part of the propellant, as a compromise solution. The downside is that this doesn’t necessarily improve many of the problems of Kr as a propellant, including Joule heating, thermal diffusion into the thruster itself, and other design headaches for an electrostatic thruster. Additionally, some papers report that there is no resonant ionization phenomenon that facilitates the increase of partial krypton utilization efficiency, so the primary advantage remains solely cost and availability of Kr over Xe.

	Atomic Mass (Ar, std.)	Ionization Energy (1st, kJ/mol)	Density (g/cm^3)	Melting Point (K)	Boiling Point (K)	Estimated Cost ($/kg)
Xenon	131.293	1170.4	2.942 (BP)	161.4	165.051	1200
Krypton	83.798	1350.8	2.413 (BP)	115.78	119.93	75
Bismuth	208.98	703	10.05 (MP)	544.7	1837	29
Mercury	200.592	1007.1	13.534 (at STP)	234.32	629.88	500
Cesium	132.905	375.7	1.843 (at MP)	301.7	944	>5000
Sodium	22.989	495.8	0.927 (at MP) 0.968 (solid)	370.94	1156.09	250
Potassium	39.098	418.8	0.828 (MP) 0.862 (solid)	336.7	1032	1000
Argon	39.792	1520.6	1.395 (BP)	83.81	87.302	5
NaK	Varies	Differential	0.866 (20 C)	260.55	1445	Varies
Iodine	126.904	1008.4	4.933 (at STP)	386.85	457.4	80
Magnesium	24.304	737.7	1.584 (MP)	923	1363	6
Cadmium	112.414	867.8	7.996 (MP)	594.22	1040	5

 

Early thrusters used cesium and mercury for propellant, and for higher-powered systems this may end up being an option. As we’ve seen earlier in this post, neither Cs or Hg are unknown in electrostatic propulsion (another design that we’ll look at a little later is the cesium contact ion thruster), however they’ve fallen out of favor. The primary reason always given for this is environmental and occupational health concerns, for the development of the thrusters, the handling of the propellant during construction and launch, as well as the immediate environment of the spacecraft. The thrusters have to be built and extensively tested before they’re used on a mission, and all these experiments are a perfect way to strongly contaminate delicate (and expensive) equipment such as thrust stands, vacuum chambers, and sensing apparatus – not to mention the lab and surrounding environment in the case of an accident. Additionally, any accident that leads to the exposure of workers to Hg or Cs will be expensive and difficult to address, notwithstanding any long term health effects of chemical exposure to any personnel involved (handling procedures have been well established, but one worker not wearing the correct personal protective equipment could be constantly safe both in terms of personal and programmatic health) Perfect propellant stream neutralization is something that doesn’t actually occur in electrostatic drives (although as time goes on, this has consistently improved), leading to a buildup of negative charge in the spacecraft; and, subsequently, a portion of the positive ions used for propellant end up circling back around the magnetic fields and impacting the spacecraft. Not only is this something that’s a negative impact for the thrust of the spacecraft, but if the propellant is something that’s chemically active (as both Cs and Hg are), it can lead to chemical reactions with spacecraft structural components, sensors, and other systems, accelerating degradation of the spacecraft.

A while back on the Facebook group I asked the members about the use of these propellants, and an interesting discussion developed (primarily between Mikkel Haaheim, my head editor and frequent contributor to this blog, and Ed Pheil, who has extensive experience in nuclear power, including the JIMO mission, and is currently the head of Elysium Industries, developing a molten chloride fast reactor) concerning the pros and cons of using these propellants. Two other options, with their own complications from the engineering side, were also proposed, which we’ll touch on briefly: sodium and potassium both have low ionization energies, and form a low melting temperature eutectic, so they may offer additional options for future electrostatic propellants as well. Three major factors came up in the discussion: environmental and occupational health concerns during testing, propellant cost (which is a large part of what brings us to this discussion in the first place), and tankage considerations.

As far as cost goes, this is listed in the table above. These costs are all ballpark estimates, and costs for space-qualified supplies are generally higher, but it illustrates the general costs associated with each propellant. So, from an economic point of view, Cs is the least attractive, while Hg, Kr, and Na are all attractive options for bulk propellants.

Tankage in and of itself is a simpler question than the question of the full propellant feed question, however it can offer some insights into the overall challenges in storing and using the various propellants. Xe, our baseline propellant, has a density as a liquid of 2.942 g/cm, Kr of 2.413, and Hg of 13.53. All other things aside, this indicates that the overall tankage mass requirements for the same mass of Hg are less than 1/10th that of Xe or Kr. However, additional complications arise when considering tank material differences. For instance, both Xe and Kr require cryogenic cooling (something we discussed in the LEU NTP series briefly, which you can read here. While the challenges of Xe and Kr cryogenics are less difficult than H2 cryogenics due to the higher atomic mass and lower chemical reactivity, many of the same considerations do still apply. Hg on the other hand, has to be kept in a stainless steel tank (by law), other common containers, such as glass, don’t lend themselves to spacecraft tank construction. However, a stainless steel liner of a carbon composite tank is a lower-mass option.

The last type of fluid propellant to mention is NaK, a common fast reactor coolant which has been extensively studied. Many of the problems with tankage of NaK are similar to those seen in Cs or Hg: chemical reactivity (although different particulars on the tankage), however, all the research into using NaK for fast reactor coolant has largely addressed the immediate corrosion issues.

The main problem with NaK would be differential ionization causing plating of the higher-ionization-energy metal (Na in this case) onto the anode or propellant channels of the thruster. While it may be possible to deal with this, either by shortening the propellant channel (like in a TAL or EDPT), or by ensuring full ionization through excess charge in the anode and cathode. The possibility of using NaK was studied in an SPT thruster in the Soviet Union, but unfortunately I cannot find the papers associated with these studies. However, NaK remains an interesting option for future thrusters.

Solid propellants are generally considered to be condensable propellant thrusters. These designs have been studied for a number of decades. Most designs use a resistive heater to melt the propellant, which is then vaporized just before entering the anode. This was first demonstrated with the cesium contact gridded ion thrusters that were used as part of the SERT program. There (as mentioned earlier) a metal foam was used as the storage medium, which was kept warm to the point that the cesium was kept liquid. By varying the pore size, a metal wick was made which controlled the flow of the propellant from the reservoir to the ionization head. This results in a greater overall mass for the propellant tankage, but on the other hand the lack of moving parts, and the ability to ensure even heating across the propellant volume, makes this an attractive option in some cases.

A more recent design that we also discussed (the VHITAL) uses bismuth propellant for a TAL thruster, a NASA update of a Soviet TsNIIMash design from the 1970s (which was shelved due to the lack of high-powered space power systems at the time). This design uses a reservoir of liquid bismuth, which is resistively heated to above the melting temperature. An argon pressurization system is used to force the liquid bismuth through an outlet, where it’s then electromagnetically pumped into a carbon vaporization plug. This then discharges into the anode (which in the latest iteration is also resistively heated), where the Hall current then ionizes the propellant. It may be possible with this design to use multiple reservoirs to reduce the power demand for the propellant feed system; however, this would also lead to greater tankage mass requirements, so it will largely depend on the particulars of the system whether the increase in mass is worth the power savings of using a more modular system. This propellant system was successfully tested in 2007, and could be adapted to other designs as well.

Other propellants have been proposed as well, including magnesium, iodine, and cadmium. Each has its’ advantages and disadvantages in tankage, chemical reactivity limiting thruster materials considerations, and other factors, but all remain possible for future thruster designs.

For the foreseeable future, most designs will continue to use xenon, with argon being the next most popular choice, but as the amount of propellant needed increases with the development of nuclear electric propulsion, it’s possible that these other propellant options will become more prominent as tankage mass, propellant cost, and other considerations become more significant.

Sources

High Power Hall Thrusters; Jankovsky et al, 1999

Energetics of Propellant Options for High-Power Hall Thrusters, Kieckhafer and King, Michigan Technological University, 2005

A Performance Comparison Of Xenon and Krypton Propellant on an SPT-100 Hall Thruster, Nakles et al 2011

Evaluation of Magnesium as Hall Thruster Propellant; Hopkins, Michigan Tech, 2015

Modeling of an Iodine Hall Thruster Plume in the Iodine Satellite (ISAT), Choi 2017

For the last year and a half, NASA has been publicly studying a concept known as the Asteroid Redirect Mission (ARM). As described by NASA, ARM:

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will employ a robotic spacecraft, driven by an advanced solar electric propulsion system, to capture a small near-Earth asteroid or remove a boulder from the surface of a larger asteroid. The spacecraft then will attempt to redirect the object into a stable orbit around the moon.

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It seems likely that NASA’s interest in such a mission is limited to executing it once or a few times to prove-out the technique, and to then move on to some other mission—perhaps a crewed trip to Mars—if and when funds become available. Within that limited ARM context, a conservative engineering approach using an existing deep-space propulsion system (e.g., xenon ion propulsion) to return the NEO to a lunar orbit, or High Earth Orbit (HEO) beyond geosynchronous orbit, will likely be chosen as a minimal risk approach.

Our interest in near Earth objects (NEOs) should be more expansive than one or a few missions, though. This essay examines an alternative propulsion system with substantial promise for future space industrialization using asteroidal resources returned to HEO.

Electrostatic propulsion is the method used by many deep space probes currently in operation such as the Dawn spacecraft presently wending its way towards the asteroid Ceres. For that probe and several others, xenon gas is ionized and then electrical potential is used to accelerate the ions until they exit the engine at exhaust velocities of 15–50 kilometers per second, much higher than for chemical rocket engines, at which point the exhaust is electrically neutralized. This method produces very low thrust and is not suitable for takeoff from planets or moons.

However, in deep space and integrated over long periods of engine operation time, the gentle push of an ion engine can impart a very significant velocity change to a spacecraft, and do so extremely efficiently: for the Deep Space 1 spacecraft, the ion engine imparted 4.3 kilometers per second of velocity change (delta-v), using only 74 kilograms of propellant to do so. As of late September, Dawn’s ion thrusters have produced 10.2 kilometers per second of delta-v, using 367 kilograms of xenon.

The solar system has planets, asteroids, rocks, sand, and dust, all of which can pose dangers to space missions. The larger objects can be detected in advance and avoided, but the very tiny objects cannot, and it is of interest to understand the effects of hypervelocity impacts of microparticles on spacesuits, instruments and structures. For over a half century, researchers have been finding ways to accelerate microparticles to hypervelocities (1 to 100 kilometers per second) in vacuum chambers here on Earth, slamming those particles into various targets and then studying the resultant impact damage. These microparticles are charged and then accelerated using an electrical potential field.

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It is a natural step to consider, instead of atomic-scale xenon ions, the application to deep space propulsion of the electrostatic acceleration of much, much larger microparticles:

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Chemical rockets achieve their large thrust with high mass consumption rate (dm/dt) but low exhaust velocity; therefore, a large fraction of their total mass is fuel. Present day ion thrusters are characterized by high exhaust velocity, but low dm/dt; thus, they are inherently low thrust devices. However, their high exhaust velocity is poorly matched to typical mission requirements and therefore, wastes energy. A better match would be intermediate between the two forms of propulsion. This could be achieved by electrostatically accelerating solid powder grains.

Several papers have researched such a possibility.

There are many potential sources of powder or dust in the solar system with which to power such a propulsion system. NEOs could be an ideal source, as hinted at in a 1991 presentation:

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Asteroid sample return missions would benefit from development of an improved rocket engine… This could be achieved by electrostatically accelerating solid powder grains, raising the possibility that interplanetary material could be processed to use as reaction mass.

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Imagine a vehicle that is accelerated to escape velocity by a conventional rocket. It then uses some powder lifted from Earth for deep-space propulsion to make its way to a NEO, where it lands, collects a large amount of already-fractured regolith, and then takes off again. It is already known that larger NEOs such as Itokawa have extensive regolith blankets.

Furthermore, recent research suggests that thermal fatigue is the driving force for regolith creation on NEOs; if that is true, then even much smaller NEOs might have regolith layers. Additionally, some classes of NEOs such as carbonaceous chondrites are expected to have extremely low mechanical strength; for such NEOs, it would be immaterial whether or not pre-existing regolith layers were present, as the crumbly material of the NEO could be crushed easily.

After leaving the NEO, onboard crushers and grinders convert small amounts of the regolith to very fine powder. (These processes would be perfected in low Earth orbit using regolith simulant long before the first asteroid mission.) Electrostatic grids accelerate and expel the powder at high exit velocities. Not all of the regolith onboard is powdered, only that which is used as propellant: a substantial amount of unprocessed regolith is returned to HEO.

The Dawn spacecraft consumes about 280 grams of xenon propellant per day. For asteroid redirect missions, a much higher power spacecraft with greater propellant capacity than Dawn is needed, and NASA is considering one with 50-kilowatt arrays and 12 metric tons of xenon ion propellant, versus just 0.43 metric tons for Dawn. If that 12 metric tons were consumed over a four-year period, then that would equate to 8.2 kilograms of propellant per day, or 340 grams per hour (29 times Dawn’s propellant consumption rate.) The machinery required to collect, crush, and powder a similar mass of regolith per hour need not be extremely large because initial hard rock fracturing would not be required. It is plausible that the entire system—regolith collection equipment, rock crushing, powdering, and other material processing equipment—might not be much larger than the 12 metric tons of xenon propellant envisioned by NASA.

One of the attractions of the scheme described here is that this system could be started with one or a few vehicles, and then later scaled to any desired throughput by adding vehicles. Suppose that, on average, a single vehicle could complete a round-trip and return 400 tons of asteroidal material to HEO once every four years. After arrival in HEO, maintenance is performed on the vehicle. Some of the remaining regolith is powdered and becomes propellant for the outbound leg of the next NEO mission. A fleet of ten such vehicles could return 1,000 tons per year on average of asteroidal material, while a fleet of 100 such vehicles could return 10,000 tons per year. The system described is scalable to any desired throughput by the addition of vehicles. Mass production of such vehicles would reduce unit costs.

A system of many such vehicles would be resilient to the failure of any single one. If one of the many vehicles were lost, then the throughput rate of return of asteroidal material to HEO would be reduced, but the system as a whole would survive. Replacement vehicles could be launched from Earth, or perhaps the failed vehicle could also be returned to HEO for repair by one of the other vehicles.

In situ resource utilization (ISRU) means “living off the land” rather than launching all mass from the Earth. Xenon costs, by some estimates, about $1,200 per kilogram, and thus the material cost alone of 12 tons of xenon propellant would be $14.4 million. The scheme discussed in this essay would use powdered asteroidal regolith instead of xenon, and would save not only the material cost of the xenon ion propellant itself, but also the vastly larger cost of launching that propellant from Earth each time. Over several or many missions, the initial cost of developing the powdered asteroid propulsion approach would justify itself economically.

Over dozens or hundreds of missions, the asteroidal material returned to HEO could serve as radiation shielding, as a powder propellant source for all sorts of beyond-Earth-orbit missions and transportation in cislunar space, and as input fodder for many industrial and manufacturing processes, such as the production of oxygen or solar cells. All of this advanced processing could be conducted in HEO, where a telecommunications round-trip of a second or two would allow most operations to be economically controlled from the surface of the Earth using telerobotics. By contrast, the processing that happens outside of Earth orbit would be limited to the collection, crushing, and powdering of regolith. These latter and simpler processes would be completed largely autonomously.

Low Earth orbit (LEO) is reachable from the surface of the Earth in eight minutes, and geosynchronous orbit—the beginning of HEO—is reachable within eight hours. The proximity of LEO and HEO to the seven billion people on Earth and their associated economic activity is a strong indication that cislunar space will become the future economic home of humankind. In the architecture described here, raw material is slowly delivered to HEO over time via a fleet of regolith-processing, electrostatically-propelled vehicles; by contrast, humans arrive quickly to HEO from Earth. This NEO-based ISRU architecture could be the foundation of massive economic growth off-planet, enabling the construction mostly from asteroidal materials of massive solar power stations, communications hubs, orbital hotels and habitats, and other facilities.

One of the ideas I had been thinking of blogging about was the thought of augmenting Enhanced Gravity Tractor (EGT) asteroid deflection with in-situ derived propellants. The gravitation attraction force is usually the bottleneck in how fast you can do an asteroid deflection, but in some situations the propellant load might matter too.

What options are there for ISRU propellants in this case?

• If the asteroid is a carbonaceous chondrite, water might be your best bet. There are some promising SEP technologies, like the ELF thrusters being developed by MSNW that can operate efficiently with water as the propellant. The challenge is that water is only present in some asteroids, might not be super easy to extract, and might require enough infrastructure to not be worth it on net.
• The other big option is asteroid regolith. This could be charged up and run in a similar manner to an electrospray engine, or if it the dust is magnetically susceptible, it could be accelerated by something similar to a coil gun, mass driver, or linear accelerator. One of my employees used to work at a LASP lab running a dusty plasma accelerator. Basically they’d charge up small particles of dust, put them in a crazy electric field, and accelerate them to ~100km/s to smash into other dust particles to study micrometeorite formation processes.

What are some of the considerations for such an idea?

• You are probably going to be very power limited. This both impacts what you can do as far as propellant extraction, and also limits the exhaust velocity/Isp that is optimal for an asteroidal ISRU-fed propulsion system. Just as ion engine systems operating in gravity wells typically tend to optimize to a lower Isp/higher thrust, the optimal deflection per unit time likely won’t come from the highest theoretical Isp.
• On the other hand, the lower the exhaust velocity, the more material you have to handle to produce the “propellant”. So the optimal exhaust velocity is likely somewhere in the middle.
• Also, if you’re extracting water, that’s likely more energy intensive than dust.

Without running the detailed numbers, my guess is you’d want a dust “electrospray” engine with an Isp in the 100-1000s range to optimize the balance between thrust per unit power and required extraction capabilities. For instance a 500s Isp is maybe 25% of the Isp of the Xenon Hall Effect Thrusters they’re thinking of using for ARM. That would imply getting somewhere between 16x the thrust per unit time as running the same amount of power through the HET.You’d need 16x the propellant mass flow rate, but if you’re gathering hundreds of tonnes of regolith, rock, and boulders, I would think that wouldn’t be that hard to get say ~125tonnes of regolith. One nice thing is that some of this material can be gathered while landing to gather the additional mass for the enhanced gravity tractor.

• 

Hall Effect
Exhaust Velocity	19,620 m/s
Specific Impulse	2,000 s
Thrust	3,300 N
Number Thrusters	300
Thrust/Engine	11 N
Thrust Power	32.4 MW
Mass Flow	0.17 kg/s
Total Engine Mass	85,469 kg
T/W	4.00e-03
Frozen Flow eff.	73%
Thermal eff.	73%
Total eff.	53%
Fuel	60MWe input
Remass	Magnesium
Remass Accel	Electrostatic Acceleration
Specific Power	2,640 kg/MW

This ion rocket accelerates ions using the electric potential maintained between a cylindrical anode and negatively charged plasma which forms the cathode.

To start the engine, the anode on the upstream end is charged to a positive potential by a power supply. Simultaneously, a hollow cathode at the downstream end generates electrons. As the electrons move upstream toward the anode, an electromagnetic field traps them into a circling ring at the downstream end.

This gyrating flow of electrons, called the Hall current, gives the Hall thruster its name.

The Hall current collides with a stream of magnesium propellant, creating ions. As magnesium ions are generated, they experience the electric field between the anode (positive) and the ring of electrons (negative) and exit as an accelerated ion beam.

A significant portion of the energy required to run the Hall Effect thruster is used to ionize the propellant, creating frozen flow losses.

This design also suffers from erosion of the discharge chamber.

On the plus side, the electrons in the Hall current keep the plasma substantially neutral, allowing far greater thrust densities than other ion drives.

Novosti Kosmonavtiki, 1999.

And it suffers from the same critical thrust-limiting problem as any other ion engine: since you are accelerating ions, the acceleration region is chock full of ions. Which means that it has a net space charge which repels any additional ions trying to get in until the ones already under acceleration manage to get out, thus choking the propellant flow through the thruster.

The upper limit on thrust is proportional to the cross-sectional area of the acceleration region and the square of the voltage gradient across the acceleration region, and even the most optimistic plausible values (i.e. voltage gradients just shy of causing vacuum arcs across the grids) do not allow for anything remotely resembling high thrust.

You can only increase particle energy so much; you then start to get vacuum arcing across the acceleration chamber due to the enormous potential difference involved. So you can't keep pumping up the voltage indefinitely.

To get higher thrust, you need to throw more particles into the mix. The more you do this, the more it will reduce the energy delivered to each particle.

It is a physical limit. Ion drives cannot have high thrusts.

• 

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

In space, an electrostatic particle accelerator is effectively an electric rocket.

The illustrated design uses a combination of microwaves and spinning magnets to ionize the propellant, eliminating the need for electrodes, which are susceptible to erosion in the ion stream.

The propellant is any metal that can be easily ionized and charge-separated. A suitable choice is magnesium, which is common in asteroids that were once part of the mantles of shattered parent bodies, and which volatilizes out of regolith at the relatively low temperature of 1800 K.

The ion drive accelerates magnesium ions using a negatively charged grid, and neutralizes them as they exit. The grids are made of C-C, to reduce erosion.

Since the stream is composed of ions that are mutually repelling, the propellant flow is limited to low values proportional to the cross-sectional area of the acceleration region and the square root of the voltage gradient.

Decoupling the acceleration from the extraction process into a two-stage system allows the voltage gradients to reach 30 kV without vacuum-arcing, corresponding to exit velocities of 80-210 km/sec.

A 60 MWe system with a thrust of 1.5 kN utilizes a hexagonal array, 25 meters across, containing 361 accelerators. Frozen flow efficiencies are high (96%).

To boost the acceleration (corresponding to the “open-cycle cooling” game rule), colloids are accelerated instead of ions. Colloids (charged sub-micron droplets of a conducting non-metallic fluid) are more massive than ions, allowing increased thrust at the expense of fuel economy.

J. Beatty of Hughes, 1990.

• 

Arcjet
Exhaust Velocity	19,620 m/s
Specific Impulse	2,000 s
Thrust	3,200 N
Number Thrusters	32
Thrust/Engine	100 N
Thrust Power	31.4 MW
Mass Flow	0.16 kg/s
Total Engine Mass	22,369 kg
T/W	0.01
Frozen Flow eff.	60%
Thermal eff.	87%
Total eff.	52%
Fuel	60MWe input
Remass	Liquid Hydrogen
Remass Accel	Thermal Accel: Arc Heater
Thrust Director	Nozzle
Specific Power	713 kg/MW

A working fluid such as hydrogen can be heated to 12,000 K by an electric arc. Since the temperatures imparted are not limited by the melting point of tungsten, as they are in a sold core electrothermal engine such as a resistojet, the arcjet can burn four times as hot. However, the thoriated tungsten electrodes must be periodically replaced.

When used as an electrothermal thruster, the arcjet attains a specific impulse of 2 ksec with frozen-flow efficiencies of 60%. When used for mining beneficiation, regolith or ore is initially processed with a 1 Tesla magnetic separator and impact grinder (3.5 tonnes), before being vaporized in the arcjet. The arcjet can also be used for arc welding.

• 

MET Steamer Amplitrons
Exhaust Velocity	9,810 m/s
Specific Impulse	1,000 s
Thrust/Engine	30 N
Number Thrusters	x400
Thrust	12,000 N
Thrust Power	58.9 MW
Mass Flow	1 kg/s
Total Engine Mass	123,302 kg
T/W	0.01
Frozen Flow eff.	95%
Thermal eff.	85%
Total eff.	81%
Fuel	60MWe input
Remass	Water
Remass Accel	Thermal Accel: Microwave Heater
Thrust Director	Magnetic Nozzle
Specific Power	2,095 kg/MW

This device works by generating microwaves in a cylindrical resonant, propellant-filled cavity, thereby inducing a plasma discharge through electromagnetic coupling. The discharge performs either mining or thrusting functions.

In its mining capacity, the head brings to bear focused energy, tuned at close quarters by the local microwave guides, to a variety of frequencies designed to resonate and shatter particular minerals or ice.

In its electrothermal thruster (MET) capacity, the microwave-sustained plasma superheats water, which is then thermodynamically expanded through a magnetic nozzle to create thrust. The MET needs no electrodes to produce the microwaves, which allows the use of water propellant (the oxygen atoms in a steam discharge would quickly dissolve electrodes).

MET steamers can reach 900 seconds of specific impulse due to the high (8000 K) discharge source temperatures, augmented by rapid hydrogen-oxygen recombination in the nozzle. Vortex stabilization produces a well-defined axisymmetric flow. However, the specific impulse is ultimately limited by the maximum temperature (~ 2000 K) that can be sustained by the thruster walls.

The illustration shows a microwave plasma discharge created by tuning the TM₀₁₁ mode for impedance-matched operation. This concentrates the most intense electric fields along the cavity axis, placing 95% of the energy into the propellant, with less than 5% lost into the discharge tube walls. Regenerative water cooling is used throughout.

For pressures of 45 atm, each unit can produce 30 N of thrust. The thrust array contains 400 such units, at 50 kg each.

“Development of a High Power Microwave Thruster, with a Magnetic Nozzle, for Space Applications.” John L. Power and Randall A. Chapman, Lewis Research Center, 1989.

• 

Microwave electrothermal thrusters

Under a research grant from the NASA Lewis Research Center during the 1980s and 1990s, Martin C. Hawley and Jes Asmussen led a team of engineers in developing a Microwave Electrothermal Thruster (MET).

In the discharge chamber, microwave (MW) energy flows into the center containing a high level of ions (I), causing neutral species in the gaseous propellant to ionize. Excited species flow out (FES) through the low ion region (II) to a neutral region (III) where the ions complete their recombination, replaced with the flow of neutral species (FNS) towards the center. Meanwhile, energy is lost to the chamber walls through heat conduction and convection (HCC), along with radiation (Rad). The remaining energy absorbed into the gaseous propellant is converted into thrust.

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Tungsten Resistojet
Exhaust Velocity	9,810 m/s
Specific Impulse	1,000 s
Thrust	9,900 N
Thrust Power	48.6 MW
Mass Flow	1 kg/s
Total Engine Mass	42,601 kg
T/W	0.02
Thermal eff.	80%
Total eff.	80%
Fuel	60MWe input
Remass	Liquid Hydrogen
Remass Accel	Thermal Accel: Resistance Heater
Thrust Director	Nozzle
Specific Power	877 kg/MW

Tungsten, the metal with the highest melting point (3694 K), may be used to electric-resistance heat ore for smelting or propellant for thrusting. In the latter mode, the resistojet is an electro-thermal rocket that has a specific impulse of 1 ksec using hydrogen heated to 3500K. The frozen flow efficiency (without hydrogen recombination) is 85%. Internal pressures are 0.1 MPa (1 atm). To reduce ohmic losses, the heat exchanger uses a high voltage (10 kV) low current (12.5 kiloamp) design. The specific power of the thruster is 260 kg/MWj and the thrust to weight ratio is 8 milli-g.

(Many readers have expressed surprise at 12.5 kiloamps being described as "low current". I am trying to get in touch with Mr. Eklund for clarification)

Once arrived at a mining site, the tungsten elements, together with wall of ceramic lego-blocks (produced in-situ from regolith by magma electrolysis) are used to build an electric furnace. Tungsten resistance-heated furnaces are essential in steel-making. They are used to sand cast slabs of iron from fines (magnetically separated from regolith), refine iron into steel (using carbon imported from Type C asteroids), and remove silicon and sulfur impurities (using CaAl₂O₄ flux roasted from lunar highland regolith).

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Wakefield E-Beam
Exhaust Velocity	19,620 m/s
Specific Impulse	2,000 s
Thrust	4,600 N
Thrust Power	45.1 MW
Mass Flow	0.23 kg/s
Total Engine Mass	41,837 kg
T/W	0.01
Frozen Flow eff.	85%
Thermal eff.	89%
Total eff.	76%
Fuel	60MWe input
Remass	Regolith
Remass Accel	Thermal Accel: Arc Heater
Thrust Director	Nozzle
Specific Power	927 kg/MW

An e-beam (beam of electrons) is a versatile tool. It can bore holes in solid rock (mining), impart velocity to reaction mass (rocketry), remove material in a computer numerical control cutter (finished part fabrication), or act as a laser initiator (free electron laser).

A wakefield electron accelerator uses a brief (femtosecond) laser pulse to strip electrons from gas atoms and to shove them ahead. Other electrons entering the electron-depleted zone create a repulsive electrostatic force. The initial tight grouping of electrons effectively surf on the electrostatic wave.

Wakefield accelerators a few meters long exhibit the same acceleration as a conventional rf accelerator kilometers in length. In a million-volt-plus electron beam the electrons are approaching lightspeed, so the term relativistic electron beam is appropriate.

The wakefield can be used as an electrothermal rocket similar in principle to the arcjet, but far less discriminating in its choice of propellant.

Tajima 1979.

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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

The solar wind dynamic pressure is about 2 nPa at one AU. An electric sail generates nanothrust from this particle stream in a manner similar to a mag sail, except that electric rather than magnetic fields are used.

Its geometry employs hundreds of long thin conducting wires, rotating with a period of 20 minutes to keep them in positive tension.

A solar-powered electron gun (typical power is a few hundred watts) keeps the spacecraft and sail in a high positive potential (up to 20 kV). This electric field surrounds each wire a few tens of meters into the surrounding solar wind plasma. Therefore the solar wind protons "see" the positively-charged wires as rather thick obstacles. It is this multiplication factor that allows sails using the solar wind to outperform those using photon pressure, which is 5000 times stronger.

Furthermore, the electric sail thrust force varies as (1/r)^{7/6} from Sol, compared to the photon pressure, which varies as the inverse square distance.

Each 100 km tether, massing but a kilogram, generates 0.01 N of thrust. Simultaneously it also attracts electrons from the solar wind plasma, which are neutralized by the electron gun. Potentiometers between each tether and the spacecraft control the attitude by fine-tuning the tether potentials. Additionally, the thrust may be turned off by simply switching off the electron gun.

Each 20 μm tether is redundantly interlinked for robustness against meteoroids.

Electric sails must avoid magnetospheres, since there is no solar wind inside these zones.

Pekka Janhunen, “Electric Sail”, 2004. P. Janhunen and A. Sandroos,“Simulation study of solar wind push on a charged wire” 2007.

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Magnetic Sail
Thrust	110 N @ 1 AU
Sail Mass	20,000 kg

At 1 AU, the solar wind comprises several million protons per cubic meter, spiraling away from the sun at 400 to 600 km/sec (256 μwatts/m²). When such charged particles move through a magnetic field formed by the mag sail, a tremendous loop of wire some 2 km across, they are deflected.

An unloaded mag sail this size has a thrust of 100 N (at 1 AU) and a mass of 20 tonnes. The wire is superconducting whisker, at 10 kg/km, connected to a central bus and payload via shroud lines. The loop requires multi-layer insulation and reflective coatings to maintain its superconducting temperature of 77 K. Because the sail area is a massless magnetic field, a mag sail has a superior thrust/weight ratio than photon sails.

Just as with photon sails, lateral motion is possible by orienting the sail at an angle to the thrusting medium. A mag sail also develops thrust from planetary and solar magnetospheres, which decrease as the fourth power of the distance from the magnetosphere source. Field strength is typically 10 μT in Earth’s magnetosphere, or less in the solar magnetosphere.

The mag sail illustrated is augmented by a spinning disk photon sail attached to its staying lines. It is maneuvered using photonic laser thrusters (propellantless thrust derived from the bouncing of laser photons between two mirrors).

Zubrin 1988.

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Kite Photon Sail
Max Thrust	182 N @ 1 AU
Useful Thrust	69 N @ 1 AU
Mass	16,000 kg

The simplest way to hold a sail out to catch sunlight is to use a rigid structure, much like a kite. The columns and beams of such a structure form a three-axis stabilization, so-named because all three dimensions are rigidly supported.

Kite sails are easier to maneuver than sails that support themselves by spinning. By tilting the sail so that the light pressure slows the vessel down in its solar orbit will cause an inward spiral towards the sun. Tilting the opposite way will cause an outward spiral.

The kite sail shown has a has a mast, four booms, and stays supporting a square sail 4 km to a side. At 93% reflectance, it develops a maximum thrust of 182 newtons at 1 AU. Control is provided by 4 steering vanes of 20,000 m² area each. The unloaded mass is 16,000 kg and the unloaded sail loading is 0.5 g/m².

The film is 300 nm aluminum. Its microstructure is formed by DNA scaffolding, which is then coated with aluminum and the DNA baked off. This leaves holes the size of the wavelength of visible light, which makes the film lighter. The perforated film is thermally limited to 600K, and cannot operate in an Earth orbit lower than 1000 km due to air drag.

Its thrust can augmented by the illumination of the 60 MW laser beam which is standard in this game. Operating at 50 Hz, this beam boils off water coolant replenished through capillary action in the perforated film. Tiny piezoelectric robot sailmakers repair ablated portions of the sail using vapor-deposited aluminum.

Twice the size of Garvey’s “Large Square Rigged Clipper Sail”, and adding the perforation feature: J. M. Garvey, "Space station options for constructing advanced solar sails capable of multiple mars missions", AIAA Paper 87-1902, AIAA/SAE/ASME 23rd Joint Propulsion Conference,1987.

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Photon Heliogyro Sail
Thrust	140 N @ 1 AU
Number Blades	192
Mass	40,000 kg

A heliogyro is a photon sail consisting of multiple spinning blades. Its blades are rigidified by centrifugal force and pitched to provide attitude control, much like a helicopter.

Although a spinning design does not need the struts of a kite sail, the centrifugal loads generated must be carried by edge members in the blades. Moreover oscillations are created when the sail’s attitude changes, which need to be restrained by transverse battens. Small sail panels prevent wrinkling from the curvature in edge members between the battens.

For these reasons, the heliogyro has no mass advantage over a kite sail, but it has the advantage of easier deployment in space.

The reference design at 1 AU generates 140 newtons maximum thrust from 4 banks of 48 blades each. Each blade has a dimension of 8 × 7500 meters. This thrust is quite low (about 31 lbs), but its game performance is comparable to an electric rocket since its impulse is imparted over a full year rather than a few days.

The sail film is 1 μm thick with reflective and emissive coatings. Each bank is fixed to a hub so the members co-rotate. The combined film masses 7 tonnes alone, and with the supporting cables masses 40 tonnes.

Scaled up from the JPL Halley Rendezvous design: Jerome Wright, “Space Sailing”, 1992.

(ed note: I asked Rob Davidoff for an estimate of the performance of beer.)

Thrust = velocity * mass_flow

Assume we model the system as the fluid starting from stagnation (V-o = 0) under pressure P_o and accelerating to a vacuum pressure P_2 = 0 at velocity v_1. We can then employ Bernoulli's equation, which says the following once we knock out some irrelevant terms:

P_o = 0.5 * rho * (V_1)²

Solve for V_1:

V_1 = sqrt( 2 * P_o / rho)

So, what's a reasonable pressure? Sheesh, I dunno. A standard fuel-driven rocket engine operates at about 35 atm for a very low-pressure combustion, let's try that. Using the density of water (1000 kg/m³), I get...84 m/s. I_sp of 8.5 seconds or so. The thrust will be this times the mass flow, so 1 kg/s would give 84 Newtons.

Is this any use? It's pretty crappy, but maybe it's good enough. Say he needs, oh, 150 m/s. That's a mass ratio of 6, which isn't terrible. To lift off from an asteroid, you basically need a T/W of anything non-zero, so it's workable. Of course, keeping beer pressurized to 35 atmospheres was the starting assumption, any maybe that was a little high.

However, the big issue is the density of the beer. Substitute in an air-like gas with a density of 1.4 kg/m² instead of 1000, and you get to an I_sp of ~220s, instead of 8. That's a lot more like it.

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Mass Driver
Exhaust Velocity	9,810 m/s
Specific Impulse	1,000 s
Thrust	10,400 N
Thrust Power	51.0 MW
Mass Flow	1 kg/s
Total Engine Mass	163,000 kg
T/W	7.00e-03
Thermal eff.	85%
Total eff.	85%
Fuel	60MWe input
Remass	Regolith
Remass Accel	Electromagnetic Acceleration
Specific Power	3,195 kg/MW

An electrodynamic traveling-wave accelerator can be used as either a thruster or a payload launcher.

The reaction mass or payload is loaded into a lightweight bucket banded by a pair of superconducting loops acting as armatures of a linear-electric guideway. The thruster illustrated accelerates the bucket at 75,000 gee's, utilizing 7 GJ of electromagnetic energy stored inductively in superconducting coils. The trackway length is 390 meters. One 36kg of reaction mass is ejected each minute at 15 km/sec. The bucket is decelerated and recovered. Cryogenic 77 K radiators cool the superconductors.

A mass-driver optimized for materials transport rather than for propulsion uses a higher ratio of payload mass to bucket mass. With a 54% duty cycle, this system can launch 10 kt/yr of factory products. Coupled with a pointing accuracy in the tens of microradians, this can launch payloads or projectiles to targets millions of kilometers distant. A terrestrial mass driver running up the side of an equatorial mountain can launch payloads at the Earth escape velocity (11 km/sec). Imparted with a launch energy of 76 GJ, a one tonne payload the size and shape of a telephone pole with a carbon cap would burn up only 3% of its mass and lose only 20% of its energy on its way to solar or Earth orbit.

Gerard K. O’Neill, “The High Frontier: Human Colonies in Space,” 1977.

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“Anjeä SysCon, this is VS Ardent Voyager, gated in-system from Loxix, identifying. Over.”

“Ardent Voyager, Anjeä SysCon, we have you arriving at 5173-09-14:7-51-11; squawk ident. Welcome to Imperial space, please specify your intentions. Over.”

“Anjeä SysCon, Ardent Voyager. Request through-clearance for immediate transit to Conclave System, minimum delta transfers. Over.”

“Wait one, Ardent Voyager… Voyager, please confirm your hull class and propulsion. Over.”

“Anjeä SysCon, we are a beehive habitat with reserve mass driver propulsion. Over.”

“In other words, Ardent Voyager, you’re flying an asteroid and moving by throwing rocks. With regret, please shut down all active drive systems immediately. You are denied transit permission under power. Over.”

“Anjeä SysCon, we are a diplomatic vessel and have the right of transit to Conclave System. Over.”

“Ardent Voyager, you have the right of transit, but that doesn’t exempt you from the rules of navigation. Over.”

“Anjeä SysCon, what’s your problem with us? Nowhere else has refused us transit. Over.”

“Ardent Voyager, this is a crowded system with too damn many loose rocks anyway, see? We don’t want any accidents, and a drive like yours is a flyin’ invitation to accidents, or a hefty cleanup bill. It’s a miracle you got clearance to transit this far. Over.”

“Anjeä SysCon, what are we supposed to do, then, just sit here? Over.”

“Ardent Voyager, hire a tug? Either to finish out your voyage or jump back out-system, but either way, you’re not runnin’ that hazard to navigation anywhere in our sky. SysCon, clear.”

- overheard on system space-control channel, Anjeä (High Verge)

(ed note: Please note that for the relativistic factor physicists use the Greek letter "gamma" or "γ". This has absolutely nothing to do with "gamma-rays". Please do not get them confused.)

Abstract

It is shown that the idea of a photon rocket through the complete annihilation of matter with antimatter, first proposed by Sänger, is not a utopian scheme as it is widely believed. Its feasibility appears to be possible by the radiative collapse of a relativistic high current pinch discharge in a hydrogen-antihydrogen ambiplasma down to a radius determined by Heisenberg’s uncertainty principle. Through this collapse to ultrahigh densities the proton-antiproton pairs in the center of the pinch can become the upper GeV laser level for the transition into a coherent gamma ray beam by proton-antiproton annihilation, with the magnetic field of the collapsed pinch discharge absorbing the recoil momentum of the beam and transmitting it to the spacecraft. The gamma ray laser beam is launched as a photon avalanche from one end of the pinch discharge channel.

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1. Introduction

The idea of the photon rocket was first proposed by Sänger, but at that time considered to be utopian. Sänger showed if matter could be completely converted into photons, and if a mirror can deflect the photons into one direction, then a rocket driven by the recoil from these photons could reach relativistic velocities where the relativistic time dilation and length contraction must be taken into account, making even intergalactic trips possible. The only known way to completely convert mass into radiation is by the annihilation of matter with antimatter. In the proton-antiproton annihilation reaction about 60% of the energy goes into charged particles which can be deflected by a magnetic mirror and used for thrust, with the remaining 40% going into 200 MeV gamma ray photons.1 With part of the gamma ray photons are absorbed by the spacecraft, a large radiator is required, greatly increasing the mass of the spacecraft.

Because of the problem to produce antimatter in the required amount, Sänger settled on the use of positrons. There, the annihilation of a positron with an electron produces two 500 keV photons, much less than two 200 MeV photons optimally released in the proton-antiproton annihilation reaction. But even to deflect the much lower energy 500 keV gamma ray photons, would require a mirror with an electron density larger than the electron density of a white dwarf star.

Here, a much more ambitious proposal is presented: The complete conversion of the proton-antiproton reaction into a coherent GeV gamma ray laser beam, with the entire recoil of this beam pulse transmitted to the spacecraft for propulsion.

This possibility is derived from the discovery that a relativistic electron-positron plasma column, where the electrons and positrons move in an opposite direction, has the potential to collapse down to a radius set by Heisenberg’s uncertainty principle, thereby reaching ultra high densities. Because these densities can be of the order 10¹⁵g/cm³, comparable to the density of a neutron star, has led the Russian physicist B.E. Meierovich to make the following statement : “This proposal can turn out to be essential for the future of physics.”

The most detailed study of the matter-antimatter , hydrogen-antihydrogen rocket propulsion for interstellar missions was done by Frisbee. It was relying on “of the shelf physics,” while the study presented here goes into unknown territory.

The two remaining problems are to find a way to produce anti-hydrogen in the quantities needed, and how to store this material. A promising suggestion how the first problem might be solved has been proposed by Hora to use intense laser radiation in the multi-hundred gigajoule range. This energy appears quite large, but the energy to pump the laser could conceivably be provided by thermonuclear micro-explosions to pump such a laser.

2. Magnetic Implosion of a Relativistic Electron-Positron-Matter-Antimatter Plasma

(ed note: Prolonged discussion of an electron-positron plasma, an "ambiplasma". Lots of heavy-duty mathematics omitted, since chapter 3 starts with how an electron-positron plasma is too inefficient. Read paper for the technical details. Main take-away is that if you can pinch beams of electrons and positrons moving at relativistic velocities ("high γ-value") in opposite directions, you can create intense pulses of near coherent gamma-rays. A gamma-ray laser if you will.)

3. Magnetic Implosion of a Hydrogen-Antihydrogen Ambiplasma

A magnetically imploded electron-positron plasma can be made by the coalescence of two intense multi-MeV electron and positron beams. A likewise magnetically imploded proton-antiproton plasma could be made by two multi-GeV proton and antiproton beams. But this would be a very inefficient way to make a proton-antiproton annihilation laser, because it would require to accelerate the protons and the antiprotons to the same γ-value as for the electrons and positrons to achieve the same kind of radiative collapse to high energies. For the example γ ≈100,it would require the protons and antiprotons to an energy by two orders of magnitude larger than their rest energy, which would be to accelerate the energy of the gamma ray photons released by such a laser.

Fortunately, there exists a better way: It is through the magnetic implosion of hydrogen-antihydrogen ambiplasma (instead of colliding beams of protons and antiprotons, collide beams of hydrogen atoms and antihydrogen atoms). There only the electrons and positrons have to be accelerated to a large γ-value, with the hydrogen-antihydrogen plasma there formed by the coalescence of a hydrogen with an antihydrogen pinch discharge. For the induced coalescence into an ambiplasma pinch discharge the currents of the pinch discharges must be in the same directions, with the electrons and positrons moving in the opposite direction as the protons and antiprotons. As for a pinch discharge in an ordinary plasma, an externally applied axial magnetic field can stabilize the pinch discharge in the ambiplasma.

Immediately following their coalescence into an ambiplasma pinch discharge, a powerful gigavolt pulse is applied to the discharge, accelerating the electrons and positrons to high energies by the run-away mechanism. The resulting high electron-positron current magnetically insulates the protons and antiprotons against the development of a significant current. This can be seen as follows:

(lots of heavy-duty mathematics omitted) This chapter can be summarized as follows: If a current equal to I = γI_A, and for a large value of γ, passes through a hydrogen-antihydrogen ambiplasma, it is going to collapse down to extremely high densities with the protons and antiprotons together with electrons and positrons compressed by the confining azimuthal magnetic field.

4. The Collapsed Hydrogen-Antihydrogen Ambiplasma as the Upper Level of a GeV Gamma Ray Laser

It is now proposed, to employ the collapsed hydrogen-antihydrogen ambiplasma as the upper laser level of the linear atom made up from a large number of hydrogen-antihydrogen atoms, held together by the ultrastrong magnetic field of the pinch discharge. The annihilation of hydrogen with the antihydrogen goes over the production of π⁰, π⁺, and π^- pions for the proton-antiproton reaction, and into two γ photons for the electrons and positrons. The π⁰ decays further into 4γ photons, with the π⁺ and π^- pions decaying into μ⁺, μ^- leptons and their associated μ neutrinos and antineutrinos. But with the high intensity of stimulated γ-ray cascade, it is likely that there is a reaction channel where all the energy of the protonantiproton annihilation reaction goes into two γ-ray photons, with the photons of the gamma ray cascade overwhelming all the other reaction channel. This is the mechanism for the electron-positron annihilation laser, and we will here assume that it also occurs for the proton-antiproton laser.

If this transformation takes place as a gamma ray laser avalanche, and if the recoil of this avalanche is transmitted by the strong azimuthal magnetic field of the pinch discharge, then with the return current conductor fastened to the spacecraft, all the momentum of the annihilation reaction goes into the spacecraft.

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The idea is explained in Fig. 1, where the laser avalanche is launched from the left end of the pinch discharge, moving to the right with a velocity close to the velocity of light. As in the Mössbauer effect, the gamma ray photons transmit their recoil momentum to the linear atom of the ultradense pinch discharge. For this idea to work requires that the recoil energy…

(ed note: more math omitted which is over my head like a cirrus cloud)

      During the CoDominium period it seems fusion drives are used to propel spaceships. Sometime during the First Empire period a new kind of reaction drive is invented. Fusion drives on warships are directed into their Langston Field which then creates an extremely efficient high-intensity beam of light in the shape of a cone that is used for propulsion. For the Field to work as described, energy must be emitted perpendicular to its surface and then naturally spreads out due to the inverse square law. The cone shape is a result of the Field being an ellipsoid with the beam coming from a small, curved section of it combined with this inverse square law spreading. This photon drive is utilized for propulsion by the Second Empire warships too. Therefore, only spaceships having a Langston Field can utilize this light-pressure propulsion system: all other spaceships still use fusion drives directly for thrust. The drive cannot be used as a long-range weapon because of beam spreading but it would be unhealthy for another ship without a Langston Field to pass through it especially if it were a close passage.

     Note that fusion drives release photons and energetic plasma into the Field. The Field absorbs the photons (energy and momentum) and the kinetic energy from the plasma (momentum). From the stories, it is clear that the Field can be controlled to release the photons directionally or uniformly in all directions. As noted above, if directionally, the Field releases the absorbed photons in one direction to propel the spaceship. The photons released must contain the momentum from both the original photons and from the plasma. Because of the requirement for the conservation of momentum, this means that the frequency (energy level) of the Field-released photons must be of a much higher frequency than those originally released by the fusion reaction.

Of course light pressure could be used for propulsion. In fact MacArthur did exactly that, using hydrogen fusion to generate photons and emitting them in an enormous spreading cone of light.

MacArthur decelerated at nearly three gravities directly into orbit around Brigit; then she descended into the protective Langston Field of the base on the moonlet, a small black dart sinking toward a tremendous black pillow, the two joined by a thread of intense white. Without the Field to absorb the energy of thrust, the main drive would have burned enormous craters into the snowball moon.

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    Light speed, c = 3 × 10⁸ meters per second, is the ultimate speed limit of the universe. The well-tested physics orthodoxy of special relativity tells us that nothing can go faster than c. When any massive object with rest mass M (taken to be in energy units) has velocity v=c (or relativistic velocity b = v/c = 1), the object's mass-energy becomes infinite. This is because the relativistic mass increase factor g = 1/(1 - b²)^1/2 has a zero in its denominator, and the net mass-energy E is given by E = gM. Therefore, it would require all the energy in the universe and more to accelerate the object to a velocity of b = 1.

    If the massive object could somehow be drop-kicked over the light-speed barrier so that v was greater than c, then both g and E would become imaginary quantities (like [-1]^½ ) because b would be larger than 1 and (1 - b²) would be negative. This, says physics orthodoxy, is Nature's way of telling us that such quantities have nothing to do with our universe, in which all measurable physical variables like E must have real (not imaginary) numbers as values.

    "Not so!" said Gerald Feinberg, the eminent physicist and SF fan who died last year at the age of 59. In a 1967 paper, Feinberg postulated a type of hypothetical particles with a rest mass M that also has an imaginary value (M²<0). Then E = gM, the observable mass-energy of these particles, becomes real and positive and is compatible with other energies in our universe. Feinberg christened his hypothetical particles "tachyons" (from the Greek word for swift) for their characteristic that they always travel more swiftly than c.

    Normal particles (or "tardyons" in Feinberg's terminology) have a velocity of 0 when their mass-energy is smallest (at E=M). They have a velocity slightly less than c when their mass energy is very large compared to its rest mass (E>>M). Tachyons (if they exist) would behave in an inverted way, so that when their mass-energy is smallest (E=0) they would have infinite velocity (1/b = 0) and when their mass energy is very large compared to their rest mass (E >> |M|) they would have a velocity slightly larger than c.

    This can perhaps be seen more clearly by considering some equations of special relativity. When any particle (tachyon or tardyon) has rest mass M and mass-energy E, it has a momentum P (in energy units) given by E² = P² + M². For tardyons (normal particles) it should be clear from this equation that E cannot be less than M and is always greater than P. For tachyons, however, we have the peculiarity that M² is negative, so that the energy equation becomes E² = P² - |M|² or P² = E² + |M|². This means that E can be as small as zero (when P = |M|) and that P is always greater than E and cannot be less than |M|. These quantities are related to the relativistic velocity ß by the equation ß = P/E. This tells us that when a tachyon has its minimum momentum P = |M|, it will also have its lowest possible mass-energy (E=0) and will have infinite velocity.

    The theoretical work on tachyons in the 1960's by Feinberg and others, particularly Sudarshan and Recami, prompted a "gold rush" among experimentalists seeking to be the first to discover tachyons in the real world. They studied the kinematics of high energy particle reactions at large accelerators, they built timing experiments that used cosmic rays, and they probed many radioactive decay processes for some hint of tachyon emission. Although there were a few false "discoveries" among these results, all of the believable experimental results were negative in the decade or so after the initial theoretical work. Some cold water was also thrown on the tachyon concept from the theoretical direction when it was demonstrated (by physicist and SF author Gregory Benford, among others) that tachyons could be used to construct an "anti-telephone" capable of sending information backwards in time in violation of the principle of causality, one of the most fundamental and mysterious laws of physics. Tachyons were therefore metaphorically placed on a dusty shelf in the museum of might-be particles for which there is no experimental evidence, and there they have languished for the past 25 years. But this may now be changing: a new and growing body of evidence from an unexpected direction supports the possible existence of tachyons.

    There is great fundamental interest in the mass of the electron neutrino (n_e), because it is a leading "dark matter" candidate. Several very careful experiments have been mounted to measure its mass through its effect on the beta decay of mass-3 hydrogen or tritium. Tritium, with one proton and two neutrons in its nucleus, is transformed by the weak interaction beta-decay process into mass-3 helium (two protons and one neutron) by emitting an electron and an anti-neutrino (³H → ³He + e^- + n_e) with an excess energy of 18.6 keV. This is the lowest energy beta decay known, and therefore the one which is affected most strongly by the mass of the electron neutrino.

    If the kinetic energy of the emitted electrons is measured for a very large number of similar tritium decays, one finds a bell-shaped "spectrum" of energies ranging from essentially zero electron energy to a maximum of about 18.6 keV. This maximum-energy tip of the electron's kinetic energy distribution is called the "endpoint", and is the place where the neutrino is emitted with near-zero energy and where the neutrino's mass will make it's presence known. When the endpoint region is made linear (using a plotting trick called a Kurie plot), then the straight-line dependence of the electron's kinetic energy takes a node-dive just before it reaches zero, displaying the effect of neutrino mass.

    Because of the relativistic relation of mass, energy, and momentum (E² = P² + M²) it is the mass-squared of the neutrino that is actually determined by the tritium end-point measurements. The mass-squared is allowed to vary from negative values (too many electrons with energies near the end-point) through M_n²=0 (the expected number of electrons with energies near the end-point), to a positive mass-squared (too few electrons with energies near the end-point), and this variation is used to fit the experimental data. The resulting fit is quoted with the measured value of M_n² plus-or-minus the statistical error in the measurement plus-or-minus the estimated systematic error in the measurement.

    At least five experimental groups have made careful measurements of M_n², and several of these groups have published their results in scientific journals. The two most recent published values are:
Zürich (Switzerland) M_n² = -158 ± 150 ± 103 eV² (1986)
Los Alamos (USA) M_n² = -147 ± 68± 41 eV² (1991)

    As the numbers imply, both groups find an excess of electrons with energies near the tritium endpoint. There have also been recent informal reports (but no further publications) from these and other laboratories, particularly a group at a well-known weapons laboratory in California, of measurements which continue to give negative values to M_n² with even more statistically meaningful error estimates. I was told by one of the experimenters that if the a similar result had been found with the same errors but with the positive of the determined value for M_n², there would have been much publicity, with press conferences announcing the discovery of a non-zero mass for the electron neutrino.

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    OK, this is a SF magazine, not a scientific journal. We are not scandalized by the possibility that M_n² is negative, indicating that the electron neutrino is perhaps a tachyon. In fact, we rather like the idea that a well known particle may routinely be breaking the light-speed barrier. Let us then suppose that the n_e is a tachyon with an imaginary mass of, say i × 12 eV. What are the physical consequences of this? The answer is disappointing. The tritium endpoint measurement is so difficult precisely because assuming a small neutrino mass (real or imaginary) has very few observable consequences. The "dark matter" implications are also nil. Since tachyons can have any mass-energy down to zero and are never at rest, they, like photons, cannot contribute to the excess of dark matter in the universe.

    The above-mentioned "tachyon anti-telephone" with its violations of causality is also essentially impossible. Neutrinos are fairly easy to produce (using an accelerator to create beta-decaying nuclei) but very difficult to detect. The only successful neutrino detectors use either neutrino-induced nuclear reactions (the Homestake and Gallex experiments) or hard neutrino-electron scatterings (Kamiokande and SNO) to detect neutrinos with extremely low efficiency. But to use the possible tachyonic super-light speed of the electron neutrinos, they must have mass-energies comparable to or less than 12 electron volts. This is about 10^-6 of the lowest neutrino energy ever detected, neither of the above detection schemes can be used in this energy range, and there is no known alternative method of detection. Thus, even if the n_e is a tachyon, the law of causality is safe from our tamperings for the foreseeable future.

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    This brings us our second question: What new SF gimmicks are suggested by the possibility of easy-to-produce tachyons? I have a delightful answer. We can make a tachyon drive.

    Consider the central problem of rocketry: how can one burn fuel at a high enough exhaust velocity to provide reasonable thrust without an unreasonable expenditure of energy. This is the dilemma that plagues our space program, and the solutions we have developed are not very good.

    So let's consider a device that makes great quantities of E=0 tachyons and uses them as the infinite velocity exhaust of a "rocket". Within the constraints of the conservation laws of physics, we can make all the tachyons we want for free, provided we make them in neutrino-antineutrino pairs to conserve spin and lepton number. Momentum conservation is not a problem because we want and need the momentum kick derived from emitting the neutrino-antineutrino pair. This leaves us to deal with energy conservation.

    The paradox here is that with a high-momentum exhaust of tachyons produced at no energy cost and beamed out the back of our space vehicle, the vehicle would seem to gain kinetic energy from nowhere, in violation of the law of conservation of energy. The solution to this paradox (as can be demonstrated by considering particle systems) is that the processes producing the tachyons must also consume enough internal energy to account for the kinetic energy gain of the system. Thus, a tachyon drive vehicle might be made to hover at no energy cost (antigravity!), but could only gain kinetic energy if a comparable amount of stored energy were supplied.

    How could we arrange for an engine to produce great floods of electron neutrino-antineutrino pairs beamed in a selected direction? All I can do here is to lay out the problems and speculate. Neutrinos are produced by the weak interaction, which has that name because is much many orders of magnitude weaker than electromagnetism. Neutrino production of any kind is improbable. On the other hand, in any quantum reaction process the energy cost squared appears in the denominator of the probability, and if that energy is zero, it should make for abig probability. The trick might be to arrange some reaction or process that is in principle strong but is inhibited by momentum conservation. Then the emission of a neutrino-antineutrino pair to supply the needed momentum with zero energy cost would make the process go. A string of similar atomic or nuclear systems prepared in this way might constitute an inverted population suitable for stimulated emission (like light, correlated neutrino-antinuetrino pairs should be bosons), resulting in a beam from a "tachyon laser" that might amplify the process and produce the desired strong beam of tachyons.

    That's about the best I can do at the moment, for providing the scientific underpinnings of a tachyon drive for SF purposes. I think it's a nifty idea to which I will devote more thought. I just hope it survives the ongoing experimental measurements of M_n² for the electron neutrino. Watch this space for further developments.

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References:

Tachyons:
"Particles That Go Faster Than Light", Gerald Feinberg, Scientific American, 69-77 (February-1970);
Tachyons, Monopoles, and Related Topics, E. Recami, ed., North Holland Publishing Co., (1978).

Neutrino Mass Measurements:
"Measurement of the Neutrino Mass from Tririum Beta Becay", E. Holzschuh, Rep. Prog. Phys. 55, 1035-1091 (1992).

• 

We’d been decelerating at two gravities for almost nine days when the battle began. Lying on our couches being miserable, all we felt were two soft bumps, missiles being released. Some eight hours later, the squawkbox crackled:

“Attention, all crew. This is the captain.” Quinsana, the pilot, was only a lieutenant, but was allowed to call himself captain aboard the vessel, where he outranked all of us, even Captain Stott. “You grunts in the cargo hold can listen, too.

“We just engaged the enemy with two fifty-gigaton tachyon missiles and have destroyed both the enemy vessel and another object which it had launched approximately three microseconds before.

“The enemy has been trying to overtake us for the past 179 hours, ship time. At the time of the engagement, the enemy was moving at a little over half the speed of light, relative to Aleph, and was only about thirty AU’s from Earth’s Hope. It was moving at 0.47c relative to us, and thus we would have been coincident in space-time”—rammed!—“in a little more than nine hours. The missiles were launched at 0719 ship’s time, and destroyed the enemy at 1540, both tachyon bombs detonating within a thousand klicks of the enemy objects.”

The two missiles were a type whose propulsion system was itself only a barely-controlled tachyon bomb. They accelerated at a constant rate of 100 gees, and were traveling at a relativistic speed by the time the nearby mass of the enemy ship detonated them.

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“All right, load ‘em up.” With the word “up,” the bay door in front of me opened—the staging area having already been bled of air—and I led my men and women through to the assault ship.

These new ships were ugly as hell. Just an open framework with clamps to hold you in place, swiveled lasers fore and aft, small tachyon powerplants below the lasers. Everything automated; the machine would land us as quickly as possible and then zip off to harass the enemy. It was a one-use, throwaway drone. The vehicle that would come pick us up if we survived was cradled next to it, much prettier.

We leveled off about a kilometer from the surface and sped along much faster than the rock’s escape velocity, constantly correcting to keep from flying away. The surface rolled below us in a dark gray blur; we shed a little light from the pseudo-cerenkov glow made by our tachyon exhaust, scooting away from our reality into its own.