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.

• 

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.

• 

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).

• 

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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The electric sail is an intriguing propulsion concept that Pekka Janhunen at the Finnish Meteorological Institute has been championing for some years. It’s currently the subject of a NASA Phase II study and continues to draw attention despite the fact that we’re in the early stages of turning what looks like sound physical theory into engineering. What captures the imagination here is the same thing that is so attractive about solar sails — in both cases, we are talking about carrying no propellant, but instead relying on natural sources to do the work.

Here we have to be careful about terminology, because it’s all too easy to refer to solar photons as a kind of ‘wind,’ especially since the predominant metaphor is sailing. So let’s draw the lines sharply. There is indeed a ‘solar wind’ in today’s parlance, but it refers not to light but to the stream of particles, plasma and magnetic fields flowing out from the Sun into the heliosphere. An electric sail will ride this solar wind to achieve interplanetary velocities. A solar sail, on the other hand, will use solar photons, which carry no mass but do convey momentum.

Two entirely different concepts, even if both have resemblance to traditional nautical sails. Then we have the other terminological complication: A sail designed to be pushed not just by sunlight but rather by a laser or microwave beam is sometimes called a ‘light sail,’ which is how I have always referred to it, but it still uses photons for propulsion, even if they don’t come from the Sun. Maybe Manasvi Lingam and Avi Loeb have it right in their new paper to refer to photon-pushed sails of any kind as ‘light sails,’ distinguishing these from both electric and magnetic sails (magsails) that use the ‘solar wind’ as their driver. Thus:

Light sails — solar sails and those driven by beamed arrays — use electromagnetic radiation and the momentum transfer of photons. Electric sails use the particle stream of the solar wind.

The electric sail that Janhunen continues to study is the subject of Lingam and Loeb’s new paper, which has been submitted to Acta Astronautica. At the Florida Institute of Technology and Harvard University respectively, the two scientists have calculated performance possibilities for a spinning spacecraft that deploys a number of long wires to which an electrostatic charge has been induced. Solar wind protons (not photons!) reflect off these wires to produce thrust. The wires are kilometers long, and with that slight positive bias, the spacecraft carries an electron gun to manage the charge, retaining the bias against ambient solar wind electrons.

Light sails, to use the Lingam and Loeb terminology, have been considered for interstellar missions for decades now (hats off to the early work of Robert Forward, Gregory Matloff and Geoff Landis, among others), but electric sails are new enough that we need information on how well an electric sail might do for this purpose. Could this technology get us to another star?

For a species like ours, anxious to see missions completed within a few human lifetimes, the answer is no. While a huge laser array like the one contemplated by Breakthrough Starshot could send a small light sail at relativistic speeds to another star, the electric sail cannot achieve the needed velocities.

A species with a different attitude toward time might fare better. The paper explains, for example, how electric sails could leverage the stellar winds of red dwarf stars, which are by far the most common kind of star in the galaxy. Because the interstellar medium itself can decelerate the sail, turning off the electron gun in deep space is essential. Careful maneuvering from star to star over millennia then allows relativistic speeds. From the paper:

…a series of repeated encounters with low-mass stars, and taking advantage of their winds, will enable the electric sail to achieve progressively higher speeds. We showed that sampling ∼ 10⁴ stars could enable electric sails to achieve relativistic speeds of ∼ 0.2 c and that this mechanism would require ∼ 1 Myr. While this constitutes a long timescale by human standards, it is not particularly long in comparison to many astronomical and geological timescales. The ensuing relativistic spacecraft would be well-suited for tackling interstellar and even intergalactic exploration.

This is an eye-opener. We can’t rule out the possibility that species capable of operating in this time frame might deploy electric sails, but the time involved precludes their use as the primary propulsion method for interstellar missions by us. The authors note as well that because an electric sail will have a low cross-sectional area, its presence would be all but undetectable, whereas a light sail driven by a laser would demand huge amounts of energy and would be theoretically detectable at interstellar distances. So for a civilization hoping to explore in ‘stealth’ mode, an electric sail would have its advantages. These are not good SETI targets.

Returning to M-dwarf stars, the authors show that if stars are small enough (less than about 0.2 solar masses), the pressure of the stellar wind dominates over photon pressure, Speeds in the range of 500 kilometers per second seem feasible for electric sails near late-type M-dwarfs. Indeed, for F-, G- and K-class stars, electric sails fare better as propulsion systems in the vicinity of the home star than light sails.

So we are looking at a technology that, if it can be properly engineered, could play a role in shaping an interplanetary infrastructure, while yielding to faster methods for missions to other stars, unless we humans somehow attain an all but geological patience.

The paper is Lingam and Loeb, “Electric sails are potentially more effective than light sails near most stars,” in process at Acta Astronautica (preprint). For Pekka Janhunen’s concept of the electric sail as a fast interplanetary probe, see Electric Sails: Fast Probe to Uranus.

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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.

• 

      The enormous disc of sail strained at its rigging, already filled with the wind that blew between the worlds. In three minutes the race would begin, yet now John Merton felt more relaxed, more at peace, than at any time for the past year. Whatever happened when the Commodore gave the starting signal, whether Diana carried him to victory or defeat, he had achieved his ambition. After a lifetime spent designing ships for others, now he would sail his own.
     Merton scarcely heard it. For the last time, he was checking the tension in the rigging. The needles of all the dynamometers were steady; the immense sail was taut, its mirror surface sparkling and glittering gloriously in the sun.
     To Merton, floating weightless at the periscope, it seemed to fill the sky. As well it might—for out there were fifty million square feet of sail, linked to his capsule by almost a hundred miles of rigging. All the canvas of all the tea clippers that had once raced like clouds across the China seas, sewn into one gigantic sheet, could not match the single sail that Diana had spread beneath the sun. Yet it was little more substantial than a soap bubble; that two square miles of aluminized plastic was only a few millionths of an inch thick.

     “T minus ten seconds. All recording cameras ON.”

     Something so huge, yet so frail, was hard for the mind to grasp. And it was harder still to realize that this fragile mirror could tow him free of Earth merely by the power of the sunlight it would trap.

     “… five, four, three, two, one, CUT!”

     Seven knife blades sliced through seven thin lines tethering the yachts to the mother ships that had assembled and serviced them. Until this moment, all had been circling Earth together in a rigidly held formation, but now the yachts would begin to disperse, like dandelion seeds drifting before the breeze. And the winner would be the one that first drifted past the Moon.
     Aboard Diana, nothing seemed to be happening. But Merton knew better. Though his body could feel no thrust, the instrument board told him that he was now accelerating at almost one thousandth of a gravity. For a rocket, that figure would have been ludicrous—but this was the first time any solar yacht had ever attained it. Diana’s design was sound; the vast sail was living up to his calculations. At this rate, two circuits of the Earth would build up his speed to escape velocity, and then he could head out for the Moon, with the full force of the Sun behind him.

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     The full force of the Sun … He smiled wryly, remembering all his attempts to explain solar sailing to those lecture audiences back on Earth. That had been the only way he could raise money, in those early days. He might be Chief Designer of Cosmodyne Corporation, with a whole string of successful spaceships to his credit, but his firm had not been exactly enthusiastic about his hobby.

     “Hold your hands out to the Sun,” he’d said. “What do you feel? Heat, of course. But there’s pressure as well—though you’ve never noticed it, because it’s so tiny. Over the area of your hands, it comes to only about a millionth of an ounce.
     “But out in space, even a pressure as small as that can be important, for it’s acting all the time, hour after hour, day after day. Unlike rocket fuel, it’s free and unlimited. If we want to, we can use it. We can build sails to catch the radiation blowing from the Sun.”
     At that point, he would pull out a few square yards of sail material and toss it toward the audience. The silvery film would coil and twist like smoke, then drift slowly to the ceiling in the hot-air currents.
     “You can see how light it is,” he’d continue. “A square mile weighs only a ton, and can collect five pounds of radiation pressure. So it will start moving—and we can let it tow us along, if we attach rigging to it.
     “Of course, its acceleration will be tiny—about a thousandth of a g. That doesn’t seem much, but let’s see what it means.
     “It means that in the first second, we’ll move about a fifth of an inch. I suppose a healthy snail could do better than that. But after a minute, we’ve covered sixty feet, and will be doing just over a mile an hour. That’s not bad, for something driven by pure sunlight! After an hour, we’re forty miles from our starting point, and will be moving at eighty miles an hour. Please remember that in space there’s no friction; so once you start anything moving, it will keep going forever. You’ll be surprised when I tell you what our thousandth-of-a-g sailboat will be doing at the end of a day’s run: almost two thousand miles an hour! If it starts from orbitas it has to, of course—it can reach escape velocity in a couple of days. And all without burning a single drop of fuel!”

     Well, he’d convinced them, and in the end he’d even convinced Cosmodyne. Over the last twenty years, a new sport had come into being. It had been called the sport of billionaires, and that was true. But it was beginning to pay for itself in terms of publicity and TV coverage. The prestige of four continents and two worlds was riding on this race, and it had the biggest audience in history.

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• 

     Diana had made a good start; time to take a look at the opposition. Moving very gently—though there were shock absorbers between the control capsule and the delicate rigging, he was determined to run no risks—Merton stationed himself at the periscope.

     There they were, looking like strange silver flowers planted in the dark fields of space. The nearest. South America’s Santa Maria, was only fifty miles away; it bore a close resemblance to a boy’s kite, but a kite more than a mile on a side. Farther away, the University of Astrograd’s Lebedev looked like a Maltese cross; the sails that formed the four arms could apparently be tilted for steering purposes. In contrast, the Federation of Australasia’s Woomera was a simple parachute, four miles in circumference. General Spacecraft’s Arachne, as its name suggested, looked like a spider web, and had been built on the same principles, by robot shuttles spiraling out from a central point. Eurospace Corporation’s Gossamer was an identical design, on a slightly smaller scale. And the Republic of Mars’s Sunbeam was a flat ring, with a half-mile-wide hole in the center, spinning slowly, so that centrifugal force gave it stiffness. That was an old idea, but no one had ever made it work; and Merton was fairly sure that the colonials would be in trouble when they started to turn.

     That would not be for another six hours, when the yachts had moved along the first quarter of their slow and stately twenty-four hour orbit. Here at the beginning of the race, they were all heading directly away from the Sun—running, as it were, before the solar wind. One had to make the most of this lap, before the boats swung around to the other side of Earth and then started to head back into the Sun.
     Time, Merton told himself, for the first check, while he had no navigational worries. With the periscope, he made a careful examination of the sail, concentrating on the points where the rigging was attached to it. The shroud lines—narrow bands of unsilvered plastic film—would have been completely invisible had they not been coated with fluorescent paint. Now they were taut lines of colored light, dwindling away for hundreds of yards toward that gigantic sail. Each had its own electric windlass, not much bigger than a game fisherman’s reel. The little windlasses were continually turning, playing lines in or out as the autopilot kept the sail trimmed at the correct angle to the Sun.
     The play of sunlight on the great flexible mirror was beautiful to watch. The sail was undulating in slow, stately oscillations, sending multiple images of the Sun marching across it, until they faded away at its edges. Such leisurely vibrations were to be expected in this vast and flimsy structure. They were usually quite harmless, but Merton watched them carefully. Sometimes they could build up to the catastrophic undulations known as the “wriggles,” which could tear a sail to pieces.

---

     It seemed a strange thing to do, what with the race having just started, but he thought it might be a good idea to get some sleep. The two-man crews on the other boats could take it in turns, but Merton had no one to relieve him. He must rely on his own physical resources, like that other solitary seaman, Joshua Slocum, in his tiny Spray. The American skipper had sailed Spray singlehanded around the world; he could never have dreamed that, two centuries later, a man would be sailing singlehanded from Earth to Moon—inspired, at least partly, by his example.
     Merton snapped the elastic bands of the cabin seat around his waist and legs, then placed the electrodes of the sleep-inducer on his forehead. He set the timer for three hours, and relaxed. Very gently, hypnotically, the electronic pulses throbbed in the frontal lobes of his brain. Colored spirals of light expanded beneath his closed eyelids, widening outward to infinity. Then nothing…

---

• 

     The brazen clamor of the alarm dragged him back from his dreamless sleep. He was instantly awake, his eyes scanning the instrument panel. Only two hours had passed—but above the accelerometer, a red light was flashing. Thrust was falling; Diana was losing power.
     Merton’s first thought was that something had happened to the sail; perhaps the antispin devices had failed, and the rigging had become twisted. Swiftly, he checked the meters that showed the tension of the shroud lines. Strange — on one side of the sail they were reading normally, but on the other the pull was dropping slowly, even as he watched.

     In sudden understanding, Merton grabbed the periscope, switched to wide-angle vision, and started to scan the edge of the sail. Yes—there was the trouble, and it could have only one cause. A huge, sharp-edged shadow had begun to slide across the gleaming silver of the sail. Darkness was falling upon Diana, as if a cloud had passed between her and the Sun. And in the dark, robbed of the rays that drove her, she would lose all thrust and drift helplessly through space.
     But, of course, there were no clouds here, more than twenty thousand miles above the Earth. If there was a shadow, it must be made by man.
     Merton grinned as he swung the periscope toward the Sun, switching in the filters that would allow him to look full into its blazing face without being blinded.
     “Maneuver 4a,” he muttered to himself. “We’ll see who can play best at that game.”
     It looked as if a giant planet was crossing the face of the Sun; a great black disc had bitten deep into its edge. Twenty miles astern, Gossamer was trying to arrange an artificial eclipse, specially for Diana’s benefit.
     The maneuver was a perfectly legitimate one. Back in the days of ocean racing, skippers had often tried to rob each other of the wind. With any luck, you could leave your rival becalmed, with his sails collapsing around him—and be well ahead before he could undo the damage.

     Merton had no intention of being caught so easily. There was plenty of time to take evasive action; things happened very slowly when you were running a solar sailboat. It would be at least twenty minutes before Gossamer could slide completely across the face of the Sun, and leave him in darkness.
     Diana’s tiny computer—the size of a matchbox, but the equivalent of a thousand human mathematicians—considered the problem for a full second and then flashed the answer. He’d have to open control panels three and four, until the sail had developed an extra twenty degrees of tilt; then the radiation pressure would blow him out of Gossamer’s dangerous shadow, back into the full blast of the Sun. It was a pity to interfere with the autopilot, which had been carefully programed to give the fastest possible run—but that, after all, was why he was here. This was what made solar yachting a sport, rather than a battle between computers.
     Out went control lines one and six, slowly undulating like sleepy snakes as they momentarily lost their tension. Two miles away, the triangular panels began to open lazily, spilling sunlight through the sail. Yet, for a long time, nothing seemed to happen. It was hard to grow accustomed to this slow-motion world, where it took minutes for the effects of any action to become visible to the eye. Then Merton saw that the sail was indeed tipping toward the Sun —and that Gossamer’s shadow was sliding harmlessly away, its cone of darkness lost in the deeper night of space.
     Long before the shadow had vanished, and the disc of the Sun had cleared again, he reversed the tilt and brought Diana back on course. Her new momentum would carry her clear of the danger; no need to overdo it, and upset his calculations by side-stepping too far. That was another rule that was hard to leam: the very moment you had started something happening in space, it was already time to think about stopping it.

---

     “Hello, Dr. Merton,” said the commentator immediately.
     “Glad you can spare a few minutes. And congratulations—you seem to be ahead of the field.”
     “Too early in the game to be sure of that,” Merton answered cautiously.
     “Tell me, Doctor, why did you decide to sail Diana by yourself? Just because it’s never been done before?”
     “Well, isn’t that a good reason? But it wasn’t the only one, of course.” He paused, choosing his words carefully. “You know how critically the performance of a sun yacht depends on its mass. A second man, with all his supplies, would mean another five hundred pounds. That could easily be the difference between winning and losing.”
     “And you’re quite certain that you can handle Diana alone?”
     “Reasonably sure, thanks to the automatic controls I’ve designed. My main job is to supervise and make decisions.”
     “But—two square miles of sail! It just doesn’t seem possible for one man to cope with all that.”
     Merton laughed. “Why not? Those two square miles produce a maximum pull of just ten pounds. I can exert more force with my little finger.”
     “Well, thank you, Doctor. And good luck. I’ll be calling you again.”

---

     This was his last chance to try for individual achievement, and he would share it with no one. There would be no more solar yachting for at least five years, as the period of the Quiet Sun ended and the cycle of bad weather began, with radiation storms bursting through the solar system. When it was safe again for these frail, unshielded craft to venture aloft, he would be too old. If, indeed, he was not too old already…

---

     The light was fading; a purple, twilight hue—the glow of many sunsets, thousands of miles below—was falling across the sail as Diana slipped silently into the shadow of Earth. The Sun plummeted below that invisible horizon; within minutes, it was night.
     Merton looked back along the orbit he had traced, now a quarter of the way around the world. One by one he saw the brilliant stars of the other yachts wink out, as they joined him in the brief night. It would be an hour before the Sun emerged from that enormous black shield, and through all that time they would be completely helpless, coasting without power.

• 

     He switched on the external spotlight, and started to search the now-darkened sail with its beam. Already the thousands of acres of film were beginning to wrinkle and become flaccid. The shroud lines were slackening, and must be wound in lest they become entangled. But all this was expected; everything was going as planned.
     For the next hour, Merton’s own sail kept him too busy to worry about Arachne and Santa Maria. It was hard to keep a good watch on that fifty million square feet of dim plastic out there in the darkness, illuminated only by his narrow spotlight and the rays of the still-distant Moon. From now on, for almost half his orbit around the Earth, he must keep the whole of this immense area edge-on to the Sun. During the next twelve or fourteen hours, the sail would be a useless encumbrance; for he would be heading into the Sun, and its rays could only drive him backward along his orbit. It was a pity that he could not furl the sail completely, until he was ready to use it again; but no one had yet found a practical way of doing this.

     Dawn flashed like an explosion along the rim of Earth as the Sun rose out of the Pacific. The sail and shroud lines glowed a brief crimson, then gold, then blazed with the pure white light of day. The needles of the dynamometers began to lift from their zeroes—but only just. Diana was still almost completely weightless, for with the sail pointing (edge-on) toward the Sun, her acceleration was now only a few millionths of a gravity.
     The next twelve hours were uneventful, as the Earth waxed in the sky from new to full. There was little to do while the fleet drifted around the unpowered half of its orbit, but Merton did not find the time hanging heavily on his hands.

     The next casualty came when they were passing the line between Earth and Sun, and were just beginning the powered half of the orbit. Aboard Diana, Merton saw the great sail stiffen as it tilted to catch the rays that drove it. The acceleration began to climb up from the microgravities, though it would be hours yet before it would reach its maximum value.
     It would never reach it for Gossamer. The moment when power came on again was always critical, and she failed to survive it.

     Blair’s radio commentary, which Merton had left running at low volume, alerted him with the news: “Hello, Gossamer has the wriggles!” He hurried to the periscope, but at first could see nothing wrong with the great circular disc of Gossamer’s, sail. It was difficult to study it because it was almost edge-on to him and so appeared as a thin ellipse; but presently he saw that it was twisting back and forth in slow, irresistible oscillations. Unless the crew could damp out these waves, by properly timed but gentle tugs on the shroud lines, the sail would tear itself to pieces.
     They did their best, and after twenty minutes it seemed that they had succeeded. Then, somewhere near the center of the sail, the plastic film began to rip. It was slowly driven outward by the radiation pressure, like smoke coiling upward from a fire. Within a quarter of an hour, nothing was left but the delicate tracery of the radial spars that had supported the great web. Once again there was a flare of rockets, as a launch moved in to retrieve the Gossamer’s capsule and her dejected crew.

     He knew the Russian pilots and designers. They had been trying to win this race for twenty years—and, after all, it was only fair that they should, for had not Pyotr Nikolaevich Lebedev been the first man to detect the pressure of sunlight, back at the very beginning of the twentieth century? But they had never succeeded. And they would never stop trying. Dimitri was up to something — and it would be spectacular.
     John Merton brought Diana around the Earth for the second time. If all went well, this would be the last circuit, both for him and for the Russians. They had spiraled upward by thousands of miles, gaining energy from the Sun’s rays. On this lap, they should escape from Earth completely, and head outward on the long run to the Moon. It was a straight race now; Sunbeam’s crew had finally withdrawn exhausted, after battling valiantly with their spinning sail for more than a hundred thousand miles.
     Merton did not feel tired; he had eaten and slept well, and Diana was behaving herself admirably. The autopilot, tensioning the rigging like a busy little spider, kept the great sail trimmed to the Sun more accurately than any human skipper could have. Though by this time the two square miles of plastic sheet must have been riddled by hundreds of micrometeorites, the pinheadsized punctures had produced no falling off of thrust.
     He had only two worries. The first was shroud line number eight, which could no longer be adjusted properly. Without any warning, the reel had jammed; even after all these years of astronautical engineering, bearings sometimes seized up in vacuum. He could neither lengthen nor shorten the line, and would have to navigate as best he could with the others. Luckily, the most difficult maneuvers were over; from now on, Diana would have the Sun behind her as she sailed straight down the solar wind. And as the old-time sailors had often said, it was easy to handle a boat when the wind was blowing over your shoulder.
     His other worry was Lebedev, still dogging his heels three hundred miles astern. The Russian yacht had shown remarkable maneuverability, thanks to the four great panels that could be tilted around the central sail. Her flipovers as she rounded the Earth had been carried out with superb precision. But to gain maneuverability she must have sacrificed speed. You could not have it both ways; in the long, straight haul ahead, Merton should be able to hold his own. Yet he could not be certain of victory until, three or four days from now, Diana went flashing past the far side of the Moon.

     And then, in the fiftieth hour of the race, just after the end of the second orbit around Earth, Markoff sprang his little surprise.
     “Hello, John,” he said casually over the ship-to-ship circuit. “I’d like you to watch this. It should be interesting.”
     Merton drew himself across to the periscope and turned up the magnification to the limit. There in the field of view, a most improbable sight against the background of the stars, was the glittering Maltese cross of Lebedev’, very small but very clear. As he watched, the four arms of the cross slowly detached themselves from the central square, and went drifting away, with all their spars and rigging, into space.
     Markoff had jettisoned all unnecessary mass, now that he was coming up to escape velocity and need no longer plod patiently around the Earth, gaining momentum on each circuit. From now on, Lebedev would be almost unsteerable—but that did not matter; all the tricky navigation lay behind her. It was as if an old-time yachtsman had deliberately thrown away his rudder and heavy keel, knowing that the rest of the race would be straight downwind over a calm sea.
     Merton did not answer; he was too busy doing some hurried calculations, based on what he knew of Lebedev’s design. By the time he had finished, he knew that the race was still in doubt. Lebedev would be catching up with him at just about the time he hoped to pass the Moon.

• 

Suppose I told you that a device you could make yourself would be a more energy efficient space drive than an ion engine with a far better thrust to weight ratio? Fantasy? No!

Such a drive exists. Called the plasma magnet, it is a development of the magnetic sail but with orders of magnitude less mass and a performance that offers, with constant supplied power, constant acceleration regardless of its distance from the sun.

At the recent Tennessee Valley Interstellar Workshop (TVIW), Jeff Greason presented this technology in his talk [1]. What caught my attention was the simplicity of this technology for propulsion, with a performance that exceeded more complex low thrust systems like ion engines and solar sails.

What is a plasma magnet?

The plasma magnet is a type of magsail that creates a kilometers wide, artificial magnetosphere that deflects the charged solar wind to provide thrust.

Unlike a classic magsail [9] (figure 1) that generates the magnetic field with a large diameter electrical circuit, the plasma magnet replaces the circular superconducting coil by inducing the current flow with the charged particles of the solar wind. It is an upgraded development of Robert Winglee’s Mini-Magnetospheric Plasma Propulsion (M2P2) [7, 8], a drive that required injection of charged particles to generate the magnetosphere. The plasma magnet requires no such injection of particles and is therefore potentially propellantless.

• 

Developed by John Slough and others [5, 6], the plasma magnet drive has been validated by experimental results in a vacuum chamber and was a NIAC phase 1 project in the mid-2000s [6]. The drive works by initially creating a rotating magnetic field that in turns traps and entrains the charged solar wind to create a large diameter ring current, inducing a large scale magnetosphere. The drive coils of the reference design are small, about 10 centimeters in diameter. With 10 kW of electric power, the magnetosphere expands to about 30 kilometers in diameter at 1 AU, with enough magnetic force to deflect the solar wind pressure of about 1 nPa (1 nN/m²) which produces a thrust in the direction of the wind of about 1 newton (1N). Thrust is transmitted to the device by the magnetic fields, just as with the coupling of rotation in an electric motor (figure 2).

For a fixed system, the size of the induced magnetosphere depends on the local solar wind pressure. The magnetosphere expands in size as the solar wind density decreases further from the sun. This is similar to the effect of Janhunen’s electric sail [2] where the deflection area around the charged conducting wires increases as the solar wind density decreases. The plasma magnet’s thrust is the force of the solar wind pushing against the magnetosphere as it is deflected around it. It functions like a square-rigged sail running before the wind.

• 

The engine is little more than 2 pairs of charged rotating coils and is therefore extremely simple and inexpensive. The mass of the reference engine is about 10 kg. Table 1 shows that the plasma magnet has an order higher thrust to weight ratio than an ion engine and 2 orders better than a solar sail. However, as the plasma magnet requires a power source, like the ion engine, the comparison to the solar sail should be made when the power supply is added, reducing is performance to a 10-fold improvement. [ A solar PV array of contemporary technology requires about 10 kg/kW, so the appropriate thrust/mass ratio of the plasma magnet is about 1 order of magnitude better than a solar sail at 1 AU]

The plasma magnet drive offers a “ridiculously high” thrust to weight ratio

The plasma magnet, as a space drive, has much better thrust to weight ratio than even the new X-3 Hall Effect ion engine currently in development. This ratio remains high when the power supply from solar array is added. Of more importance is that the plasma magnet is theoretically propellantless, providing thrust as long as the solar wind is flowing past the craft and power is supplied.

Name	Type	Thrust/weight (N/kg) Engine mass only	Thrust/weight (N/kg) with power supply
SSME	Chemical	717	N/A
RD-180	Chemical	769	N/A
plasma magnetosphere	Electro-magnetic	0.1	.01
NSTAR-1	Ion (Gridded)	0.004	0.002
X-3	Ion (Hall Effect)	0.02	0.004
Solar Sail	Photon Sail	0.001 (at 1 AU)	N/A

Table 1. Comparison of thrust to mass ratios of various types of propulsion systems. The power supply is assumed to be solar array with a 10 kg/kW performance.

The downside with the plasma magnet is that it can only produce thrust in the direction of the solar wind, away from the sun, and therefore can only climb up the gravity well. Unlike other propulsion systems, there is little capability to sail against the sun. While solar sails can tack by directing thrust against the orbital direction, allowing a return trajectory, this is not possible with the basic plasma magnet, requiring other propulsion systems for return trips.

Plasma magnet applications

1. Propulsion Assist

The most obvious use of the plasma magnet that can only be used to spiral out from the sun is as a propellantless assist. The drive is lightweight and inexpensive, and because it is propellantless, it can make a useful drive for small space probes. Because the drive creates a kilometers sized magnetosphere, scaling up the thrust involves increased power or using multiple drives that would need to be kept 10s of kilometers apart. Figure 3 shows a hypothetical gridded array. Alternatively, the plasma magnets might be separated by thrusters and individually attached to the payload by tethers.

• 

For a mixed mode mission, the plasma magnet engine is turned on for the outward bound flight, with or without the main propulsion system turned on. The use of power to generate thrust without propellant improves the performance of propellant propulsion systems where the accumulated velocity exceeds the performance cost of the power supply mass or reduced propellant. For an ion engine as the main drive, the plasma magnet would use the same power as 4 NSTAR ion engines but provide 3x the thrust.

2. Moving Asteroids for Planetary Defense

The propellantless nature of the plasma magnet drive makes it very suitable for pushing asteroids for planetary defense. Once turned on, the drive provides steady thrust to the asteroid, propelling it away from the sun and raising its orbit. Because the drive does not need to be facing any particular direction, it can be attached to a tumbling asteroid without any impact on the thrust direction.

3. Charged particle radiation shield for crewed flights

The magnetosphere generated by the engine makes a good radiation shield for the charged particles of the solar wind. It should prove to be a good solution for the solar wind, solar flares and even coronal mass ejections (CME). This device could, therefore, be used for human flight to reduce radiation effects. For human crewed flights, the 1N of thrust is insufficient for the size of the spacecraft and would have a marginal propulsion compared to the main engines. Given the plasma magnet’s small size and mass, and relatively low power requirements, the device provides a cost-effective means to protect the crew without resorting to large masses of physical shielding. The plasma magnet would appear to be only effective for the charged solar wind, leaving the neutral GCRs to enter the craft. However, when an auxiliary device is used in the mode of aerobraking, the charge exchange mechanism should reduce the galactic cosmic ray (GCR) penetration (see item 8 below).

4. Asteroid mining

The plasma magnet thruster might be a very useful part of a hybrid solution for automated mining craft. The hybrid propulsion would ally the plasma magnet thruster with a propellant system, such as a chemical or ion engine. The outward bound trip would use the plasma magnet thruster to reach the target asteroid. The propellant tanks would be empty saving mass and therefore improving performance. The propellant tanks would be filled with the appropriate resource, e.g. water for an electrothermal engine, or for a L2/O2 chemical engine. This engine would be turned on for the return trip towards the inner system. The reverse would be used for outward bound trips to the inner system

5. Interstellar precursor using nuclear power

A key feature of the plasma magnet is that the diameter of the magnetosphere increases as the density of the solar wind decreases as it expands away from the sun. The resulting expansion exactly matches the decrease in density, ensuring constant thrust. Therefore the plasma magnet has a constant acceleration irrespective of its position in the solar system.

As the solar wind operates out to the heliopause, about 80 AU from the sun, the acceleration from a nuclear powered craft is constant and the craft continues to accelerate without the tyranny of the rocket equation. Assuming a craft with an all up mass of 1 MT (700 kg nuclear power unit, 10 kg engine, and the remaining in payload), the terminal velocity at the heliopause is 150 km/s. The flight time is 4.75 years, which is a considerably faster flight time than the New Horizons and Voyager probes.

Slough assumed a solar array power supply, functional out to the orbit of Jupiter at 5 AU. This limited the velocity of the drive, although the electrical power output of a solar array at 1 AU is about 10-fold better than a nuclear power source, but rapidly decreases with distance from the sun. Assuming a 10 kW PV array, generating decreasing power out to Jupiter, the final velocity of the 1 MT craft is somewhere between 5 and 10 km/s, but with a much larger payload.

In his TVIW talk [1], Greason suggested that the 10kW power supply could propel a 2500 kg craft with an acceleration of 0.5g, reaching 400-700 km/s in just half a day. Greason [i] suggested that with this acceleration, the FOCAL mission for gravitational lens telescopes requiring many craft should be achievable. *

6. Mars Cycler

Greason suggested that the plasma magnet might well be useful for a Mars cycler, as the small delta v impulse needed for each trip could be easily met.[1]

7. Deceleration at target star for interstellar flight

For interstellar flights, deploying the plasma magnet as the craft approaches the target star should be enough to decelerate the craft to allow loitering in the system, rather than a fast flyby. Again, the high performance and modest mass and power requirements might make this a good way to decelerate a fast interstellar craft, like a laser propelled photon sail.[1]

8. Magnetoshell Aerocapture (MAC)

While the studies on the plasma magnet seemed to have stalled by the late 2000s, a very similar technology development was gaining attention. A simple dipole magnet magnetosphere can be used as a very effective aerocapture shield. The shield is just the plasma magnet with coils that do not rotate, creating a magnetosphere of a diameter in meters, one that requires the injection of gram quantities of plasma to be trapped in the magnetic field. As the magnetosphere impacts the atmosphere, the neutral atmosphere molecules are trapped by charge exchange. The stopping power is on the order of kilonewtons, allowing the craft to achieve orbit and even land without a heavy, physical shield. The saving in mass and hence propellant is enormous. Such aerobraking allows larger payloads, or alternatively faster transit times. Because the magnetoshell is immaterial, heat transmission to the shield is not an issue. The mass saving is considerable and offers a very cost-effective approach for any craft to reduce mass, propellant requirements or increase payloads. This approach is suitable for Earth return, Mars, outer planets, and Venus capture. Conceivably aerocapture might be possible with Pluto.

• 

Making the plasma magnet thrust directional

A single magnetosphere cannot deflect the solar wind in any significant directional way, which limits this drive’s navigational capability. However, if the magnetosphere could be shaped so that its surface could result in an asymmetric deflection, it should be possible to use the drive for tacking back to the inner system.

Figure 5 shows an array of plasma magnets orientated at an angle to the solar wind. The deflection of the solar wind is no longer symmetric, with the main flow across the forward face of the array. Under those conditions, there should be a net force against the grid. This suggests that like a solar sail, orientating the grid so that the force retards the orbital velocity, the craft should be able to spiral down towards the Sun, offering the possibility of a drive that could navigate the solar system.

• 

Pushing the Boundaries

The size of the magnetic sail can be increased with higher power inputs, or increasing the antenna size. Optimization will depend on the size of the craft and the mass of the antenna. Truly powerful drives can be considered. Greason [12] has calculated that a 2 MT craft, using a superconducting antenna with a radius of 30 meters, fed with a peak current of 90 kA, would have a useful sail with a radius of 1130 km and an acceleration of 2 m/s², or about 0.2g. As the sail has a maximum velocity of that of the solar wind, a probe accelerating at 0.2g would reach maximum velocity in a few days, and pass by Mars within a week. To reach a velocity of 20 km/s, faster than New Horizons, the Plasma magnet would only need to be turned on for a few hours. Clearly, the scope for using this drive to accelerate probes and even crewed ships is quite exciting.

Coupling a more modest velocity of just 10’s of km/s with the function of a MAC, a craft could reach Mars in less than 2 months and aerobrake to reach orbit and even descend to the surface. All this without propellant and a very modest solar array for a power supply.

An Asteroid, a tether and a Round Trip Flight

As we’ve seen, the plasma magnet can only propel a craft downwind from the Sun. So far I have postulated that aerobraking and conventional drives would be needed for return flights. One outlandish possibility for use in asteroid mining might be the use of a tether to redirect the craft. On the outward bound flight, the craft driven by the plasma magnet makes a rapid approach to the target asteroid which is being mined. The mined resources are attached to a tether that is anchored to the asteroid. As the craft approaches, it captures the end of the tether to acquire the new payload, and is swung around the asteroid. On the opposite side of the asteroid, the tether is released and the craft is now traveling back towards the Sun. No propellant needed, although the tether might cause some consternation as it wraps itself around the asteroid.

Conclusion

The plasma magnet as a propulsion device, and the same hardware applied for aerocapture, would drastically reduce the costs and propellant requirements for a variety of missions. Coupled with another drive such as an ion engine, a craft could reach a target body with an atmosphere and be injected into orbit with almost no propellant mass. The return journey would require an engine delivering just enough delta V to escape that body and return to Earth, where aerocapture again would allow injection into Earth orbit with no extra propellant. If direction deflection can be achieved, then the plasma magnet might be used to navigate the Solar System more like a solar sail, but with a far higher performance, and far easier deployment.

Using a steady, nuclear power or beamed power source, such a craft could accelerate to the heliopause, allowing interstellar precursor missions, such as Kuiper belt exploration and the FOCAL mission within a short time frame.

The technology of the plasma magnet combined with a MAC could be used to decelerate a slowish interstellar ship and allow it to achieve orbit and even land on a promising exoplanet.

The size of the magnetic sail can be extended with few constraints, allowing for considerably increased thrust that can be applied to robotic probes and crewed spacecraft. For crewed craft, the magnetosphere also provides protection from the particle radiation from the sun, and possibly galactic cosmic rays.

Given the potential of this drive and relatively trivial cost, it seems that testing such a device in space should perhaps be attempted. Can a NewSpace billionaire be enticed?

* These numbers are far higher than those provided by Winglee and Slough in their papers and so I have used their much more conservative values for all my calculations.

References

Greason, Jeff “Missions Enabled by plasma magnet Sails”, Presentation at the Tennessee Valley Interstellar Workshop, 2017. https://www.youtube.com/watch?v=0vVOtrAnIxM

Janhunen, P., The electric sail – a new propulsion method which may enable fast missions to the outer solar system, J. British Interpl. Soc., 61, 8, 322-325, 2008.

Kelly, Charles and Shimazu, Akihisa “Revolutionizing Orbit Insertion with Active Magnetoshell Aerocapture,” University of Washington, Seattle, WA, 98195, USA.

Kirtley, David, Slough, John, and Pancotti, Anthony “Magnetoshells Plasma Aerocapture for Manned Missions and Planetary Deep Space Orbiters”, NIAC Spring Symposium, Chicago, Il., March 12, 2013

Slough, John. “The plasma magnet for Sailing the Solar Wind.” AIP Conference Proceedings, 2005, doi:10.1063/1.1867244.

Slough, John “The plasma magnet” (2006). NASA Institute for Advanced Concepts Phase 1 Final Report.

Winglee, Robert. “Mini-Magnetospheric Plasma Propulsion (M2P2): High Speed Propulsion Sailing the Solar Wind.” AIP Conference Proceedings, 2000, doi:10.1063/1.1290892.

Winglee, R. M., et al. “Mini-Magnetospheric Plasma Propulsion: Tapping the Energy of the Solar Wind for Spacecraft Propulsion.” Journal of Geophysical Research: Space Physics, vol. 105, no. A9, Jan. 2000, pp. 21067–21077., doi:10.1029/1999ja000334.

Zubrin, Robert, and Dana Andrews. “Magnetic Sails and Interplanetary Travel.” 25th Joint Propulsion Conference, Dec. 1989, doi:10.2514/6.1989-2441.

Greason, Jeff. Personal communication.

• 

This strange web of struts and superconducting cables is a plasma magnet, with its field acting as a million km drag device against the solar wind. In a combat context, it can shed hundreds of km/s of velocity in weeks to months — very useful for recovering a ship after battle.

Using drag devices introduces terrain concerns. The solar wind moves away from the star at hundreds of km/s, so the device works until you're moving with it. If you fly away from the star at a similar velocity, it won't do much anything. This makes approaching from the antisolar direction preferable, giving a kind of high ground because then you have more delta-v to spare given you can use the drag device to recover the ship afterwards.

I still only have a cursory understanding of this stuff. Thanks to @JeffGreason (Jeffrey K. Greason) for taking the time to explain it to me. Military stuff aside, there are all kinds of solar wind tricks you can pull for general traveling purposes too.

The interstellar probe coasted at 4% c after her fusion drive first stage was spent. It massed 50,000 kg, mostly propellant water ice stored as a conical shield ahead of the probe that did double duty as a particle shield. The probe extended a spine, several hundred kilometers in length behind the shield. Then the plasma magnet sails at each end started to cycle, using just the power from a small nuclear generator. The magsails captured and extracted power from the ISM streaming by. This powered the ionization and ejection of the propellant. Ejected at the streaming velocity of the ISM, the probe steadily increased in velocity, eventually reaching 20% c after exhausting 48,000 kg of propellant. The probe, targeted at Proxima Centauri, would reach its destination in less than 20 years. It wouldn’t be the first to reach that system, the Breakthrough microsails had done that decades earlier, but this probe was the first with the scientific payload to make a real survey of the system and collect data from its habitable world.

(sound of a needle skidding across a vinyl record). Wait, what? How can a ship accelerate to 20% c without expending massive amounts of power from an onboard power plant, or an intense external power beam from the solar system?

In a previous article, I explained the plasma magnet drive, a magsail technology that did not require a large physical sail structure, but rather a compact electromechanical engine whose magnetic sail size was dependent on the power and the surrounding medium’s plasma density.

Like other magsail and electric sail designs, the plasma magnet could only run before the solar wind, making only outward bound trips and a velocity limited by the wind speed. This inherently limited the missions that a magsail could perform compared to a photon sail. Where it excelled was the thrust was not dependent on the distance from the sun that severely limits solar sail thrust, and therefore this made the plasma magnet sail particularly suited to missions to the outer planets and beyond.

Jeff Greason has since considered how the plasma magnet could be decelerated to allow the spacecraft to orbit a target in the outer system. Following the classic formulations of Fritz Zwicky, Greason considered whether the spacecraft could use onboard mass but external energy to achieve this goal. This external energy was to be extracted from the external medium, not solar or beamed energy, allowing it to operate anywhere where there was a medium moving relative to the vehicle.

The approach to achieve this was to use the momentum and energy of a plasma stream flowing past the ship and using that energy to transfer momentum to an onboard propellant to drive the ship. That plasma stream would be the solar wind inside the solar system (or another star system), and an ionized interstellar medium once beyond the heliosphere.

Counterintuitively, such a propulsion system can work in principle. By ejecting the reaction mass, the ship’s kinetic energy energy is maintained by a smaller mass, and therefore increases its velocity. There is no change in the ship’s kinetic energy, just an adjustment of the ship’s mass and velocity to keep the energy constant.

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Box 1 shows that net momentum (and force) can be attained when the energy of the drag medium and propellant thrust are equal. However this simple momentum exchange would not be feasible as a drive as the ejection mass would have to be greater than the intercepted medium resulting in very high mass ratios. In contrast, the Q-Drive, achieves a net thrust with a propellant mass flow far less than the medium passing by the craft, resulting in a low mass ratio yet high performance in terms of velocity increase.

Figure 1 shows the principle of the Q-Drive using a simple terrestrial vehicle analogy. Wind blowing through a turbine generates energy that is then used to eject onboard propellant. If the energy extracted from the wind is used to eject the propellant, in principle the onboard propellant mass flow can be lower than the mass of air passing through the turbine. The propellant’s exhaust velocity is matched to that of the wind, and under these conditions, the thrust can be greater than the drag, allowing the vehicle to move forward into the wind.

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Box 2 below shows the basic equations for the Q-Drive.

Let me draw your attention to equations 1 & 2, the drag and thrust forces. The drag force is dependent on the velocity of the wind or the ship moving through the wind which affects the mass flow of the medium. However, it is the change in velocity of the medium as it passes through the energy harvesting mechanism rather than the wind velocity itself that completes this equation. Compare that to the thrust from the propellant where the mass flow is dependent on the square of the exhaust velocity. When the velocity of the ship and the exhaust are equal, the ratio of the mass flows is dependent on the ratio of the change in velocity (delta V) of the medium and the exhaust velocity. The lower the delta V of the medium as the energy is extracted from it, the lower the mass flow of the propellant. As long as the delta V of the medium is greater than zero, as the delta V approaches zero, the mass of the stream of medium is greater than the mass flow of the propellant. Conversely, as the delta V approaches the velocity of the medium, i.e. slowing it to a dead stop relative to the ship, the closer the medium and exhaust mass flows become.

Equations 3 and 7 are for the power delivered by the medium and the propellant thrust. As the power needed for generating the thrust cannot be higher than than delivered by the medium, at 100% conversion the power of each must be equal. As can be seen, the power generated by the energy harvesting is the drag force multiplied by the speed of the medium. However, the power to generate the thrust is ½ the force of the thrust multiplied by the exhaust velocity, which is the same as the velocity of the medium. Therefore the thrust is twice that of the drag force and therefore a net thrust equal to the drag force is achieved [equation 9]. [Because the sail area must be very large to capture the thin solar wind and the even more rarified ISM, the drag force on the ship itself can be discounted.]

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Because the power delivered from the external medium increases as the ship increases in velocity, so does the delivered power, which in turn is used to increase the exhaust velocity to match. This is very different from our normal expectations of powering vehicles. Because of this, the Q-Drive can continue to accelerate a ship for as long as it can continue to exhaust propellant.

Figure 2 shows the final velocity versus the ship’s mass ratio performance of the Q-Drive compared to a rocket with a fixed exhaust velocity, and the rocket equation using a variable exhaust but with the thrust reduced by 50% to match the Q-drive net thrust equaling 50% of the propellant thrust. With a mass ratio below 10, a rocket with an exhaust equal to the absolute wind velocity would marginally outperform the Q-drive, although it would need its own power source to run, such as a solar array or nuclear reactor. Beyond that, the Q-drive rapidly outperforms the rocket. This is primarily because as the vehicle accelerates, the increased power harvested from the wind is used to commensurately increase the exhaust velocity. If a rocket could do this, for example like the VASIMR drive, the performance curve is the same. However, the Q-drive does not need a huge power supply to work, and therefore offers a potential for very high velocity without needing a matching power supply.

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Equation A16 [1] and Box 3 equation 1 show that the Q-Drive has a velocity multiplier that is the square root of the mass ratio. This is highly favorable compared to the rocket equation. The equations 2 and 3 in Box 3 show that the required propellant and hence mass ratio is reduced the less the medium velocity is reduced to extract power. However, reducing the delta V of the medium also reduced the acceleration of the craft. This implies that the design of the ship will be dependent on mission requirements rather than some fixed optimization.

BOX 3 Implications of equations

1. The Q-Drive multiplies its velocity by the square root of the mass ratio

VelocityMultiplier = V_final / V_start = √(MassInitial / MassFinal) = √(MassRatio)

2. The ratio of medium mass to propellant mass is a function of how much the medium velocity is reduced to extract power

MassMedium / MassPropellant = Vmedium / (2 ⋅ ΔVmedium)

3. For any given velocity and sail area, the acceleration is a function of how much the medium velocity is reduced to extract power

a = func(ΔVmedium

See JBIS paper [1] for details

Box 4 provides some illustrative values for the size of the mag sails in the solar system for the Q-Drive and the expected performance for a 1 tonne craft. While the magnetic sail radii are large, they are achievable and allow for relatively high acceleration. As explained in [4], the plasma magnet sails increase in size as the medium density decreases, maintaining the forces on the sail. Once in interstellar space, the ISM is yet more rarefied and the sails have to commensurately expand.

BOX 4 Velocity increase and mass ratios

To provide some sense of the performance of a Q-Drive spacecraft in the solar system, the following is illustative.

At 1 AU, the solar wind has a pressure of 1E-9 Nm^-2.

For a spacecraft payload of 1,000 kg and an unspecified mass ratio, the radius of the plasma magnetic field with a drag coefficient of 2.0 would be about 180 × √MassRatio kilometer to accelerate the spacecraft at 1/10th g.

The radius would be about 55 × √MassRatio kilometer to accelerate the spacecraft at 1/100th g.

How might the plasma medium’s energy be harvested?

The wind turbine shown in figure 1 is replaced by an arrangement of the plasma magnet sails. To harvest the energy of the medium, it is useful to conceptualize the plasma magnet sail as a parachute that slows the wind to run a generator. At the end of this power stroke, the parachute is collapsed and rewound to the starting point to start the next power cycle. This is illustrated in figure 3. A ship would have 2 plasma magnet sails that cycle their magnetic fields at each end of a long spine that is aligned with the wind direction to mimic this mechanism. The harvested energy is then used to eject propellant so that the propellant exhaust velocity is optimally the same as the medium wind speed. By balancing the captured power with that needed to eject propellant, the ship needs no dedicated onboard power beyond that for maintenance of other systems, for example, powering the magnetic sails.

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Within the solar system, the Q-Drive could therefore push a ship towards the sun into the solar wind, as well as away from the sun with the solar wind at its back. Ejecting propellant ahead of the ship on an outward bound journey would allow the ship to decelerate. Ejecting the propellant ahead of the ship as it faced the solar wind would allow the ship to fall towards the sun. In both cases, the maximum velocity is about the 400 km/s of the peak density velocity of the solar wind.

Can the drive achieve velocities greater than the solar wind?

With pure drag sails, whether photon or magnetic, the maximum velocity is the same as the medium pushing on the sail. For a magnetic sail, this is the bulk velocity of the solar wind, about 400 km/s at the sun’s equator, and 700 km/s at the sun’s poles.

Unlike drag sails, the Q-Drive can achieve velocities greater than the medium, e.g. the solar wind. As long as the wind is flowing into the bow of the ship, the ship can accelerate indefinitely until the propellant is exhausted. The limitation is that this can only happen while the ship is facing into the wind (or the wind vector has a forward facing component). In the solar system, this requires that there is sufficient distance to allow the ship to accelerate until its velocity is higher than the solar wind before it flies past the sun. Once past perihelion, the ship is now running into the solar wind from behind, and can therefore keep accelerating.

What performance might be achievable?

To indicate the possible performance of the Q-drive in the solar system, 2 missions are explored, both requiring powered flight into the solar wind.

Two Solar System Missions

1. Mercury Rendezvous

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To reach Mercury quickly requires the probe to reduce its orbital speed around the sun to drop down to Mercury’s orbit and then reduce velocity further to allow orbital insertion. The Q-Drive ship points its bow towards the sun, and ejects propellant off-axis. This quickly pushed the probe into a fast trajectory towards the sun. Further propellant ejection is required to prevent the probe from a fast return trajectory and to remain in Mercury’s sun orbital path. From there a mix of propellant ejection and simple drag alone can be used to place the probe in orbit around Mercury. Flight time is of the order of 55 days. Figure 4 illustrates the maneuver.

2. Sundiver with Triton Flyby

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The recent Centauri Dreams post on a proposed flyby mission to Triton indicated a flight time of 12 years using gravity assists from Earth, Venus, and Jupiter. The Q-Drive could reduce most of that flight time using a sundiver approach. Figure 5 shows the possible flight path. The Q-Drive powers towards the sun against the solar wind. It must have a high enough acceleration to ensure that at perihelion it is now traveling faster than the solar wind. This allows it to now continue on a hyperbolic trajectory continually accelerating until its propellant is exhausted.

This sundiver maneuver allows the Q-Drive craft to fly downwind faster than the wind.

For a ship outward bound beyond the heliosphere, the ISM medium is experienced as a wind coming from the bow, While extremely tenuous, there is enough medium to extract the energy for continued acceleration as long as the ship has ejectable mass.

Up to this point, I have been careful to state this works IN PRINCIPLE. In practice there are some very severe engineering challenges. The first is to be able to extract energy from the drag of the plasma winds with sufficient efficiency to generate the needed power for propellant ejection. The second is to be able to eject propellant with a velocity that matches the speed of the vehicle, IOW, the exhaust velocity must match the vehicle’s velocity, unlike the constant exhaust velocity of a rocket. If the engines to eject propellant can only eject mass at a constant velocity, the delta V of the drive would look more like a conventional rocket, with a natural logarithm function of the mass flow. The ship would still be able to extract energy from the medium, but the mass ratio would have to be very much higher. The chart in Figure 2 shows the difference between a fixed velocity exhaust and the Q-Drive with variable velocity.

The engineering issues to turn the Q-Drive into hardware are formidable. To extract the energy of the plasma medium whether solar wind or ISM, with high efficiency, is non-trivial. Greason’s idea is to have 2 plasma magnet drag sails at each end of the probe’s spine that cycle in power to extract the energy. The model is rather like a parachute that is open to create drag to push on the parachute to run a generator, then collapse the parachute to release the trapped medium and restart it at the bow (see figure 3). Whether this is sufficient to create the needed energy extraction efficiency will need to be worked out. If the efficiencies are like those of a vertical axis wind turbine that works like drag engines, the efficiencies will be far too low. The efficiency would need to be higher than that of horizontal axis wind turbines to reduce the mass penalties for the propellant. It can be readily seen that if the efficiencies combine to be lower than 50%, then the Q-Drive effectively drops back into the regime illustrated in Box 1, that is that the mass of propellant must become larger than the medium and ejected more slowly. This hugely raises the mass ratio of the craft and in turn reduces its performance.

The second issue is how to eject the propellant to match the velocity of the medium streaming over the probe. Current electric engines have exhaust velocities in the 10s of km/s. Theoretical electric engines might manage the solar wind velocity. Efficiencies of ion drives are in the 50% range at present. To reach a fraction of light speed for the interstellar mission is orders of difficulty harder. Greason suggests something like a magnetic field particle accelerator that operates the length of the ship’s spine. Existing particle accelerators have low efficiencies, so this may present another very significant engineering challenge. If the exhaust velocity cannot be matched to the speed of the ship through the medium, the performance looks much more like a rocket, with velocity increases that depend on the natural logarithm of the mass ratio, rather than the square root. For the interstellar mission, increasing the velocity from 4% to 20% light speed would require a mass ratio of not just 25, but rather closer to 150.

Figure 6 shows my attempt to illustrate a conceptual Q-Drive powered spacecraft for interstellar flight. The propellant is at the front to act as a particle shield in the ISM. There is a science platform and communication module behind this propellant shield. Behind stretches a many kilometers long spine that has a plasma magnet at either end to harvest the energy in the ISM and to accelerate the propellant. Waste heat is handled by the radiator along this spine.

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In summary, the Q-Drive offers an interesting path to high velocity missions both intra-system and interstellar, with much larger payloads than the Breakthrough Starshot missions, but with anticipated engineering challenges comparable with other exotic drives such as antimatter engines. The elegance of the Q-Drive is the capability of drawing the propulsion energy from the medium, so that the propellant can be common inert material such as water or hydrogen.

The conversion of the medium’s momentum to net thrust is more efficient than a rocket with constant exhaust velocity using onboard power allowing far higher velocities with equivalent mass ratios. The two example missions show the substantial improvements in mission time for both and inner system rendezvous and an outer system flyby. The Q-Drive also offers the intriguing possibility of interstellar missions with reasonable scientific and communication payloads that are not heroic feats of miniaturization.

References

1. Greason J. “A Reaction Drive Powered by External Dynamic Pressure” (2019) JBIS v72 pp146–152.

2. Greason J. ibid. equation A4 p151.

3. Greason J. “A Reaction Drive Powered by External Dynamic Pressure” (2019) TVIW video https://youtu.be/86z42y7DEAk

4. Tolley A. “The Plasma Magnet Drive: A Simple, Cheap Drive for the Solar System and Beyond“ (2017) https://www.centauri-dreams.org/2017/12/29/the-plasma-magnet-drive-a-simple-cheap-drive-for-the-solar-system-and-beyond/

5. Zwicky F. The Fundamentals of Power (1946). Manuscript for the International Congress of Applied Mechanics in Paris, September 22-29, 1946.

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Abstract

A new class of reaction drive is discussed, in which reaction mass is expelled from a vehicle using power extracted from the relative motion of the vehicle and the surrounding medium, such as the solar wind. The physics of this type of drive are reviewed and shown to permit high velocity changes with modest mass ratio while conserving energy and momentum according to well-established physical principles. A comparison to past propulsion methods and propulsion classification studies suggests new mission possibilities for this type of drive. An example of how this principle might be embodied in hardware suggests accelerations sufficient for outer solar system missions, with shorter trip times and lower mass ratios than chemical rockets.

1 INTRODUCTION

In the sixty years since the first interplanetary spacecraft (Luna 1), scientific probes have been flown to all the large bodies in the solar system, and, after decades of flight time, the twin Voyager 1 and 2 spacecraft are entering the boundary between the solar system and interstellar space. However, missions to the outer solar system are still very difficult, with long trip times, even with use of gravity assist maneuvers.

     Substantial reductions in trip times to the outer solar system or for interstellar precursor missions are difficult for fundamental physical reasons. Fast trips imply high velocities: a constant speed of 100 km/s is only ~20 AU/year, beyond any demonstrated capability (though achievable with a close-solar flyby Oberth maneuver). Fast trips also imply that acceleration cannot be too small: a 29 AU trip (Neptune from Earth) of 100km/s peak velocity requires a constant acceleration of at least 0.005 m/s² to achieve a two-year flight time (ignoring Solar gravity), otherwise too much time is spent in acceleration and braking to take advantage of high speed.

     With rocket propulsion, high velocity implies either high mass ratio (expense) or high exhaust velocity (high specific energy of the propellant). High acceleration implies high specific power, which is why electric rockets have not been able to overcome these limitations. Nuclear propulsion systems offer high specific energy, but whether they can combine high specific energy with high specific power remains to be demonstrated.

     These well-known challenges have led to exploration of various types of ‘sail’ which use either the photons or the solar wind particles as an external source of momentum to harvest. Most of these approaches offer low accelerations because of the large collection areas required, but at least one, the “plasma magnet”, offers useful accelerations by using large-scale magnetic fields from small generators. This work was motivated by the realization that while such sails offer near-term prospects for acceleration to high heliocentric velocities away from the sun (hundreds of km/s), that there is no current propulsion system which permits braking from those velocities or sunward acceleration.

     The widely known methods of accelerating and decelerating in a surrounding medium, including propellers, ramjets, turbojets, rockets, parachutes, and sails, form distinct classes of propulsion. Energy can be provided by the vehicle or by the surrounding medium, while reaction mass can be carried aboard or harvested from the surrounding medium. By classifying propulsion systems in this way (a “morphological analysis”, following the methods of Zwicky), a promising form of propulsion is identified, in which the reaction mass is carried aboard the vehicle, but the energy to expel that reaction mass is provided by the passage of the vehicle through the medium. This was anticipated by Alan Bond in the limit of high-speed operation of ram-augmented interstellar rockets in which inert, rather than energetic, reaction mass could be used. The principle however is useful in contexts beyond the original application. We review the physics of the classical systems, and then explore the physics of this alternative form of propulsion. Finally, some examples of how this might be realized in an implementable device for fast transportation in the interplanetary medium are given.

2 REVIEW OF CLASSICAL APPROACHES AND THEIR PHYSICS

A review of the fundamental physics of existing propulsion is needed to understand how this method differs. The methods are grouped depending on whether propulsive energy is internally carried or externally harvested, and whether reaction mass is internally carried or externally harvested. Beginning with the equations of those well-known systems also provides the basis for deriving the physics of the new approach.

2.1 Propeller Systems (internal energy, external reaction mass)

The earliest known forms of propulsion (rowing, paddlewheels, propellers, turbojets, ramjets) involve pushing against the medium surrounding the vehicle, using energy carried aboard the vehicle. These forms of propulsion use the same basic physics: they are reaction drives, accelerating the medium around the vehicle. They all depend on the surrounding medium, and the energy requirements to produce thrust increase with speed relative to the medium, governed by the propeller equations, so maximum velocities are limited. Where m_wind is the streamtube of the surrounding medium captured by the propulsion device, and to which mechanical work is done, and Δv_wind is the change in velocity of the wind caused by the propulsion system:

     Note that care is required in observing the sign of these quantities, because the ship, medium, and reaction mass are all moving relative to each other. In the case of high freestream velocities ( ), Equation 3 becomes:

     This simplified form illustrates that the higher the freestream velocity, the more power is required for a given thrust, which is why rockets tend to dominate at higher speeds even when used within the atmosphere. Recently, systems extending the propeller principle to the interplanetary plasma as a medium have been suggested, with the same general physical principles.

2.2 Rockets (internal energy, internal reaction mass)

As the limitations of propeller systems in reaching high velocities became apparent, the application of the rocket principle became attractive. All rocket-type systems, regardless of power source, have broadly similar behavior. They are governed by the rocket equations.

     In rocket systems, the reaction mass that is ejected to conserve momentum is carried aboard the ship, as is the energy that is converted into the kinetic energy of both the ship and the exhaust. For example, the chemical energy of fuels and oxidizers are converted to reaction mass. The rocket equation is derived from the conservation of energy and momentum. While such a form of propulsion works in a vacuum, the amount of velocity gain is limited by the onboard energy and mass storage. In the case of chemical rockets, with practical exhaust velocities of ≤4500 m/s, maximum vehicle propulsive velocity gains of ~20000 m/s are the greatest achieved to date, though missions with higher heliocentric velocities have been achieved by gravity assist maneuvers.

2.3 Drag Devices (external energy, external reaction mass)

Where the surrounding medium is moving relative to the ship, the application of drag can be useful, either to accelerate downwind (simple sails) or to brake a preexisting velocity (parachutes and aerobrakes). In these cases, any energy required is provided by (or carried away by) the surrounding medium, and the reaction mass is also formed by the surrounding medium. Drag devices are usually considered a distinct class of device from propellers and rockets.

     One motivation for the current work is the recent proliferation of proposals for using the interplanetary or interstellar plasma as a medium for drag devices, which show that in spite of the low density (~10^-20 kg/m³ for the interplanetary medium at 1 AU, as low as ~10^-22 kg/m³ in hot plasma interstellar regions), useful accelerations can be achieved through electromagnetic interactions. This was first conceived as a magnetic sail or magsail, and more recently as an electric sail. A particularly high drag to mass configuration is the “plasma magnet” magnetic sail, which offers a streamtube capture area far larger than the physical dimension of the coils involved in the device. Fundamentally these are all drag devices, although the capture area, and hence the value of involved at a given phase of flight, differ significantly. As drag devices, they provide thrust as in Equation 1 above, although the power, as shown in Equation 5, is then delivered to the ship rather than being provided by the ship. Power can be large in cases where is large.

     These drag devices have great promise for certain missions including outer solar system flybys or missions to the heliosphere boundary, and for braking systems for interstellar missions. By harvesting thrust power from outside sources, they can operate at levels of thrust power well beyond our current ability to provide propulsive energy storage aboard a spacecraft. Unfortunately, by the nature of a drag device, they can only accelerate “downwind”, and so can only partially reduce propulsion requirements in cases such as outer solar system orbiters. Many desirable missions require thrust both for acceleration and for deceleration (stopping and starting a fast transit). It is worth noting that the ideal Bussard Ramjet while not a ‘drag’ device, would also fall in to this category of both the energy and the reaction mass being provided externally. The many practical difficulties in implementation of such a device have been discussed in the literature.

3 THE REMAINING OPTION

A morphological analysis of the suite of propulsion devices shows that there is a remaining class of reaction devices: one in which the reaction mass is carried aboard the ship and is expelled using the power extracted from the flow of the surrounding medium (in other words, Mr. Greason has discovered an interesting hole in the morphological analysis of propulsion devices, and is using it as a springboard to devise a totally new propulsion system). This approach does not appear in the common surveys of the propulsion art, and the first mention of it appears to be in Bond’s discussion of the Ram-Augmented Interstellar Rocket, in which he points out that in the limit of high speed operation, the energy contribution of the rocket propellant becomes nearly negligible and that indeed the RAIR could then function with inert reaction mass. However, there is no reason to limit the application of this principle to that particular implementation (meaning that the box is still an interesting hole, even though it is occupied by the RAIR and thus technically is not a hole) – indeed, as Bond notes, the process of ram-compression of the interstellar medium to densities where RAIR operation is plausible introduces inefficiencies (parasitic drag) which make that particular implementation difficult (Fig.1).

Interesting hole at bottom left, occupied by RAIR

     The key element of the type of drive contemplated here is that if the interplanetary or interstellar medium is dense enough to provide meaningful drag using plasma techniques, then it can be a source of power as well as drag. The medium can do mechanical work on a system, thus extracting power from the ‘wind’: analogous to a ram air turbine in atmospheric flight. Since in doing so the vehicle experiences drag, the fundamental equations of this class of propulsion system must be examined to determine its performance and behavior. There is no need in general to compress the interstellar or interplanetary medium to operate a drive on these principles; one need only extract energy from it to expel onboard inert reaction mass.

3.1 Nomenclature of This Type of Drive

The nomenclature for such a device is not obvious. While it might be classified under the broad heading of ‘jet propulsion’ since it expels reaction mass, that classification also includes propellers, which are broadly recognized as different from rockets. As will be seen, the governing equations are also different from rockets (the rocket equation does not apply), so calling them some form of ‘rocket’ seems misleading. And since they produce thrust and consume propellant mass, ‘sail’ hardly seems appropriate. Following Zwicky, one might think of them as a ‘dynamic-pressure-powered mass driver’, but that is rather clumsy. Bond suggests this as the high-speed, inert reaction mass limit of a ram-augmented interstellar rocket, but since in the general implementation, there is neither ram-pressure recovery, nor a rocket, nor augmentation, nor interstellar flight, that nomenclature seems ill-suited to the general case. This propulsive principle might be called a “wind drive”, or, “ram drive”, but using the common abbreviation q for dynamic pressure suggests the name q-drive – which is the name used in the balance of this text.

3.2 Momentum and Energy Conservation

Fundamentally, as a propeller takes advantage of the fact that at low speed, it takes little energy to make thrust, the q-drive principle takes advantage of the fact that at high speed, a small drag device can extract a great deal of power. The power from a wind-harvesting device follows Equation 5, while the power required to expel stored reaction mass follows Equation 8. In the ideal case of no losses and no parasitic drag, this leads to the following fundamental equations for minimum use of reaction mass:

     Contrast Equation 11 with Equation 6 and three dramatic differences are apparent, all favoring the q-drive principle in high velocity flight. First, in cases where v_∞(initial) is large compared to a rocket exhaust velocity ( ), the scaling is more favorable for the q-drive. Second, mass ratio for a q-drive scales with the square of velocity rather than with the exponential of velocity as in a rocket. Third, in cases where Δv is much less than v_∞(initial), as in most flight in the solar system due to the high velocity solar wind, the required mass ratio is even smaller (bearing in mind that the q-drive principle is only useful in situations where v_∞(initial)>>0).

     Two examples help to illustrate the q-drive principle. Consider operating in a medium that is essentially at rest in the stationary reference frame, such as the interstellar medium in heliocentric coordinates. If given (through the use of some other propulsion system), an initial velocity v_ship of 600 km/s, which for zero wind speed is also of 600km/s, using the q-drive principle with a mass ratio of 16 gives a final velocity of 2400 km/s. This rather startling velocity does not rely on an onboard nuclear reactor or energetic propellant; it is simply the result of momentum and energy exchange with the rest of the medium. The reaction mass is carried away by the surrounding medium and is at rest with respect to it, so the kinetic energy of the initial high-mass ship plus reaction mass has been concentrated into a final, low-mass ship at much higher velocity. It is worth noting that use of drag devices such as the Plasma Magnet sail purely in a drag configuration can produce heliocentric velocities of this magnitude, and that the abrupt deceleration of the solar wind in the termination shock at the heliopause then means that same heliocentric velocity, which tended towards of zero within the solar wind now presents a high in the interstellar medium.

     The second example is a case relevant to maneuvering inside the solar system. Consider the solar wind to have a constant velocity of 450 km/s, and suppose a ship has been brought to a velocity radially outward from the sun of 150km/s (for example, by the use of a plasma magnet drag device). To brake from that outward velocity to achieve a state of rest in heliocentric coordinates is then a Δv of 150km/s, where the relative ‘wind’ speed is initially 300 km/s and rises during the maneuver to 450 km/s. (When the vehicle is at rest in heliocentric coordinates, it has equal to the wind speed.) In this case, the mass ratio required is 2.25 from Equation 11. By comparison, to achieve the same maneuver with the same mass ratio using a rocket, an exhaust velocity of 185 km/s would be required, which is far beyond any chemical rockets’ capability, and if based on an onboard power plant, would require a very high power-to-mass ratio. By using the q-drive principle, the result can be achieved with inert reaction mass and with power harvested from the motion of the ship through the surrounding medium.

     At first glance, the q-drive principle appears to offer “something for nothing”. Propellant is expended but where does the energy come from? The answer is that the energy comes from the loss of velocity of the reaction mass to the surrounding medium. One may think of it as an inelastic collision between the expended reaction mass and the surrounding medium, where the resulting change in energy is carried away by the ship. In this sense, it is very reminiscent of the Oberth effect, in which there are also three masses involved: the ship, the exhaust mass, and a planet. The q-drive principle is much more flexible, however, since it uses the surrounding medium as the third mass, and so the q-drive is not restricted to operation near a gravitating body.

     Finally, while the analogy is imperfect, this has some similarity to the method by which sailing vessels on Earth can sail upwind. In that case, the energy is derived from the motion of the surrounding air, and the “reaction mass” is provided by the action of the keel on the water. In space, we can achieve comparable results by expelling reaction mass from the vehicle.

4 EXAMPLE IMPLEMENTATIONS

The propulsive principle outlined in this paper could apply to high-speed atmospheric flight or to travel in the interplanetary or interstellar medium. However, to determine whether the q-drive principle has real engineering utility, some concept of how this principle can be embodied in hardware is helpful. Furthermore, the question of whether the acceleration achieved is useful for fast transits can only be assessed in the light of a hardware implementation. Realize that these examples are just that: guideposts for two ways to apply the q-drive principle to real hardware. The first example is presented only because it is physically very simple, and so enhances understanding of the physical principles. The second example may be a practical implementation, with acceleration > 0.02 m/s².

4.1 Continuous Mode, Electric Field Power Extraction

Flow of the solar wind or interstellar plasma over electrodes can be used to generate electrical power to expel reaction mass, following the q-drive principle. Flow of a neutral plasma across a tandem pair of grids, with the solar wind flowing over them, will develop a voltage difference from which power can be extracted. This principle is well known as a means of extracting power from conceptual fusion reactors, and its use in the reversed mode, applying power to make thrust, is noted. Because the Debye sheath formed around each conductor limits the amount of plasma intercepted, this approach requires high mass and offers low acceleration, but the principle of operation is helpful to understand. The velocity of the wind over the ship produces electrical power. Extracting that power creates a voltage difference between the grids, which manifests as drag, precisely as in a windmill or ram air turbine operating in the air. Lower mass might be achieved by using a tandem set of radial wires similar to the “e-sail”.

     In turn, the electrical power can be used to expel reaction mass. Any type of electrically powered thruster could be used, provided the reaction mass can be expelled at approximately the same exhaust velocity as the freestream velocity (). While existing electric thrusters operating at ~4x10⁵ m/s exhaust velocity are immature, they are plausible under known physical principles. The expelled reaction mass ends up nearly at rest with respect to the solar wind, while the ship accelerates sunward (or reduces its outward velocity).

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4.2 Pulsed Mode, Magnetic Field Power Extraction

For accelerations that enable fast transits, a method of extracting power from the solar wind is needed that provides a high drag-to-mass ratio, and it seems likely that a low parasitic drag is also important. In atmospheric applications, rotating devices (windmills, anemometers) are used to draw power from the wind, and magnetic field analogies of both are possible, but the relatively low lift-to-drag ratio of magnetic fields in plasma suggests these approaches may have high parasitic drag. A useful approach may lie in a linear, reciprocating motion of a magnetic field, where essentially all the drag goes into pushing on a moving field. High drag-to-mass is achievable using the plasma magnet approach.

     The basic principle of the plasma magnet, illustrated in Fig. 2, is that a rotating magnetic field, driven by alternating current in a crossed pair of coils, creates a circulating current in the plasma, and that current then expands in radius until it creates a dipolar magnetic field much larger than the physical coils.

     If such a field is turned on and the generating coils are attached to a tether, the tether will be pulled by the solar wind, which could rotate the shaft of a conventional generator. Then, the field could be turned off, the tether reeled back in, and the cycle repeated. In principle this approach of mechanically moving the field coils in a reciprocating manner would extract power, and it illustrates the principle involved, but the mechanical motions would be too slow to provide adequate power-to-mass ratio. We need a more rapid motion of the field, which can be achieved by replacing the reciprocating motion of the coils carrying the magnetic field with the reciprocating motion of the magnetic field itself.

• 

     In the approach illustrated in Fig.3, a pair of plasma magnet generating coil sets are used, separated by a tether with wires to transfer power from one set of coils to the other. Initially, the windward coil set is energized and the solar wind pushes on it, transferring the energy in the dipole field to the leeward coils. During the power stroke, energy is extracted from the wind, which can be used to power an electric thruster to expel reaction mass. A third coil set, omitted from the illustration for clarity but located at the windward end with a closed (toroidal) configuration that does not generate a magnetic field outside the coils, receives the energy on the return stroke, so that drag is only pushing on the field during the power stroke. Then, the energy is again transferred to the windward coil, and the cycle repeats.

     A detailed design would be required to estimate mass but a sizing study, based on peak currents in superconducting MgB₂ tapes at 20K of 2.5 ×10⁸ A/m², suggests that accelerations in the 0.025-0.05 m/s² range may be feasible using this approach. The long tether, carrying oscillating currents in the 1 KHz range from end to end, modulated by a reciprocating frequency in the 20 Hz range, is admirably suited to form a Wideröe style ion accelerator, thus providing an integrated method for converting the resulting electric power to thrust.

5 CONCLUSION

A new class of reaction drives appears capable of generating vehicle velocities greater than those practical for propeller or rocket devices. The basic principles of this drive are those employed in the “inert reaction mass, high velocity limit” of the Ram-Augmented Interstellar Rocket, but they do not require that particular implementation, nor do they require fusion technology, and by exploiting the solar wind, they are particularly useful for interplanetary flight. A conceptual design suggests that, by using plasma magnet techniques, such a drive could offer accelerations and mass ratios sufficient for rapid transits to the outer solar system.

     To explore further, the analysis of the physics involved needs to be extended in two ways. First, the analysis needs to include the effects of efficiencies in power conversion and parasitic drag, to assess whether the approach is practical. Second, to extend the application of this technique for inner solar system missions, the theory needs to be extended to include thrusts that are not parallel to the drag vector, which would enable a wider range of maneuvers.

     This paper begins to examine routes for embodying this type of reaction drive in hardware. To assess the achievable accelerations, designs will need to be carried to a level of detail at which masses can be estimated credibly.

(ed note: the appendix in the report derives the equations behind the q-drive principle. It is not for the faint of heart, lots of heavy math and physics.)

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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.

• 

      The problem of travel beyond low orbit is quite a different one: the advantages of full-time solar energy and easy access to lunar materials can only be enjoyed at escape distance, but to go from low orbit to a great distance requires a far longer time and, if Earth is still the source of supplies, a longer and thinner supply line.   The problem is analogous to that of an extremely long-range aircraft flight.   If we require that the plane reach its destination, turn around, and return without refueling, we make the problem far more difficult than if we permit refueling at the destination for the return trip.

     The problem of low orbit to L5 transfer is, for passengers, first that of time: even with high-thrust engines, able to make large changes in the velocity of the rocket within a period of only an hour or less, the travel time to escape distance is about three days.   The simple type of accommodations that would be adequate for a flight of half an hour or even of several hours would be quite unbearable for a trip lasting for a number of days.   "Steerage to the stars" is not the image that we would like to look forward to in connection with the humanization of space.

     Fortunately, there are compensating advantages of which use can be made to get around this problem: from low-orbital distance out, there is no requirement that vehicle engines be capable of supplying a thrust greater than the vehicle weight.   If we are willing to settle for a slow trip, engine thrust and acceleration can be quite low.   If we make use of the fact that L5 will be a site at which reaction mass will be relatively cheap, it seems clear that instead of developing monster vehicles for liftoff from Earth, we would be better advised to solve the problem from both ends.   L5 is the ideal site for construction of large spaceships, whose design could be free of any of the limitations forced by entry into planetary atmospheres.   Mass-driver engines for those ships can "fuel up" at L5 with reaction mass either in the form of industrial slag or of liquid oxygen.

     The spaceships Konstantin Tsiolkowsky and Robert H. Goddard are assumed to have empty masses of about 3,000 tons, of which about two-thirds would be their mass-driver engines and their solar-power plants.   The mass-driver engines would have exhaust velocities about twice as high as for the best chemical rocket-about the same as for the much earlier but similar machines studied intensively in the late 1970s for the early days of space manufacturing.   Those engines, carrying solar-cell arrays like the sails on a square-rigger, would stretch out for several kilometers, but that would be quite tolerable for vessels never intended to enter an atmosphere.

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     To find the performance of the Goddard we have to know how much the solar-cell arrays will weigh.   I'm assuming three and a half tons per megawatt.   The NASA Johnson Space Center, in a detailed study, concluded it could do that well even by the 1980s, for a satellite power station.

     For the Goddard, years later in time, that should be attainable: especially so when one remembers that for a spaceship engine there is no need to hold the cost down to the low value that would be required for an economical central power station.   For the Tsiolkowsky, the Goddard, and their sister vessels the corresponding travel times would be around three weeks for the inbound leg of the journey, and just over a week for the outbound: about the same time that it takes to cross the Atlantic on a medium size vessel.   The differences in trip time arise from the fact that the engine would have constant thrust and that on departure from L5 each ship would be heavy with reaction mass.   That difference would be a happy one for the outbound travelers, who would enjoy a higher average speed than would the crew when spiraling down to low orbit from L5.   Later on by perhaps two decades, when transport requirements may be much greater, the engineers may be able to make still lighter solar-cell arrays.   If they can produce something in the ton-per-megawatt range, the travel time can be reduced to little more than three days.   Other approaches, including the possibility of laser or micro-wave beamed power, are not out of the question.   I am not considering the possibility of nuclear power.   The reason is straightforward: if the development of the communities is to go on without check for a long period, one must not design into it "absurdities" that would pose a limit as soon as total numbers or total required transport exceeded some modest value.   It does not seem to me to make sense to design a deep-space transport system around an energy source that would have to come from Earth.

     We can get lower and upper limits to the ticket price for a trip to L5 in the late 1990s-early 2000s time period.   The lower limit comes by assuming round trip times of a month, and ship costs per ton that are three times as high as those of present-day commercial aircraft.   The total comes out around $ 6,000.   The cost of reaction mass would only be a small fraction of that total, because it would be so abundant at L5.   A still lower ticket-price could exist if the ships carry full loads of either passengers or cargo both on the inbound and outbound legs of the journey.

     The upper limit is $ 30,000, and comes by assuming that each vessel must collect in revenue an amount equal to its own cost, within a time of eighteen months.   Ticket costs on commercial jets within the United States have about that ratio to aircraft-purchase price; they include, though, total fuel costs which are a higher fraction of the cost of the capital equipment.   Either the $ 6,000 or the $ 30,000 figure would be a small fraction of the productivity of an industrial worker in a single year, at the favored location of L5, and would probably equal only a few months' earnings.

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The concept of launching cargoes and passengers off the moon using an electromagnetic track originated with Arthur C. Clarke, who first wrote about it in 1950 in the pages of the Journal of the British Interplanetary Society. The 1954 book The Exploration of the Moon, written by Clarke and illustrated by artist R.A. Smith, depicted such a device (image right). Eight years later (April 1962), Clarke published "Maelstrom II," a science fiction story based on the concept. Escher explained that he was unaware of Clarke's priority when he began his Lunatron work. After learning of it, however, he engaged in a "helpful correspondence" with the British author and spaceflight thinker.

Escher noted a limitation on the Lunatron's speed: "the centripetal acceleration resulting from the circular path imposed on the spacecraft as it is retained upon being accelerated to above circular velocity on the Moon-fixed track." As they passed lunar orbital speed (1.7 kilometers per second), trolley and payload would tend to rise away from the track. Lunar escape speed is, however, 2.4 kilometers per second, so they would need to be held down so acceleration could continue.

As the Lunatrom continued to accelerate the trolley, passengers would feel "down" shift by up to 180°, from toward the moon's center to directly away from it. Escher proposed that they "be mounted in swivel support systems to compensate for this effect." The faster the trolley moved, the more acceleration the passengers would feel in the new "down" direction. In effect, the Lunatron would become a centrifuge and the payload would become its gondola.

Escher calculated that, for a 50-to-500-kilometer-long Lunatron for launching cargoes and passengers from the moon to the Earth, acceleration would top out at a tolerable eight times the pull of Earth's gravity. However, for larger systems — such as the 870-kilometer Lunatron for throwing payloads out of the Solar System — acceleration could reach 60 Earth gravities.

The MSFC engineer proposed siting the Lunatron for launching beyond the Solar System at the center of the moon's Farside hemisphere. Launching there at local midnight would take advantage of the orbital speeds of the moon around the Earth and the Earth around the Sun, slashing the velocity the Lunatron would need to provide from 42.5 kilometers per second to just 12 kilometers per second. This would in turn limit the acceleration to which its passengers would be subjected.

Building a long Lunatron track, Escher wrote, would constitute "an almost overwhelmingly large construction job," with "extensive cuts. . .through mountains [and] fills or bridge structures. . .across low areas." He maintained that the magnitude of the construction task, combined with the large amount of electricity needed to accelerate payloads, would mean that the Lunatron would probably not become available until "well after the start of colonization of the Moon."

"On the Utility of the Moon in Space Transportation: the Lunatron Concept," William J. D. Escher, Engineering Problems of Manned Interplanetary Exploration, pp. 102-112; paper presented in Palo Alto, California, September 30-October 1, 1963.

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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)

Nomenclature

21.41 Introduction

     The limits of space flight are determined by the exhaust velocity of the propulsion systems available, more than any other parameter. Chemical propulsion systems deliver exhaust velocities up to 5 km/sec, thermonuclear rocket engines up to 15 km/sec, and electrical propulsion systems up to 200 km/sec. Thus,the largest possible exhaust velocity within reach of the presently known technology is less than one-tenth of one percent of the velocity of light. Therefore, other ways and means will have to be found to make it feasible to accomplish missions requiring flight velocities approaching the velocity of light to appreciable extent.

     Modern physics has shown, so far, only one theoretical way of doing this, which has been termed the "photon rocket."

     The ideal photon rocket converts its fuel, by a hypothetical process, completely into radiation, and emits the radiation in a collimated beam without losses, thus producing thrust. The problem encountered is not so much the production of photons, but, at a thrust level, mass conversion efficiency and collimation quality, which are of any practical interest. The technical means of producing the required thrust are presently beyond the state of the art, and thus the photon rocket is at the present time in the stage of theoretical investigation and early experimentation.

21.42 Area of Application

     Before the problems of the photon rocket are described in some detail an indication of the areas of application of such a propulsion concept will be given. Figure 21.94 shows the relationship of distance and velocity for the entire field of aeronautical and astronomical operations. The ordinate is the altitude or distance, respectively, in logarithmic scale, which extends to the nearest stars. If this scale were extended by another seven logarithmic units, one would obtain the radius of the entire universe as known today (maybe in 1960 but not now. Seven more logarithmic units is out to one billion light-years, the observable universe is out to 45.7 billion light-years which is eight more logarithmic units.). The abscissa represents the flight velocities in kilometers per hour relative to earth up to the largest possible velocity, the velocity of light. Manned space flight is assumed to be limited by a constant acceleration of 2g and an accelerated flight time of 10 years. It is quite apparent from this diagram that the photon rocket is of interest mainly beyond the solar system, when the mission objective is to reach other stars and when approaching the light velocity where the laws of relativistic mechanics will have to be applied. In many cases, however, these effects will be very small, even for photon rockets (vertical line labled Relativistic Mechanics).

21.43 Basic principles and Performance

     As discussed in [3], photons exerta reactive force upon the source from which they are emitted. Each photon carries a well defined momentum

p = (hν) / c

which can be written in the alternate form

p = E / c = mc     (21.149)

If a source emits electromagnetic radiation concentrated withina parallel beam, a total impulse P is carred by this beam

P = (ΣE) / c = cΣm     (21.150)

and the reactive force or thrust exercised by this beam is

F = (dP/dt) = c (dm/dt)     (21.151)

It should be noted that these relations are independent of the frequency of the radiation.

     The basic problem in using photons for rocket propulsion is not to produce light velocity but to transform a sufficient portion of the fuel into radiant energy. The present technology permits only transforming an extremely small portion of εm_s, of the rocket fuel mass m_s into useful kinetic energy. In principle, the photon rocket becomes more attractive with increasing ε, but, at the same time, it will be more difficult to realize such a device.

     There are three different cases of interest. The first one is the ideal photon rocket, which converts its fuel completely into radiation (ε = 1) and emits the radiation in a collimated beam without losses.

     Another type, the partial photon rocket, converts only a certain fraction of its fuel mass into radiation (εm_s), and drops the remainder of the fuel (1 - ε)m_s, left over from the conversion process, overboard as waste, without contributing to the thrust. These partial photon rockets deserve consideration because their technical realization may be easier than that of the ideal photon rockets. There are, of course, less efficient.

     A third type of interest for comparison purposes is a nuclear rocket, which is not strictly a photon rocket. Its fuel also is partially converted into energy. However, this energy is not emitted in the form of photons, but is further convered into kinetic energy of the waste products. The rocket emits particles at an exhaust velocity Ʋ < c, and Ʋ depends essentially on the conversion factor ε. As ε approaches one, the exhaust velocity approaches c, and, for ε = 1, this nuclear rocket is again an "ideal" photon rocket.

     This third type is particularly interesting because it covers chemical, nuclear, plasma, ion, and photon rockets alike, but it excludes the partial photon rocket.

     Assuming that the conversion of the energy back into kinetic energy of the exhaust particles proceeds without losses, the following conversion factors are found as representatives for the transformation of mass into kinetic energy [3]:

Chemical	5 × 10-11
Plasma	5 × 10-10
Ion	5 × 10-5
Nuclear fission	10-2
Nuclear fusion	4 × 10-2
Ideal photon	1

For the nuclear transformations, it is assumed that the entire amount of fuel consists of fissionable or fusionable material, and that the fission or fusion energy is transformed entirely into kinetic energy of the fission or fusion products. No working fluid is used. Techniques for this process are still completely unknown.

     In considering performance, the laws of relativity have to be observed. If u is the desired velocity of the rocket (the deltaV or ΔV) and the exhaust velocity is approaching the velocity of light, the mass ratio of such a photon rocket becomes

r = m₀ / m_e = √(1 + u/c) / (1 - u/c)     (21.152)

This relationship is shown graphically in Fig. 21.95.

     In case the exhaust velocity Ʋ is smaller than the velocity of light, the mass ratio of such a rocket becomes [1,3]

r = m₀ / m_e = ((1 + u/c) / (1 - u/c))^{c / 2Ʋ}     (21.153)

     This relationship is shown in Fig. 212.96 where the Ln(r) is plotted versus the velocity ratio u/c with the dimensionless exhaust velocity Ʋ/c as a parameter (i.e., the graph plots a relativistic version of the Tsiolkovsky rocket equation). This graph shows that, unless the mass ratio is unrealistically high, only the ideal photon rocket, or a particle rocket with an exhaust velocity very close to light velocity, can reach an end velocity approaching the velocity of light. Even an energy source like nuclear fusion is far from providing end velocities near that of light.

     For photon rockets with a conversion factor less than one, the relationship between ε and the exhaust velocity is given by [2,3]

Ʋ = c √2ε - ε²      (21.154)

This relationship, which is taken from [3], is shown in Fig. 21.97.

     Another interesting relationship can be arrived at for the ratio of the mass ratios of a photon rocket and a particle rocket for one and the same conversion factor. This ratio [3] is

r_photon / r_particle = ((1 + u/c) / (1 - u/c))^{(√2/(ε-1)-1) / (2√2ε-ε2)}     (21.155)

Abscissa Ʋ/c is relativistic exhaust velocity,
Ordinate ln(m₀ / m_e) is relativistic mass ratio,
Diagonal lines u/c are relativistic deltaV,
all related by the relativistic version of the Tsiolkovsky rocket equation

It is easy to see that the mass ratio of the photon rocket must become larger than that of a particle rocket, since the waste mass does not contribute to the thrust as it does in the particle rocket.

     Considering a typical example, one may select the highest possible conversion factor of a nuclear reaction known today with ε = 10^-2. This is representative for a hypothetical reaction in which protons and neutrons are fused together to form a medium-weight nucleus. No methods are presently known, even theoretically, for converting mass into energy on a large, controlled scale with a greater mass conversion factor. Using this for a numerical example of a rocket which is to reach 90 per cent of light velocity, the initial mass of a photon rocket is 10⁶⁰ larger than that of a particle rocket. If, however, the conversion factor could be increased by a factor of 99 to ε = 0.99, the photon rocket would be only 5 per cent heavier than the particle rocket for the same end velocity. It remains to be seen, however, which one of the two, the particle rocket or the photon rocket, has a better chance of technical feasibility. Thus it is quite apparent that the photon rocket will be of particular interest when conversion factors close to one become possible. In that case, however, the ideal photon rocket has the largest potential of all known propulsion principles.

21.44 Sources of Radiation

(ed note: I would note that the laser was being invented about the time this paper was written)

     One of the basic problems of the photon rocket to be solved by the engineer is the development of an effective source of radiation which forms the photon beam if properly collimated. The light pressures which are required for photon rockets of practical interest are in the neighborhood of about 0.01 kg/cm² for low accelerated vehicles and around 10 kg/cm² for high accelerated vehicles. Such light pressures would be reached by black-body radiation at temperatures between 50,000 and 250,000°K. The radiation maximum would be located in the region of ultraviolet or X rays, respectively. It is well known, however, that any crystal structure which could produce black body radiation would cease to exist already at 4500°K, which would result in a radiation pressure of only 10^-6 kg/cm². Therefore, it is apparent that only gases will be able to produce the desired radiation pressures. At these temperatures the gases are plasmas.

     The electrons of the atoms are pushed by thermal collisions into quantum orbits with higher energy. They are radiating photons with well-defined frequencies if they fall back into orbits with less energy. A typical example is the yellow light of the sodium steam lamp. Black radiation with light elements can be obtained only with gas lasers of astronomical dimensions if the gas pressures are modest [4]. Only elements with low ionization and excitation temperatures such as cesium, potassium, sodium, aluminum, etc., can be used if black-body radiation is desired at low temperatures and pressures, as well as a small thickness of the gas layer. It is well known that cesium plasma with a thickness of a few millimeters and at a pressure of a few atmospheres can produce black-body radiation similar to the sun at temperatures of 5000 to 6000° K. The problem, however, is to reach body radiation at much higher temperatures.

     The differences in the term-excitation and ionization energies of different elements are small, compared to the very high energy contents of these plasmas. A very high atomic-weight and the highest possible nuclear-charge number are most influential in obtaining recombinations between ions and electrons in a satisfactory number.

     Figure 21.98 shows the specific radiation and the radiation pressure for a heavy plasma of the upper end of the periodic system, as a function of the plasma pressure and the geometric thickness of the gas layer, with plasma temperatures as a parameter. This diagram was estimated with the help of the well-known derived by Kramer.

     It can be seen that, for conditions which seem to be within reach, for experiments such as plasma pressures of 1 kg/cm², geometric-layer, thickness of about 1 mm, and plasma temperatures of 60,000°K, it should be possible to produce radiation energy concentrations of about 10⁷ cal/cm²

     It also looks probably that radiation pressures in the order of 1 to 10 kg/cm², which are of great technical interest, could be produced in the laboratory. This would mean a plasma pressure of about 100 kg/cm², and a layer thickness of 1 to 10 mm. The required temperatures of 300,000 to 400,000°K, however, have not yet been obtained by input of electric energy into the plasma. It seems to be of technical interest that the same radiation pressure of 1 kg/cm² can also be obtained at the same plasma pressure, and at 140,000°K if larger layer thickness can be materialized. It also helps that the nature of the used chemicals in the upper portion of the periodic system is less important, so that considerable freedom exists in the choice of the radiating plasmas. This also means that the plasma can be selected according to the requirements of the nuclear reaction.

21.45 Collimation of Photons

     In order to produce a jet beam, one needs a reflector, which collimates the photons without losses on a surface consisting of metals, liquids, or gases. Reference is made to Figure 21.99. Heading rates of 10³ cal/(cm²)(sec) can be tolerated today in liquid-cooled rocket engines. In photon rockets, however, heat-transfer rates of the order of 10⁹ cal/(cm²)(sec) will have to be mastered. Regenerative-cooled metal surfaces will not longer be able to handle these; a complete (mirror-like) reflection of the total energy must be obtained. This reflectivity in the short-wave ultraviolet range or in the long x-ray range must be at least R = 1 - 10^-6 = 0.999999; silver-plated mirrors only have R = 1 - 10^-2 in the infrared spectrum range, and even less in the ultraviolet range.

     Using the collision laws of classical mechanics, one can define the reflecttivity coefficient also as

R = 1 - (E₂/E₂)
R = 1 - 4 ((m₁/m₂) / (1 + m₁/m₂)²)     (21.156)

where m₁ is the mass of the impacting particle, and m₂ is the mass of the surface particle, which in the average is at rest. This relationship is shown in Fig. 21.99. Atom masses are of the order m₂ = 10^-23, as long as the energy of the impacting particles m₁ is smaller than the separation energy of the electrons when separating from the atom or molecule. Thus m₁ must be as small as possible, in order to obtain highest possible reflectivity, which requires long-wave photons, e.g., light photons with a mass of m₁ = 10^-32. In that case, elastic reflectivity coefficients of about R = 1 - 10^-9 result, as required for complete optical reflection. The heat-transfer rates within the reflector to the wall would be smaller in this case, compared to present-day heat-transfer rates of rocket engines. Reflections of photons is always a complex absorption and reemission process of electromagnetic waves at the electron gas of the participating material. This is true, whether radio waves are reflected at the ionosphere, or radar waves are reflected at flying objects, or the visible light at metal surfaces, or X rays at crystal surfaces.

     A primary electric wave which penetrates the electron gas incites the free and bound electrons to oscillate. As result of this incitement, the individual electrons radiate elementary spherical waves, which are called secondary waves. These in turn are the reason for the next class of waves; etc. All these waves are superimposed upon one another. The result of this process is that the primary wave is destroyed by interference, and a new wave is produced, which is reflected under a certain angle into the vacuum. All investigations of the reflection process are concentrating, therefore, on the reciprocal action between photons and electrons or electron gas, respectively.

     The results of investigation so far have shown [5] that the electron gases of solid and liquid metals are not satisfactory as reflector material for short wavelengths. The reflectivity of metals at very low temperatures is increasing, but, as can be seen from Fig. 21.100, there are no indications today that it will be possible to build suitable reflectors with metals even at cryogenic temperatures. Somewhat more promising are the plasmas, the reflectivity of which is shown in Fig 21.101. One can recognize that the reflectivity at short wavelength is primarily dependent upon electronic density N. It can also be seen that extremely small electron densities (1 per cm³) will offer high reflectivity, provided one works in the area of very long waves of several kilometers in length. The desired reflectivity of R = 1 - 10^-6 can be obtained at a temperature of 100°K and one electron per cubic centimeter for a wavelength of 30 km, e.g., for photons with very little mass.

     If electron densities are in the order of 10¹² per cm³ (as often experienced in combustion gases), then these reflectivities are reached already, with a wavelength in the order of centimeters, but at several million degrees temperature. In case of extreme temperatures, which would occur at the nuclear fusion of light elements, and high electron densities of 10²⁴ per cm³ (as in metals), good reflectivity could be reached down to ultraviolet wavelengths. Thus, it might be possible to produce the required reflectivities with the help of plasmas. However, at the present time this appears to be questionable [6].

     Finally, of particular interest is the reflection using pure electron gas. In this case, the electron collisions vanish against the heavy atoms and ions no longer in existence. The distance between electrons in a pure electron-gas mirror should be in the order of r = 10^-9 cm, where the electrostatic pressure is approximately

p_el = 2.3 × 10¹¹ kg/cm²

This is assumed to be the initial pressure at the explosion of hydrogen bombs. If the mentioned approach of the electrons is supposed to be produced by the dynamics of the collision, then the energy required has to come from the kinetic energy of the electron. Thus its velocity before the collision has to be

Ʋ = √2e²/mr = 7.1 × 10⁸ cm/sec

This is 2.38 per cent of the light velocity. Cathode rays and beta rays possessing such velocities can be produced. The influence of the temperature upon the reflectivity is eliminated for pure electron gases, and R becomes independent of temperature. This is very important, as a photon mirror consisting of colliding cathode rays, which possibly might not be in the state of equilibrium, could have an undefined temperature. If the other limiting case is considered where the electron gas is in equilibrium, the effective cross sections of the electron-electron collisions become of the same order of magnitude as those of the electron-ion collisions. Under these circumstances, the conditions for plasmas, mentioned above, are also valid for electron gas, and thus Fig. 21.101 can be used. The fundamental possibility of electrical production of the required collision velocities make this solution of pure electron gas much more attractive than any other solution.

21.46 Effects of the Photon Beam

     The energy release from a photon rocket can be higher than that of a hydrogen bomb, because an ideal photon rocket may have a mass conversion efficiency of ε = 1, whereas, for the nuclear-fusion reaction, ε is only 4×10^-2. Ideally, all the energy will be beamed into the photon jet; therefore, this light beam can be a means to destruction.

     The reflector cone of a 100-ton light-pressure rocket, having a total vertex angle of 10°, will generate the terrestrial radiative intensity of the sun at a distance of 3000 miles. At a distance of 600 miles, forests, fields, and housing areas would be ignited by this beam on an area of about 3000 square miles. At a distance of 300 miles, all life would be destroyed instantly; at 30 miles, metal slabs would be melted in a few seconds, and even the best silver reflector would melt at a distance of 6 miles. It is obvious that many geophysical conditions could, thereby, be affected in particular climatological and meteorological processes. This undesirable aspect of photon rockets entails some limitations for the application of this propulsion system. It is obvious that the photon beam of such a rocket must never hit the terrestrial surface or any other surface, or any flying object, except from a very great distance. Vertical take-off from the surfaces of celestial bodies does not seem to be feasible at the present time except in emergencies.