As it happens, charged particles, not x-rays or gamma rays, are the main radiation danger for space travelers and lunar explorers. The International Space Station is within the protection zone of the Earth's magnetic field, but the Moon is not. On the airless Moon, which has almost no magnetic field, the usual radiation level is about sixty times that on the Earth and more than twice the level that calls for the evacuation and decontamination of nuclear facilities as specified by the International Commission on Radiation Protection.3 And during a solar flare the radiation level on the lunar surface becomes orders-of-magnitude higher than this.
Proposals for radiation protection of a lunar base usually involve burrowing underground. This approach does not protect people working or exploring on the surface, but a magnetic shield would. And it turns out that very large magnetic shields can readily be produced in craters at the lunar poles. Magnetic shields can easily protect much more of the lunar surface from charged particle radiation than the possible alternative of using electrostatic towers, which need to be constantly charged up to hundreds of millions of volts in order to repel these particles. The magnetic approach is a completely different way to provide radiation protection. Magnetic shields work because charged particles traveling in a magnetic field experience a force whose magnitude depends on the strength of the field as well as on the particle's electric charge and velocity. If a charged particle is moving in a direction perpendicular to the magnetic field, this force will cause it to travel in a circle. In most cases, particles are not moving perpendicularly to the field and end up going in spirals around the field direction: The stronger the field, the tighter the spiral. This is how the magnetic field of the Earth shields us from charged particle radiation. The auroral lights that shimmer in the artic night sky are the result of charged particles spiraling down the Earth's magnetic field and hitting the atmosphere high above the magnetic poles, causing the upper air to glow.
Two key points about magnetic shields: (a) The weaker the magnetic field, the larger its effective volume must be for the shield to work, and (b) the stronger the field, the greater the energy needed to generate it. By using coils made with superconducting wire, only the act of raising the shield requires an energy input. After that, the persistent electric current circulating in the superconducting wire maintains the shield. In the 1960s the use of magnetic shields for radiation protection of the Apollo moon missions was evaluated in detail. But at that time, available superconductors only worked at near liquid helium temperatures, so the wire coils used to produce the magnetic shield would have to be submerged in a helium cryostat onboard the ship. Using a wire coil of small size to generate the magnetic field needed for keeping near light-speed particles away from the hull requires the coil to carry a huge amount of current. If these particles did hit the ship, their impact would produce electromagnetic radiation, which cannot be stopped by a magnetic shield. A high magnetic field intensity means the energy stored in it is enormous. If this energy were released suddenly, it could destroy the ship. In the end, the concept of magnetic shielding was abandoned, and the Apollo missions were timed to avoid solar flares. But avoiding solar flares is tricky, and Apollo 16 made it back to Earth only hours before a major solar flare occurred.
So, any lunar base is going to need permanent shielding; this is where high temperature superconductors come in. In 1986 Bednorz and Müller discovered a new class of superconducting materials and won a Nobel prize for this discovery.4 A lot of these new superconductors work at temperatures more than twenty times higher than the boiling point of liquid helium, and some can even work at temperatures over 200 oF above absolute zero. Such temperatures are well above those found on the floors of many polar lunar craters. As it turns out, the most resource-rich region on the Moon is also the best place to generate a large, low intensity magnetic shield. Acting like the gigantic, but weak, field of Earth, it would protect not just the base habitat, but also the working area for miles around. In the permanently shadowed, cryogenically cold craters at the lunar poles, such a magnetic shield can be created using a long loop of superconducting wire deployed directly on a crater floor. And long wires of high temperature superconductors are now commercially available. The existence of craters, where the temperature is always so cold that superconducting wire doesn't need refrigeration to carry an electric current without any resistance, makes possible and practical the generation of an enormous magnetic shield over a lunar polar base.
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Why a Polar Base?
The Moon is not tilted like the Earth. At the lunar poles, the Sun is perpetually near the horizon, and shadows there are always very, very long. The floors of deep polar craters are always shaded and cryogenically cold. Although the Apollo missions found the sunlit Moon to be bone dry, Harold Urey had commented in 1952: “Near its [the Moon's] poles there may be depressions where the Sun never shines, where condensed volatile substances might be present.... “5 Just as frost can accumulate in your freezer, some of the water vapor that appears from time to time on the Moon (from crashing comets, for instance) becomes trapped in the form of icy damp dust on the floors of permanently shadowed craters.6 Both radar reflection and neutron data give evidence that this ice is actually there, especially in the permanently shadowed Shackleton crater, which is located almost exactly at the South pole of the Moon. The ice frozen on the dust in lunar polar craters has been estimated to amount to many millions of tons. This indigenous water supply is a tremendous resource for a lunar base. And there is more solar power available from the slanting sunlight on the outer walls of polar craters than from the diurnal overhead rays at the lunar equator. In their study of illumination conditions at the lunar poles, Bussey, Spudis, and Robinson discovered that the outer wall of the Shackleton crater is illuminated 80% of the time.7 At the lunar equator the Sun shines only 50% of the time.
And there may be a still more important reason for going to the lunar poles.
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Helium 3 and a Polar Base
There are undoubtedly many scientifically important things to be found on the Moon, but helium 3 is very special and one of the very few—perhaps the only—lunar resource economically valuable enough to be worth carrying home. Common helium has two protons and two neutrons. Its isotope, helium 3, has two protons but only one neutron. This special isotope is extraordinarily hard to obtain on Earth, but polar craters may have the highest concentration of this stuff on the lunar surface and possibly the highest natural concentration anywhere in the solar system. Jupiter has lots of helium 3, for example, but it's diluted to trace levels by the rest of the Jovian atmosphere. Using lunar helium 3 as fuel for thermonuclear power on Earth was first suggested by Wittenberg et al, 8 who calculated the energy it would take to go to the Moon, recover helium 3, and transport it back here. When used to produce energy via fusion of this helium 3 with deuterium (hydrogen that has one proton plus one neutron), their calculations show an overall increase in energy by a factor of 250. For comparison, the energy payback for coal mining is only sixteen to one. Neutrons are not generated by this fusion reaction, and it produces very little residual radioactivity. Naturally, there are lots of technological hurdles to all this. Fusing helium 3 and deuterium is not easy. But bringing lunar helium 3 to the rescue of Earth's energy woes is a wonderful vision, and it's not beyond the realm of possibility.
There is a lot of deuterium on the Earth. The oceans are loaded with it. But helium 3 is very rare on our home world. Most of our helium 3 comes from solar flares, although there are tiny amounts in natural gas. On the Earth, helium 3 from solar flares ends up diluted to trace levels in our atmosphere after the glowing curtains of light from polar auroras have faded away. On the Moon, helium 3 from the Sun collides with the ground and is concentrated on the lunar surface.
Data from the Apollo missions indicates that the lunar helium 3 concentration decreases toward the poles. So, why should there be lots of helium 3 in polar craters? The swirling nature of the charged parti
cle flux from the Sun means that protons and helium ions can still hit the floors of shadowed craters even though sunlight can't. Whether in shadowed or sunlit areas, helium in the wind from the Sun is collected on the Moon because it impacts the lunar surface at several hundred kilometers per second. Even so, it only penetrates to a depth of about 0.2 microns when it hits. That's not much, and in sunlit lunar areas 99% of it is eventually lost due to the high temperatures produced by sunlight. Estimates differ, but the floors of permanently shadowed craters may only receive 10% as much solar wind as the sunlit surface. Even so, they could still have ten times as much helium 3 per gram of lunar soil as the sunlit areas because they keep all they get. Frozen crater floors are the lunar equivalent of the “cold traps” used in high vacuum systems to freeze gas molecules into immobility. The helium 3 in permanently shadowed polar craters could be an energy treasure trove, but a lunar base will be needed to extract it. The men and women working there are going to need radiation shielding.
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Engineering a Magnetic Shield
Nowadays it's popular in designing magnetic shields to use Monte Carlo methods to determine the region that will be protected from particles of different charges and energies. These methods involve a myriad of computations, but approximate answers can be obtained using the method developed by Störmer,9 who found a way to characterize the distance over which protection extends outwards from the wire coil that generates the magnetic field. For a given set of incoming particles, this distance, called the Störmer radius, Cst, increases as the square root of the product NIA, where N is the number of turns of wire in the coil, each wire carrying a current of I amps, and A is the area encircled by the wire. Cst can be increased by steadily injecting ions into the magnetic shield in order to combine electrostatic and magnetic shielding, but this approach requires a continuous power and ion input, and it would also interfere with Moon-to-Earth communications.
Cst decreases as the square root of the momentum of the incoming charged particles, which are moving so fast that calculating their momentum must take into account relativistic effects. For such particles, the value of NIA that gives a reasonable Störmer size is very large. For spaceships that carry onboard the coil of superconducting wire used to generate a magnetic shield, A will be small, so NI must be big. In permanently shadowed polar craters, where the superconducting wires needed to generate the magnetic field can be deployed on the crater floor, A can be big, so NI can be small. This result is important because the energy needed to raise the shield decreases dramatically as A increases. The energy, E, needed to raise the shield isthe energy stored in the magnetic field and is determined by the inductance, L, of the coil of wire and I, the current circulating in it: E = 1/2 L I [2]
With the inductance of a circular coil, plus the current circulating in it and all the complicating relativistic factors caused by high particle velocities, the energy needed to create a magnetic shield can be calculated. The resulting algebra is messy, but the essential result is this: For a given particle velocity, mass, and charge, the energy needed to produce the magnetic shield decreases approximately as the cube of the area encircled by the wire coil used to produce it. This means that superconducting wire deployed around a large area of the lunar surface doesn't need much energy input to give a lot of protection. In going from a circular coil one meter in diameter to a coil one kilometer in diameter, the energy needed to create the shield is decreased by a factor of about one billion. At the same time, the total protected area increases as the area encircled by the coil gets larger, since the protected surface area extends on both sides of the coil wire out to a distance characterized by Cst. The energy needed to protect lots of lunar surface plunges as the area enclosed by the coil of superconducting wire goes up.
It is remarkable that less energy is needed to create a large shield than a small one. And not just the energy per square meter of shielded area, but the total energy also decreases as the coil of superconducting wire encloses more area. A large weak field provides high speed charged particles with long pathways where the forces resulting from their movement through the field can act. Deflecting incoming charged particles in a distance of only a few feet requires an extremely strong magnetic field that takes a lot of energy to produce. Producing intense fields requires wire coils with thousands of turns. The inductance of such coils increases with the square of the number of wire turns. For a field coil that encloses a large area, only a few, or even just a single loop of wire, can produce the necessary shielding, and the circulating current and inductance are low. Remember that the energy to raise the shield increases or decreases as the inductance times the square of the current. Decreasing both inductance and current drives the energy down. For this reason, magnetic shields have the unusual feature that the energy needed to raise a shield of any given degree of effectiveness ends up getting rapidly smaller as the field coil encloses more area. The possibility of deploying an enormous loop of superconducting wire directly on a cryogenically cold crater floor makes it practical to take advantage of this characteristic feature of magnetic shielding for a polar lunar base.
For a circular coil, the protected volume will have a shape like a donut, with the superconducting wires of the field-generating coil inside this donut. To see exactly how all this goes, imagine cutting a donut side-to-side so that the two resulting donut-halves are circular. Lay the superconducting wire along the middle of the cut surface of one of the donut halves so that it forms a circular loop around the donut hole. Then place this donut half cut-side down on the lunar surface. The circular annulus on which the cut face of the donut half sits, as measured by Cst, represents the lunar surface where the shield intersects the ground. The degree of protection increases as the wire of the coil that generates the magnetic shield is approached, but the lunar surface at the center of the donut hole is not protected at all. An extremely large base area can be shielded with very little energy by using a superconducting wire loop deployed around a large area on a permanently shadowed crater floor and used to produce a very large, but weak, magnetic field. A wire coil that enclosed a much smaller area would require hours of the output of a multi-megawatt power station to raise a shield of similar effectiveness because its inductance and circulating current would have to be huge. That's why magnetic shields were not used on the Apollo missions. But only minimal energy is needed if the field coil encloses a large area, because the inductance and the current can both be small and still give the required protection. In the case of 500 MeV solar protons, to raise a magnetic shield with a Störmer protection dimension of 20 meters on each side (40 meters total) of the deployed wire coil takes many billions of joules if the circular coil generating the shield is 50 meters in diameter. But if the diameter of the coil is 20 kilometers, the energy needed to raise the shield is only a few hundred joules, and the circulating current needed is less than 50 amps! It takes only a single superconducting wire to carry a current this low. The total mass of a 50 km length of commercially available high-temperature superconducting wire capable of carrying 100 amps amounts to less than 275 kg.
For a coil that's deployed in a circle 20 km in diameter, the protection zone extends alongside both sides of this coil over the entire 62.8 kilometers of its circumference. With Cst equal to 20 meters, that amounts to more than 2.5 million square meters of the lunar surface. Of course, if a Störmer distance of greater than 20 meters is needed, the current flowing in the deployed loop and the energy stored in the shield must both be increased. As an illustration, the energy needed to generate a shield with a Störmer dimension of 50 meters, using a 20 km deployed coil, is about 10,000 joules, with a circulating current of about 300 amps. A car battery can supply this much energy and current. The beneficial effect of increased field coil size is so great that it makes possible protection against even galactic radiation, whose energy can easily be more than an order of magnitude higher than that of solar protons. Using mass to shield against very high energy galactic particles is
hampered because their interaction with the atoms in the mass shield produces additional penetrating radiation. A thick layer is needed for a mass shield to be effective. Magnetic shielding does not have this problem. That's one reason why the radiation level on the Earth is so low—because we're protected from most galactic radiation by the Earth's magnetic field (and our atmosphere). To produce a shield with a Störmer protection dimension of 20 meters against galactic protons, whose energy is 5 GeV, requires an energy input of about 7,000 joules and a persistent circulating current of 250 amps, if a 20 km deployed superconducting wire coil is used. The numbers for 50 meters of protection are 265,000 joules and 1600 amps. That's getting up there, but it is still achievable.
Importantly, the magnetic field intensity needed by large deployed coils is low, even if a shield against galactic radiation is needed, and only amounts to about that of a refrigerator magnet. Magnetic fields like this present no health hazard. As on Earth, protection is gained from the very large volume of the magnetic field rather than from its intensity.
The reduction in total magnetic shield energy as field coil size is increased is of such enormous magnitude that it brings to mind the far-out possibility of shielding the Moon (or Mars) by using colossal superconducting coils deployed in space. Solar sails or other methods would be needed for stabilizing these coils. Keeping them cryogenically cold by using selective emitter coatings combined with a thin ribbon coil geometry oriented edge-on to the Sun would also be necessary. No doubt there would be other problems, too. Meanwhile, with current technology and the cryogenic temperatures available in craters at the lunar poles, charged-particle radiation shielding can be provided for a very large polar lunar base with little energy and mass cost. The establishment of a polar lunar base will be a monumental achievement. If such a base could help solve Earth's inevitable energy problems, it would be civilization-altering. Magnetic shielding could be a critical factor in making such dreams come true.
Analog SFF, January-February 2007 Page 8