Ions and electrons will collide with one another, but not like billiard balls because they have electrical charges. Like charges repel, so an ion approaching another ion will feel the repulsion well before they come close and will veer off. There is an occasional head-on fusion collision, of course, but these are very infrequent. The result of the more distant collisions is to form the most probable distribution of velocities; namely, the Maxwellian distribution shown in Fig. 3.3. Electrons will do the same thing, only faster because they are lighter and move faster at the same energy. So their velocities will also fall into a Maxwellian distribution. However, it does not have to be at the same temperature as the ion distribution. The way we heat a plasma usually heats one species preferentially. For instance, driving a current through a plasma will preferentially heat the electrons, so that the electron tempera­ture, called Te, will be higher than the ion temperature, T. A plasma can have two different temperatures, Te and T, at the same time, or even more if there are other species in the plasma. It may seem unusual that a plasma can have two temperatures at the same time, but imagine turning on the heat in a cold room. The air will get hot first, while the furniture stays cold. It will take some time for everything to come to the same temperature. Though ions and electrons in a plasma are inter­mixed, they exchange their heat comparatively slowly because they collide infre­quently and have vastly different masses. Plasma particles are always being regenerated as they leave the container, and usually they leave before they can come into equilibrium with other species, so it is normal for T to be different from T.

When an electron collides with an ion, their opposite charges attract, and the electron will orbit the ion the way a comet orbits the sun. These collisions will tend to equalize Te and T, but it takes much longer because an electron is so much lighter than an ion that very little energy is exchanged at each collision. Generally, parti­cles do not stay in the plasma long enough for Te and Ti to equalize, so the tempera­tures are usually different.

What do we mean by a collision when particles do not actually touch? The mag­nitude, so to speak, of a collision depends on how much the particles’ paths have been deflected or how much their energies have changed. In this type of collision at a dis­tance, each particle feels the electric field of the other particle during the time when they are close. This time becomes very short when the particles are moving fast. An electron with 10 keV of energy, for instance, will go past an ion so fast that there is hardly any time for the ion’s electric field to deflect the electron or change its energy. It makes sense, therefore, that a hot plasma, whose particles have large velocities, hardly makes any collisions at all; in other words, it is a superconductor. Even plasmas with only 100-eV temperature can act like superconductors. We call these collision­less plasmas. Being able to neglect collisions makes theory much simpler, and most of the early work concerned collisionless plasmas. In most cases, this was a good approximation, since an electron can travel around a torus many times before it makes an effective collision. Later in the development of magnetic confinement, people finally realized that these weak collisions cannot be neglected after all.

The colorful language of plasma physics cannot compete with the charmed and colored quarks of high-energy theory, but we have so far had bananas, sawteeth, and ELMs. We now have fishbones. These arise from their oscilloscope traces, not from the hunger for better funding. Fishbones were first seen in the PDX tokamak at Princeton during neutral-beam injection [21]. Recall that the most powerful way to heat a plasma is to inject beams of high-energy deuterium atoms. Since the atoms are not charged, they can penetrate the magnetic field and get inside the plasma. Once there, they are rapidly ionized by the electrons and become a beam of deuterium ions of 50-keV energy. Oscillations in the plasma could be seen with several different

diagnostics, and they look like those in Fig. 8.14. Fishbones often occur on the q = 1 surface where the sawtooth oscillations (Chap. 7) occur, and sometimes they can excite the sawteeth and appear simultaneously with them. The bad news is that fishbones cause injected ions to be lost before they have transferred their energy to the plasma. As much as 20-40% of the energy can be lost, greatly reducing the efficiency of this primary heating method.

Beams are notorious in exciting plasma instabilities. As usual, the plasma finds a way to come to thermal equilibrium rapidly by generating an instability. Theorists had no problem in finding a suitable instability for this. Initially, there were two somewhat different theories [22, 23], each having to do with an internal kink mode. In Chap. 6, we described the kink instability that occurs to the whole plasma when too large current is driven through it. A localized current can also drive a kink inside a plasma, and this is what happens in the sawtooth region in the presence of a current of fast injected deuterium ions.

The theories could predict the frequency of the oscillations and the conditions when they would occur. Computations of the nonlinear behavior gave traces very much like the experimental ones in Fig. 8.14b. Subsequent work has cleaned up many of the details of the fishbone instability.

The fact that fast ions can be lost via instability is worrisome not only because of the loss of heating power, but even more so because of the fast helium ions (the “ash”) that are generated in fusion. The helium has to remain in the plasma long enough to give up their energy to keep the plasma “burning.” Fortunately, the theorists can tell us not to worry. Roscoe White et al. [24] have found that there is a regime in a fusion-quality plasma in which neither sawteeth nor fishbones will occur, and this parameter regime is actually larger at higher temperatures and with more fast particles. This has yet to be tested, but there is another mitigating factor. In the next generation of tokamaks, starting with ITER, the plasma will be much larger than the widths of the banana orbits. Since the fast ions are lost with a step size of the order of the banana width, it will take many steps for them to reach the wall. Though not finished, the physics of fishbone instabilities is far enough advanced to tell us that this is not a big problem.

Disruptions

No picturesque name here, because this is a really serious problem. Tokamak discharges are known to disrupt themselves, suddenly stopping and releasing all the energy put into them into the containment chamber. Unless we can stop disruptions from occurring, the entire structure of the tokamak, especially the divertors, would have to be beefed up to absorb all that energy. This is not the kind of accident that can happen in fission, because in fusion no energy is released that has not already been put in; it is just that we do not want it to come out all at once and melt or otherwise harm the tokamak structure. The problem is so serious that a large experimental data base has been accumulated on numerous tokamaks, even in the interim between the two ITER planning documents, the ITER Physics Bases of 1999 [25] and 2007 [26].

To get a DT plasma to fuse, we need to heat it to temperatures of the order of a half-billion degrees. The amount of heat in a large experiment like ITER will be about 400 MJ, the energy of 100 pounds of TNT. The poloidal magnetic field created by the tokamak current will hold another 400 MJ of energy. Fortunately, the toroidal mag­netic field energy, which is much larger, is not released in a disruption unless the toroidal field coils are damaged. Normally, the plasma energy escapes slowly into the divertors, which are designed to handle that heat load; and when the plasma is turned off, the current decays slowly, and the poloidal field energy goes back into the coils that drove the current. In a disruption, all this energy sprays out in a matter of 10 milli­seconds and is hard to handle. What happens to the plasma in a disruption has been caught by the M. I.T.7 group working with the intermediate-size Alcator-C tokamak. In a typical elongated D-shaped tokamak, the plasma has to be kept from drifting up or down with specially shaped coils. When an instability causes a disruption, the plasma moves vertically, as shown in Fig. 8.15, shrinking as it loses its energy and current. In this case, it moves downward toward the divertor, but it could as well move upwards. The time scale shows that the whole event took less than 4 ms.

The damage caused by a disruption can be divided into three parts: thermal quench, current quench, and runaway electrons. In thermal quench, the plasma’s heat is deposited in the walls, vaporizing them in spots. This influx of impure gas raises the resistivity of the plasma, and the tokamak current decays. Even if most of the plasma outflow is channeled into the divertor, there is no time for the heat to be conducted away, and the refractory materials in the divertor — tungsten and carbon — will be vaporized also. In current quench, the fast decrease of the toroidal current will drive a counter-current, by transformer action, in the conducting parts of the confining vessel. Since this counter-current is located inside the strong DC toroidal magnetic field, it will exert a tremendous force on the vessel, moving or deforming it unless it is made sturdy enough. As plasma shrinks toward the divertor, it will drive a “halo current,” shown by the dark arrows in Fig. 8.15, flowing through the conducting parts of that structure. The halo current can be as much as 25% of the original tokamak current; and since that current was flowing along helical field lines, the halo current will try to find a helical path through the conducting parts around the divertor.

The third deleterious effect of disruptions is the generation of “runaway” elec­trons. In Chap. 5, we showed that a hot plasma is almost a superconductor because fast electrons do not make many collisions. The faster the electron, the farther it will go before it collides with an ion. This distance is its free path. If there is a large electric field pushing the electron, its free path can increase faster than the electron is going, and it never makes a collision! It is a runaway and can get up to MeVs of energy before it loses confinement. Of course, this depends on the number of scat­tering centers; namely, on the plasma density. Normally, runaway electrons occur during the startup of the plasma. If the electric field is turned up too high before the density is high, runaways can occur. Machine operators know how to prevent this. In a disruption, however, there is no control. If the density falls below a critical value while a strong toroidal electric field is still on, a horde of runaway electrons will be created, amounting to 50-70% of the original tokamak current. When these hit the wall, they will certainly cause damage. In ITER, the tokamak current will be 15,000,000 A. By comparison, household circuits carry only 15-20 A.

The obvious questions are then: What causes disruptions? How often do they occur? Can they be eliminated? It turns out that disruptions mostly occur when we try to push the envelope. There are known limits to the plasmas that a tokamak can confine. There is a density limit, called the Greenwald density, which we will describe shortly. There is a pressure limit called the Troyon limit. And there has to be enough shear stabilization, as specified by the quality factor q, which has to be above 2 at the edge. When the plasma is pushed too close to one of these limits, a disruption is likely to occur. Exactly how it occurs is not entirely clear. Sometimes two island chains with different numbers of islands can lock onto each other and merge. If there is a detected precursor, this locking can be avoided by setting the plasma into rotation. Sometimes this change in magnetic geometry brings a bubble of cold gas in from the periphery, disrupting the whole plasma. When the density or pressure limits are approached, known instabilities can occur. These are the ideal MHD instability, called the Rayleigh-Taylor instability in Chap. 5, and the neoclassical

tearing mode, which is triggered by finite resistivity, as described in Chap. 6. Here, “ideal” means that no resistivity has to be considered for the instability to occur, and “neoclassical” means that banana orbits are considered in the calculation. Figure 8.16 shows a computer simulation of how an instability can bring cold plasma in from the edge, thus cooling the core.

Up to now, tokamak discharges have been pulsed and not run continuously as in an eventual reactor. An average over all tokamaks shows that 13% of these pulses have suffered a disruption. This would be an unacceptable rate, but these are experi­ments meant to probe the stability of a plasma. In long pulses, lasting many seconds in the large tokamaks such as TFTR and JET, the disruption rate is less than 1% because the machine is run conservatively. In the experimental stage, much depends on the experience of the machine operator. He learns the settings on various controls that will produce a stable discharge. For instance, the currents on the various magnetic coils have to be turned on at the right time and increased at the right rate, and the heating power from various sources have to come on at the right time. Operator experience is valuable in the use of almost any machine; snow plows, cranes, and ordinary cars, for instance. Even in the use of a toaster, one sets the darkness level intuitively depending on the dryness of the bread. Nonetheless, in a reactor even one disruption would be disastrous, and methods must be found to eliminate them.

This task is being tackled on three fronts: avoidance, prediction, and ameliora­tion. As already shown in experiment, disruptions can be avoided if the plasma parameters are not pushed close to the instability limits. As shown in Fig. 8.17, these limits have been extensively tested, and the occurrence of disruptions from this cause is predictable. The quantity BN is a measure of the plasma pressure, and stable discharges are all below the theoretical limit, with disruptions occurring when the limit is exceeded. Prediction of imminent disruption can be obtained from many sensors, for instance of magnetic precursor signals; and neural net­works have been successfully used to integrate these signals to give a definite warning of an oncoming disruption. After many trials, these networks can be

trained to suppress false positives. To stop a disruption from occurring, automatic controls can change such parameters as the plasma density, the toroidal current, or the plasma elongation; but this response may be too slow. A faster method would be to drive electron current with electron cyclotron waves in order to change the current profile, and thus the q profile, to a more stable shape. Once an unavoidable disruption starts, there are still ways to ameliorate the damage. For instance, a massive injection of a gas such as neon or argon can reduce the halo currents by 50% and the electromagnetic forces by 75% [26]. Raising the plasma density by about two orders of magnitude this way would also suppress runaway electrons. As tokamaks get larger, the damage from disruptions can be expected to get worse, because the energy released varies as the cube of the radius (i. e., the volume), whereas the energy has to be absorbed by the surface area, which varies only as the square of the radius. On the other hand, the disruptions will evolve more slowly, giving more time to control them.

For tokamaks, the problem of disruptions is receiving a great deal of attention because of its importance. However, tokamaks may not be the machines ultimately chosen for fusion reactors. Stellarators, which do not need large currents, do not suffer from disruptions. The reason that tokamaks are now prevalent is that they gave the best initial results, and there has not been enough money to study other toruses to the same extent. The next generation of tokamaks — the ITER — will allow

us to study a burning plasma, one in which the helium products can be used to keep the plasma hot. After that, we still have a choice; we are not stuck with the tokamak if disruptions continue to be a problem.

In 1995, noting the inadequacy of the IFMIF for blanket development, an interna­tional team headed by Abdou [23] proposed a high-volume plasma-based neutron source. A tokamak, naturally, was the best choice for a neutron source that

could cover large areas for blanket development. The group considered both superconducting and normal-conducting toroidal field coils, and it was found that coils made of a single turn rather than multiple windings of copper resulted in a smaller device. This is shown in Fig. 9.31. The major radius is only 80 cm and the toroidal field only 2.4 T; yet the plasma current is 10 MA and the neutron wall loading can be as large as 2 MW/m2. The last number is indicative of how well the device can duplicate the damage to materials in a reactor like DEMO. This is done well even though the volume neutron source (VNS) is only 0.5% of ITER in vol­ume, 2% in wall area, and 4% in fusion power produced. Significantly, the group did a risk-benefit analysis comparing the ways to obtain an 80% confidence level for DEMO to have, say, 50% availability, taking into account the mean time between failures and the time for repairs. Needless to say, operating ITER with VNS wins hands down over ITER alone. VNS also uses much less tritium in the process. The incremental cost is small: the total of capital cost and operating cost over the life of the machine is $19.6B for ITER and $24.4B for ITER plus VNS.

Direct drive is what we have pictured so far: a spherical target is compressed by laser light impinging on it uniformly from all directions. The main problem is that the laser beams must have no hotspots that can cause Rayleigh-Taylor instabilities to develop. Research on direct drive is the main mission of the Omega laser in the Laboratory for Laser Energetics in Rochester, New York. After years of trials, optical tricks have been devised to produce beams of the required uniformity.

Indirect drive is considerably more complicated. The laser is first fired into a cylindrical cavity called a hohlraum, German for “hollow space.” Upon striking the inside wall of the hohlraum, which is usually made of gold, the laser light generates intense X-rays. The capsule in the center is bathed in a sea of X-rays, which com­press it uniformly. Because of their high frequencies, X-rays are not subject to parametric instabilities. However, the laser beams must enter the hohlraum through a small hole in either end. Any stray light that hits the side of the holes will generate plasma and excite parametric instabilities there. Figure 10.47 is a view of a gold hohlraum, and Fig. 10.48 is an artist’s rendering of laser beams entering a hohlraum with a capsule in the center.

Indirect drive, the main emphasis of the programs at Livermore, is known to work well in bombs, but it is much more complicated for fusion than direct drive is. The hohlraums are hard to make, and the capsules have to be suspended at the center. (For this, there has been talk of using spider-web strands, for which there is no man-made replacement.) The hohlraums have to be shot to the center of the target chamber because the DT would melt if they were dropped slowly. Even then, cooled holders, shown in Fig. 10.49, have to be used to keep the hohlraum at cryo­genic temperature during its transit through the chamber. The holders also help protect the hohlraum from the force applied to accelerate them. Fast ignition is a new complication. To achieve better efficiency, this new method uses a very short prepulse focused with a cone (Fig. 10.50) to ignite the DT gas at the center of the pellet. The fusion energy from that burn helps to ignite the main fuel.

Imagine the sequence of each shot. A laser pulse is generated in an oscillator and is divided into 196 beamlets, each of which is passed through numerous amplifiers and optical switches in a 300-m path until the total energy exceeds 1 MJ. These beamlets form 48 beams, which the switch yard sends into the target chamber, shown in Fig. 10.51. Each beam is focused onto the target with micron accuracy in space and nanosecond accuracy in time. For indirect drive, the beams are divided

Fig. 10.50 Diagram of a fast-ignition hohlraum [44]

into two bunches, each entering the hohlraum at one end. The beams must not spill over onto the edges of the holes, or else they would make plasma and block the entrance. The cylinder must be aligned perfectly with the beams. In fast ignition, the hohlraum must also be in the right rotational position for the cones to be

aligned. After the shot, everything is vaporized, and the chamber has to be cleared for the next shot. In experiments, the targets are rigidly held by an arm, and successful implosions of the pellet have been achieved.

If one were to build a solar power plant to compete with coal or nuclear plants, a number of problems have to be overcome: cost, transmission, storage, and energy payback time. Solar shares with wind the problems of transmission and storage, but wind is cheaper. Solar thermal has an easy way to store energy for short periods, but this is not available for solar photovoltaic. Let us first consider the problem of cost. Solar cells made of silicon are expensive, but nonetheless 90% of installed cells are made of silicon because those were invented first. The fastest growing market nowadays is in thin-film solar cells, which are much cheaper. Led by First Solar of the USA, rapid buildup of solar power in Germany, China, and the USA is being done with thin-film cells.

To compete with standard energy sources in cost, the magic number of $1/W of peak installed power is sometimes quoted. Silicon cells have been working their way down in cost but are still far from this goal. Thin film, however, may have already reached “grid parity.” Where does this magic number come from? A rough calculation is given in Box 3.2 to show that it is quite reasonable.3435 The diluteness of sunshine means that central solar power would require lots of acreage. Box 3.3 shows that a solar plant generating the same power as a coal plant would occupy at least 100 km2 (10,000 hectares or 24,700 acres). Figure 3.28a shows what a solar farm looks like. It is a 100-hectare, 14-MW plant opened in 2008 in southern Spain. The 120,000 panels can handle 23 MW of peak power. Figure 3.28b shows an aerial view of the area, which was cut out of sunny wine-growing country. This amount of land is necessary to supply electricity for a small town of 20,000 homes.

Box 3.2 Price of Solar Cells for “Grid Parity” [4] [5]

Box 3.2 (continued)

which is three times higher. However, $1/W is the cost of the solar cells only. The cells have to be mounted, transported, and installed, and substa­tions have to be built to convert the low-voltage DC from the cells into high — voltage AC for the grid. Some mechanism must be built to store the energy for nighttime use, and long transmission lines have to be built to carry the electricity from the desert to population centers. The price for thin-film cells is reported to be as low as $1.18/W in 2009.35 However, First Solar executives estimate that the price of $1/W may have to be halved before grid parity is achieved.

Box 3.3 Covering the Desert with Glass

A typical large coal or nuclear plant produces 1 GW of electricity. How much area would a comparable central solar photovoltaic plant take up? Using the figure of 200 W/m2 given above for average solar radiation, we multiply by a solar cell efficiency of 8% to get a net power of 16 W/m2 from thin-film solar panels. More power is lost in the electronics and the inability to tilt the panels economically to follow the sun. A more realistic estimate for net power may be 10 W/m2 for a power plant. At this rate, a 1-GW power plant would require 100,000,000 m2 of space, the area of a square 10 km (6.25 miles) on a side. How much does it cost to cover such an area with solar cells? At $1 per peak watt or $5 per average watt, 1 GW would cost $5 billion for the cells alone. Compare this with covering the desert with other materials. Cheap plywood costs about $20 for a 4 x 8 foot sheet, 3/4-in. thick. This works out to $6.73/m2, or $670 million for 100 million m2, only about seven times less. Cheap win­dow glass costs about $58/m2 or $5.8 billion for 100 million m2. This is more than the $5 billion for solar cells! To produce photovoltaic cells at $1/W would be a remarkable achievement. Solar cells, which are glass coated with multiple delicate layers of semiconductor material, with electrodes, have to be manufactured at less cost than the retail price of ordinary glass!

With prices near grid parity, industrial investment in solar panels is expanding so fast that the numbers of dollars and megawatts given now will change rapidly. China is the largest manufacturer of solar panels, 99% of which are exported. China had only 140 MW of photovoltaic cells installed in 2009 but has plans to expand to 20 GW (gigawatts or thousands of MW) by 2020.36 The USA plans to have 5-10 GW installed by 2015. Spain added 2.3 GW in 2008, catching up with Germany’s 5.8 GW already in place.37 First Solar has ramped production to 192 MW/year, but at this rate many manufacturers will have to participate in the growth of central-station solar photovoltaic.

Plutonium is very good for making a bomb. It does not need enrichment. Uranium has to be highly enriched for explosive purposes, and gas diffusion plants are so large that a terrorist would have to be quite an industrialist to build one. It is easier to steal plutonium. Breeder reactors make plutonium. Recycling nuclear waste also recovers plutonium and makes MOX. Places where plutonium is made or trans­ported have to be heavily guarded.

The development of gas centrifuges has posed a new problem [43]. These devices are relatively small and much more efficient. The separation factor is 1.2—1.5, compared with 1.004 in gas diffusion. Uranium has to pass through a cen­trifuge only 30-40 times before it reaches weapons grade. It would take many times more in gas diffusion. The uranium is in the form of UF6 in gaseous form. It has to be under partial vacuum so that it does not solidify and gum up the works. This means it cannot leak out. Centrifuges are small enough that a hundred of them can be installed in a building that looks like any other industrial building. Centrifuges can be connected in series so that the output of one goes into the next for further separation. A cascade of over 100 centrifuges can be designed to optimize the num­ber used at each stage of enhancement. One cannot prevent the construction of such a cascade for peaceful production of 5% U235 for power plant. The problem is that the cascades can be reconfigured in a few days to produce weapons-grade uranium. For instance, the output of 5% U235 from two-thirds of the cascades in a plant can be sent to the remaining one-third for further enrichment to 90% U235. The power used in either case is only about 160 W/m2, compared with 10,000 W/m2 in gas diffusion, so the clandestine activity cannot be detected by the power consumption, which is like that of any well-lighted building.

India and, in response, Pakistan were the first to use gas centrifuges. This is the reason for the recent attention given to Iran for its construction of an isotope separa­tion facility. The danger exists whether or not nuclear power is used for energy.

Before leaving this basic description of a tokamak, there is one more essential part that needs to be described: the vertical field. A ring of hot plasma will try to expand. Its internal pressure will push outwards so as to make the cross section fatter, and we have countered this force with a strong toroidal magnetic field. However, the plasma pressure will also tend to make the entire ring expand in radius, as shown in Fig. 6.19. The toroidal field is not good at restraining this motion because it is weaker on the outside of the ring than on the inside. Furthermore, the toroidal current in a tokamak creates a hoop force that also pushes on the ring to expand its major radius. This force arises from the magnetic field that the plasma current generates. This field is also stronger inside the hole of the torus than outside, so that its magnetic pressure is outward. Fortunately, these hoop forces are easily balanced by applying a small magnetic field in the vertical direction. Remember that in a tokamak there is always a current in the toroidal direction to give the field lines a twist. This current is mostly carried by the electrons. The Lorentz force on a moving charge, described in Chap. 4, is perpendicular to both the velocity of the particle and the magnetic field. By superposing a magnetic field in the vertical direction, either up or down, depending on the direction of the current, the tokamak current creates a Lorentz force that pushes the plasma ring inwards, toward the center of the torus.

Note that this effect is different from all the plasma drifts that we discussed previously. Those concerned individual particle motions; it did not matter how many particles there were. Here, we are considering the immense pressure of a hot gas.

VERTICAL-FIELD COIL

*- INWARD FORCE

EXPANSION

CURRENT

VERTICAL B-FIELD

Thus, there are three main types of fields in a tokamak: the toroidal field generated by poloidal coils; the poloidal field generated by a plasma current; and a vertical field generated by large toroidal coils above and below the torus. These vertical- field coils can be combined with the coils that drive the plasma current, as will be described in the next chapter, so they do not always appear as a separate set.

Deuterium and tritium are not the only fuels in fusion; lithium is needed for breeding tritium, which occurs only in minute amounts in nature. Lithium is an abundant element on earth, occurring in two isotopes, 92.6% Li7 and 7.4% Li6. (The super­script is the atomic weight, the total number of protons and neutrons in the nucleus.) Lithium-6 is the more useful one and can easily be enriched to 30-90% for use in a blanket. A 1,000-MW fusion plant will consume 50-150 kg of tritium a year, much more than can be supplied by other sources, such as fission reactors. To generate this amount of tritium in blankets, less than 300 kg of Li6 will be needed by each reactor per year. About 1011 kg of lithium is available on land, and 1014 kg in the oceans. If all the world’s energy is generated by fusion, the lithium will last 30 million years [6]. Deuterium will last even longer. There are 5 x 1016 kg of deuterium in the oceans, and at the rate of 100 kg per reactor per year, that will last 30 billion years! That’s what we mean when we say that fusion is an infinite power source.

The way tritium is made from lithium-6 is shown in Fig. 9.10. The neutron, which started out at 14-MeV energy, has been slowed down by collisions with a moderator material and collides with a lithium nucleus, breaking it into an alpha (a) particle (helium nucleus) and a triton (tritium nucleus). Together, these carry the 4.8 MeVs of energy which is gained in splitting the lithium nucleus. This energy, as well as the neutron’s energy, is transferred to a liquid or gas coolant and eventually transferred to steam for generating electricity. The n-Li7 reaction is the same, except that a slow neutron is left over which can undergo another tritium-producing reaction. The n-Li7 reaction works only with fast incoming neutrons, however.

The problem with this scheme is that not enough tritium is produced, since only 20-40% of the neutrons actually react with the lithium [3]. Some of the neutrons are lost through gaps in the blanket needed for plasma heating and measuring equipment. Some are lost by striking support structures instead of the lithium­bearing material, and a few are lost by passing through the whole blanket. To make up for this, there are fortunately neutron multipliers, mainly lead (Pb208) and beryllium (Be9). These can yield two neutrons for each incoming one. The reaction for beryllium is shown in Fig. 9.11.

Blankets will contain lithium, lead, beryllium, and a structural material; but the main problem is to cool them to take out all the heat that is the power output of the reactor. Blanket designs differ in the way they are cooled and in the form of lithium that is used. To show what is involved, we shall describe three of the leading proposals that have been worked out in detail.

The largest programs that kept stellarators alive during the tokamak era were the Wendelstein program in Germany and the large helical device (LHD) in Japan. How stellarators look nowadays is a far cry from the first primitive devices. A schematic of the magnet coil structure in a classical stellarator is shown in Fig. 10.2. The circular coils generate the toroidal field, and the helical coils add the poloidal field. The number of conductors on a minor circumference determines the periodicity of the helical field. The magnetic island structure is fixed externally and not by the internal plasma current. Note that the plasma is no longer circular; it follows the helical structure of the coils.

Now imagine that the circular and helical coils are combined into individual coils that produce the same magnetic fields. We then have the structure shown in Fig. 10.3, which is a diagram of Wendelstein 7-X, the newest stellarator being con­structed in Greifswald, Germany (formerly East Germany). These coils are easier

to assemble, since the poloidal-field coils do not have to be threaded through the toroidal-field coils. To conserve magnetic-field volume (which is costly), the coils are also shaped to conform to the shape of the plasma.

Design of the coils can be done with computers, but these unusual coils have actually been constructed in special jigs. The coils are of superconducting NbTi cooled with liquid helium. Not all the coils are different, of course. There will be seven different types, 10 of each, and 70 coils overall. Figure 10.4 shows two of these being lifted. The vacuum chamber will also conform to the plasma shape; a section of it is shown in Fig. 10.5. This will link the coils together and have to be assembled with them.

Wendelstein 7-X is a very large and complicated machine to be finished in 2014. Plans are to reach 30-min pulses with 40 MW of heating power, reaching condi­tions approaching those in ITER but only with aneutronic fuels.

Research on space science, astronomy, and high-energy particles has produced incred­ibly detailed knowledge of our environment on both macroscopic and microscopic scales. It has been a long journey for Homo Sapiens to have evolved from simple food gathering to these intellectual heights. This knowledge, however, will be of little com­fort if we cannot find the means to assure the preservation of our species.

We have benefited from the discoveries made by adventurers driven by the urge to explore the unknown and to reach the inaccessible, even at great risk or expense. Magellan, Columbus, Roald Amundsen, Edmund Hillary, Roger Bannister,

Neil Armstrong… One climbs Mt. Everest because it is there. To shrink from pursuing the goal of unlimited energy borders on cowardice.

We close on a philosophical note. We have been incredibly lucky. Our planet settled at just the right distance from the sun so that H2O, a very stable molecule, is in liquid form most of the time, forming the basis for life. As plant life lived and died, its fossils lay buried for millennia as human life developed. This legacy of fossil energy allowed humans to form a civilization and develop brains that could think abstractly and explore our surroundings and the whole universe. Our intel­lectual capacity grew to such an extent that we could design and make computers that someday can do the thinking for us. The energy source that allowed all this to happen will soon be depleted; but, luckily, we now have the smarts to create our own energy source. But do we have the wisdom to actually do it?

[1] For instance, C. Seife, Sun in a Bottle, The Strange History of Fusion and the Science of Wishful Thinking (Viking Books, 2008).

[2] Numbers in superscripts indicate Notes and square brackets [] indicate References at the end of this chapter.

F. F. Chen, An Indispensable Truth: How Fusion Power Can Save the Planet,

DOI 10.1007/978-1-4419-7820-2_2, © Springer Science+Business Media, LLC 2011

[3]Numbers in superscripts indicate Notes and square brackets [] indicate References at the end of this chapter.

F. F. Chen, An Indispensable Truth: How Fusion Power Can Save the Planet,

DOI 10.1007/978-1-4419-7820-2_3, © Springer Science+Business Media, LLC 2011

This is a little complicated because “$1 per watt” refers to watts, which are not units of energy. We have to take into account that kilowatts give instanta­neous power, while electricity costs are given in units of kilowatt-hours, which are energy units. A kilowatt-hour is the amount of energy generated by a 1-kW source of energy in an hour.

As deduced earlier, one peak kW of solar power yields an annual average of about 200 W as sunlight varies from day to night and summer to winter. This is the same as saying that the Peak-Equivalent Hours per Day is about five. So at $1 per peak watt, 1 kW of peak power would cost $1,000; and

[5] kW of average power would cost about five times as much or $5,000. For this much investment, how many kilowatt-hour do we get? Well, that depends on the life of a solar cell. There are 8,766 hours in a year; and if we assume a lifetime of 20 years for the cells, they will last about 175,000 h. Dividing $5,000 by this, the cost of solar electricity would be $0.03/kWh, compared with $0.10/kWh for average electricity cost in the USA in 2009,34

[6]Numbers in superscripts indicate Notes and square brackets [] indicate References at the end of this chapter.

F. F. Chen, An Indispensable Truth: How Fusion Power Can Save the Planet,

DOI 10.1007/978-1-4419-7820-2_4, © Springer Science+Business Media, LLC 2011

[7] Numbers in superscripts indicate Notes and square brackets [] indicate References at the end of this chapter.

F. F. Chen, An Indispensable Truth: How Fusion Power Can Save the Planet,

DOI 10.1007/978-1-4419-7820-2_6, © Springer Science+Business Media, LLC 2011