With the price of solar cells under control, the next problem is to find a way to store the energy collected during the day for use at night. Storage of energy is not the same as storage of fuel. For instance, gasoline does not take much space, but after it is burned, the energy can only be stored in batteries and such, which are large and expensive. Storage is not a big problem for rooftop solar because that energy is only a small supplement to the electrical grid, and large power plants are still needed to supply nighttime energy. If solar farms are to provide backbone power, however, storage is needed to cover nights and cloudy days. The same methods described above for wind power are also available for solar. Capacitors or batteries to serve a GW-size solar farm would be prohibitively large and expensive, and making them would greatly increase the fossil footprint. Pumping uphill to get hydro at night is not practical, since deserts have few hills. For lack of a better idea, what is usually proposed is the unproven concept of compressed air energy storage (CAES), as shown in Fig. 3.17. Excess solar energy is used to force compressed air into under­ground caverns or salt domes. Unlike CO2 storage in such natural structures, the gas does not stay there. It is taken out at night, and its pressure is used to drive turbines to generate electricity. As explained under Wind, there is a large energy loss due to the heating of air when it is compressed.

If energy is so hard to store, what about transmitting it from the southwestern USA to the east coast? A Smart Grid for the USA is under discussion for distribu­tion of renewable energies. This is a huge project that cannot be carried out in less time or for less money than developing fusion reactors. The electrical grid is a complex network of high-voltage lines, ranging from 115 to 765 kV, connecting power generators to user sites. It has to respond to sudden changes in power needs,
and its reliability is tightly regulated. Even without the special needs of renewable energies, it has to be modernized in any case because of aging equipment and the especially stringent requirements of digital circuits [3]. Another publication from the Electric Power Research Institute proposes superconducting transmission lines cooled by liquid hydrogen, which would not only lower transmission losses but also supply hydrogen for cars [4]. Even if it makes sense, it will take many years for such a new idea to reach the design, costing, and building stages. Rights-of-way will be legal roadblocks for new transmission lines. Carrying central-station solar power straight from Arizona to New York or from North Africa to Paris requires changing the whole infrastructure.

In the early days of civilian nuclear power, there have been a number of small accidents in different countries, but usually there was little release of radiation. Workers were exposed to it, and four died, one in Yugoslavia, one in Argentina, and two in Japan.83 This does not include deaths in Russia. The two well-known, large accidents are Three Mile Island and Chernobyl.

At Three Mile Island in Pennsylvania, USA, the 1-GW Unit 2, a PWR, had a problem in March 1979. A mechanical failure was compounded by operator error. A pump for the cooling water stopped, and the water got hot, increasing the pres­sure. Automatically, a relief valve opened to let the steam out into the containment building, and control rods dropped in to stop the chain reaction. The relief valve was supposed to close at a certain pressure, but it got stuck open. The hot fuel rods continued to produce steam, and most of the water was lost out the open valve. The operators misinterpreted the signals and thought that there was too much water, so they shut down the pumps, making things worse. Only the bottom of the fuel elements was covered with water. The tops got so hot that the cladding electrolyzed steam into hydrogen, and a hydrogen bubble was formed, preventing water from entering for days. The fuel melted, and 700,000 gallons of radioactive water covered the floors of the buildings [41]. Although the people in surrounding areas were scared and were evacuated, only a small amount of radioactive material escaped. There were no deaths. Statistically, the amount of radiation could have caused three deaths in 20 years, but none has been reported.

The Three Mile Island accident turned a lot of Americans against nuclear power, but compare its safety with that of other energy sources. In 2010 alone, we have had the methane explosion in a West Virginia mine which killed 25 miners, followed by the Deepwater Horizon disaster in the Gulf of Mexico, which killed 11 workers. In each case, families waited and waited for good news about their loved ones, but in vain. The grief is repeated hundreds of times all over the world. The oil leak fol­lowing the fiery destruction of the Deepwater drilling platform was far larger than the Exxon Valdez spill in Alaska and covered hundreds of square miles of the Gulf. Both aquatic wildlife and migrating birds suffered from the environmental damage. Compared to the fossil-fuel industry, a well-regulated nuclear industry is a far safer way to get energy.

The Chernobyl accident is another matter. The dire consequences of the accident were caused by the organization of the Soviet Union.84 Failures were covered by lies. Tight secrecy kept workers from learning from the experiences of others. Those in command made policies without caring about the actual situations they covered. The chief engineer disregarded the protocols anyway. Workers were not well trained to know about the dangers, and they disregarded orders. One of the four reactors at Chernobyl in the Ukraine was being shut down for maintenance. The chief engineer decided to test whether power could still be produced while shutting down. He did not consult the safety personnel or the set rules. The workers turned off safety devices. The control rods were withdrawn to get power while the chain reaction was slowing down due to xenon poisoning. A decrease in cooling water caused the fuel rods to heat up, increasing the power output. The reactor had not been designed to shut down automatically when this happens. There was a runaway reaction and a power surge that ruptured fuel tubes. The hot fuel reacted with water to cause a steam explosion which blew off the 1,000-ton top of the reactor. This broke all the fuel tubes, and a second explosion sent most of the reactor core into the air.

The explosion was like the volcano in Iceland that erupted in 2010, stopping all air traffic in Europe. This time, a radioactive cloud went as high as 10,000 m (30,000 feet), carrying 50 tons of nuclear fuel. The surrounding area was sparsely populated; a nearby village was in great danger. Nonetheless, the man in charge, arriving from Moscow, gave orders not to evacuate because it would create panic. It was a plasma physicist, Evgeny Velikhov, who finally convinced him that people had to get away. Meanwhile a large crew (200,000 in the first year) was trying to clean up the mess. They were walking directly on radioactive material, receiving a lethal dose within minutes. Winds carried the radioactivity all over Europe, but where it landed was random, depending on rain. Most of the volatiles were iodine-131 and cesium-137. The iodine fortunately has a half-life of only eight days, but the cesium lasts for 30 years. The Cs137 carried 500 times more radioactivity than created by the bombs on Hiroshima and Nagasaki.

Statistically, health experts calculate that this accident would cause 30,000 deaths in 20 years. However, this is still a small number compared with other types of accidents. It amounts to a probability of 0.6 deaths per 100,000 people per year. For a well-regulated industry with accidents like that at Three Mile Island, the figure is 0.00007 per 100,000 per year. This is to be compared with 16 for motor vehicle accidents, 0.41 for airplanes, and 5.15 for falls [41]. Falls were considered earlier in the Solar Energy section. Chernobyl was a lesson in bad management, but it will never happen again. Nuclear power poses less risk than almost anything we do.

In the exploration of space, the launching of Sputnik proved the possibility of sending an object into orbit around the earth. Subsequent development of spacecraft led to the landing of man on the moon with Apollo 11, followed by construction of the space station, serviced by shuttles that could re-enter the atmosphere repeatedly. In the development of fusion reactors, the success of early experimental tokamaks is analogous to the success of Sputnik. The simple drawings of tokamaks in previous chapters resemble modern tokamaks no more than Sputnik resembles Apollo 11. A lot of development has occurred, and a lot more has been learned about toka — maks. There have been both pleasant and unpleasant surprises. There is, however, a big difference between the two programs. In space science, the basic physics — namely, Newton’s laws of motion — were already known; while in fusion, the physics of plasmas and of toroidal confinement had to be worked out first. After the initial successes, there was much more to learn about spacecraft, such as their interaction with the plasmas, solar wind, and magnetic fields in the solar system. This chapter describes what we have learned about tokamaks, once they were up and running.

The main coolants available are pressurized water, liquid metals, and helium. Water can be used only for near-term experiments. Reactors will probably need helium gas at a high temperature. The structural materials would be the same as those considered for the first wall: ferritic steels, vanadium alloys, or silicon carbide composites. The lithium can be in the form of solid pebbles of lithium ceramic, a liquid mixture of lead and lithium, or a molten salt called FLiBe [3]. Figure 9.12 shows how a TBM will be inserted into one of the ports in ITER.

The helium-cooled ceramic breeder (HCCB) uses solid material, with the beryllium multiplier and the lithium breeder in separate compartments. Figure 9.13 shows

the parts of an HCCB module. The slabs containing the beryllium and the lithium ceramic are shown in red and blue. Between the slabs are cooling channels through which helium is pumped under 80 atmospheres of pressure [3]. The temperature of the helium can reach 500°C, and the breeder material can reach 900°C. Note that the front of the blanket is part of the first wall. In a reactor, a blanket module can be assembled from submodules, as shown in Fig. 9.14. The thickness of the blanket is about 50 cm and its width about 3 m.

The solid breeding material consists of ceramic pebbles of lithium orthosilicate (Li4SiO4), lithium metatitanate (Li2TiO3), or other similar materials. Techniques have been developed to manufacture identical spherical pebbles which can distribute themselves uniformly. The size should be small, less than 1 mm in diameter, to minimize the temperature difference across the radius so that the brittle spheres do not crack [7]. To extract the tritium, a flow of helium containing some deuterium (D2) or hydrogen (H2) is passed through the pebble bed, and the tritium (T2) is carried out in the flow. The gases are then frozen and separated by distillation, since each has a different boiling point. The important thermal properties of a pebble bed have been measured [8].

A helium-cooled lithium lead (HCLL) blanket uses a molten alloy of lithium and lead called a eutectic. Meaning easily melted in Greek, a eutectic melts at a lower temperature than its constituents. The preferred eutectic is Pb-17Li, contain­ing 17% lithium enriched to 90% Li6. This melts at 234°C, compared with 328°C for lead and 181°C for lithium. In a blanket, the eutectic is heated from 400 to 660°C by the neutrons [3]. Since lead is a neutron multiplier like beryllium (Fig. 9.11), the multiplying and breeding are done in the same liquid. The submodules

Unit backplate

Fig. 9.15 Helium cooling arrangement in an HCLL blanket submodule [ ] in Fig. 9.14 will have circulating paths for the Pb-Li interspersed with channels for the helium coolant. The helium part is shown in Fig. 9.15, and the Pb-Li will go between the cooling plates. The tritium generated in the Pb-Li can be recovered by one of the two methods: permeation or bubbling. Hydrogen has a tendency to diffuse through walls, and tritium is just another form of hydrogen. Inside the blanket, tritium permeation into the helium coolant or other places where it does not belong is to be avoided. Outside the blanket, however, permeation windows can be made to allow hydrogen to go through and mix with a helium flow headed for a tritium separation facility. Alternatively, the Pb-Li can be formed into bubble columns where bubbles of helium capture the tritium in the liquid Pb-Li and carry it to the processing plant.

In earlier work, a molten salt called FLiBe, containing beryllium fluoride (BeF2) and one or two parts of lithium fluoride (LiF) was proposed as a breeder fluid, but now Pb-Li is preferred. The work on FLiBe uncovered the problem of magnetohy­drodynamic flow [9], which also applies to Pb-Li [10]. Both are electrically con­ducting fluids, and when these move inside a magnetic field, electric currents are generated in the fluid; and these currents react back on the magnetic field to pro­duce a drag on the fluid motion. Considering how strong the magnetic fields are in a tokamak, this drag is a serious problem that increases the required pumping power. The drag is less if the flow goes along the magnetic field lines, but eventu­ally the fluid has to cross the field lines to get out of the breeding region.

A dual-cooled lithium lead (DCLL) blanket uses both helium and the Pb-Li itself as coolants. This concept is shown in Fig. 9.16. Since Pb-Li is a liquid, it can be sent to its own heat exchanger and act as its own coolant. Helium is used to cool

Pb-47Li

EUROFER structure
(FW + grids)

Fig. 9.16 Schematic of a dual-cooled Lithium lead blanket module [34]. ODS, EUROFER, and SiC/SiC refer to high-temperature materials described under The First Wall and Other Materials the first wall separately. The flow in the Pb-Li channels is shown in Fig. 9.17 for a case in which the magnetic field direction is into the paper. Computer models have been developed to describe the flow of the conducting liquid, including the buoyancy effect when the temperatures at the top and bottom are different. The eddies in the flow, as calculated, are shown in the inset. Since each module in a tokamak will be oriented at a different angle to the magnetic field, the structure of the flow, and hence the pressure drop, will be different at each location in the machine.

In advanced designs, the helium is eliminated, resulting in a self-cooled lithium lead breeding blanket, in which Pb-Li does all the cooling. It may take a lot of power to pump Pb-Li fast against the drag by the magnetic field. The possibility also depends on the development of the wonder-material SiC/SiC, which can operate at 1,000°C and contain a higher temperature fluid than other materials.

These blanket designs do not show all the auxiliary equipment necessary to operate the blanket. The roomful of pipes, heat exchangers, shields, and instru­ments for a single TBM in ITER is shown in Fig. 9.18. The blanket module itself is only the curved unit at the left, which forms part of the first wall.

Blankets for a full-scale reactor would have to satisfy many other requirements besides cooling and breeding. Maintenance and operation presents serious problems for a reactor designed to operate for over 25 years. The blanket material will have to be replaced many times during the life of the reactor. Solid breeders such as the

TBM system integrated inside port cell 16 of ITER

(systems for both TBMs are shown)

Equatorial floor
only poet 16 shown

Fig. 9.18 Diagram of a proposed test blanket installation in ITER [6]

pebble-bed HCCB have to be physically removed to change the pebbles. In liquid blankets, the Pb-Li can be circulated outside the blanket and renewed without removing the blanket. Eventually, however, blankets will have to be replaced, requir­ing a shutdown. For easier replacement, banana-shaped blankets fitting the contour of the D-shaped plasma have been proposed. These would be lowered from the top of the tokamak during a shutdown, and all the connections to the blanket would have to come from the top. All this has to be done with remote handling, since there will be too much radioactivity for humans to work on the reactor.

Since the blankets are located inside the vacuum, they must be leak proof. Welds must be secure. Inside the blanket there are many interfaces between breeders and coolants, and a leak there would be impossible to fix without removing the blanket. There are also numerous joints in the pipes connecting the blanket to the world outside the vacuum tank. In 2008-2009, the Large Hadron Collider in Geneva suffered from a single leak in the liquid helium system which delayed the startup of the machine for over a year. In 2003, a single piece of loose foam brought down the shuttle Columbia, killing seven astronauts. Accidents happen, and extreme care must be taken in a tokamak reactor, where there are a million places where a leak can occur.

There are also safety issues in the case of an accident, including decay heat and radiotoxicity after shutdown [11]. Recycling and treatment of waste have also to be considered. However, these are not specific to blankets and will be covered in another section.

The first noncircular stellarator may have been the Heliac in Canberra, Australia, but the granddaddy of them all is the LHD in Toki, Japan, shown in Fig. 10.6. Envisioned by Koji Uo while on sabbatical at Princeton in the 1960s and completed in 1998, this machine showed that large superconducting coils producing 30-T magnetic fields could be manufactured and operated reliably for years. The most amazing accom­plishment, however, was the demonstration that the weird, twisting vacuum chamber and similarly complicated magnet coils could actually be manufactured to the required tolerances. Figure 10.7 shows an artistic photograph of the vacuum chamber.

In operation, the LHD has outperformed tokamaks in several aspects. The plasma density has reached 1021 m-3 (1015 cm-3), which is many times larger than the Greenwald limit (Chap. 8). This shows that this unexplained, empirical limit may apply only to tokamaks and can be exceeded in stellarators. The maximum ion and electron temperatures achieved were 13.5 and 10 keV, respectively, though not at the same time. Nonetheless, T exceeds Te in normal operation, as is desirable since it is Г that causes fusion. Beta, the ratio of plasma pressure to magnetic-field pressure (Chap. 8), is an important measure of the quality of a fusion plasma. The beta value of 5% achieved in LHD is higher than is normal for tokamaks. Not all these record-breaking numbers can be obtained at the same time, of course. What counts is the triple product Tut, the simultaneous ion temperature, density, and confinement time plotted in Fig. 8.1. On that scale, the LHD would be at 0.44, at about the middle of the plot. With fueling by pellet injection, discharges an hour long can be produced in LHD when the power is lowered so that Tut is at 80% of its maximum value.

A Hydrogen Economy?

If we were to replace gasoline with hydrogen to fuel most of our cars, here is how it might work.48 Until nonfossil energy sources are available on a large scale, hydro­gen will be made from natural gas. Gas stations would be replaced by hydrogen stations to which natural gas will be delivered. Hydrogen would be generated locally and stored in underground tanks under pressure. Cars will have plastic tanks in their trunks to hold enough hydrogen for 200-300 miles. These tanks have to be under at least 300 atm pressure, but hose connections can safely handle the filling of the tanks. Hydrogen does not explode unless it is first mixed with oxygen. Inside the car, a fuel cell combines the hydrogen with oxygen from air to produce electricity. There is an electric motor, and the car then runs as an electric car, with H2O as the only emission. The fuel cell-electric motor combination is much more efficient than a gas engine, and less energy is used than if the natural gas or hydrogen is burned directly. Wind or solar power can produce electricity to use directly in the electric motor, but batteries need further development and in any case need a long time to charge. Hydrogen serves as a way to carry the energy. It is not burned directly in hydrogen cars. The main problems are the fuel cell, which is very expen­sive, and the sequestration of the CO2 if natural gas is used. Discussion of these subjects will follow. Right now it is not clear whether hydrogen cars or plug-in electrics will ultimately win out as the better solution for clean mobile power.

We have shown that transmuting hydrogen into helium would release a large amount of energy. Let’s be more specific. The first step is to use the easiest reaction possible, which is the following:

D + T ^ a + n + 17.6 MeV.

Remember that D stands for deuterium, a hydrogen isotope containing one proton and one neutron, and T stands for tritium, containing one proton and two neutrons. Alpha (a) stands for a helium nucleus (He4), containing two protons and two neu­trons. There is one neutron (n) left over, which flies off carrying most of the energy released in the fusion, which is 17.6 million electron volts. This reaction is depicted in Fig. 4.3. The intermediate state shown there with five nucleons in it is not stable and immediately breaks up into an a particle and a neutron. The a particle, being ordinary helium, is very stable; and its energy will be used to keep the reaction going. The neutron carries 80% of the energy released (about 14 MeV), and it has to be captured and its energy transformed into heat, replacing the heat we now get from burning fossil fuels to run a power plant. Although neither reaction product is itself radioactive, the neutron can induce radioactivity in the walls of the reactor, and this material has to be buried. We shall see in Chap. 9 that the amount of long — lived radioactive waste is about 1,000 times smaller than for fission reactors. The D-T reaction is the worst of the fusion reactions in this regard, but it is the easiest to start with. Chapter 10 will show advanced reactions which have less radioactivity or none at all.

Fig. 4.3 The D-T reaction

As pointed out before, deuterium is easy to separate out from water, but tritium has to be made in a nuclear reaction. In a fusion reactor, tritium is regenerated in a “blanket” containing lithium. Leaving this Chap. 9 topic aside for the moment, let us see how we can make this reaction go, because it’s not easy. Since D and T have one proton apiece, they each have a positive charge. Like charges repel, so if we fire a beam of deuterons into a tritium target, the D’s will most likely bounce off the T’s without ever getting close enough to combine. Only a head-on collision with energy larger than 280 keV can overcome the electric repulsion (the so-called Coulomb barrier). Once inside this barrier, the nuclear force takes over, and the force becomes attractive instead of repulsive. Most of the time, however, the D’s will bounce off without penetrating the barrier and lose most of the energy used to accelerate them. It is possible to use beams of around 60 keV energy and get net energy out, but not enough to justify the large number accelerators needed to make a dent on the power grid. There is a better solution. And that is not to use beams of particles at all but to heat a hydrogen gas, half in the form of deuterons and half in the form of tritons (tritium nuclei), to such a high temperature that there are always some high-energy collisions that result in fusion. The energy in failed collisions is not lost; it returns to the gas to keep it hot. This hot gas, called a plasma, perks away steadily, releasing enough fusion energy to keep itself hot and generate power besides. That’s what happens in the interior of the sun. The fusion power generated comes out as solar radiation, of which the earth receives a small portion.

It is hard for people to understand why a hot plasma is necessary when you can simply shoot a beam of deuterons from a particle accelerator and hit a solid tritium target with enough energy to penetrate the electric barrier and get the D and T close enough to fuse. Or, one might circulate a beam of deuterons in one direction and a beam of tritons in the opposite direction in a round accelerator. Once in a while there will be a head-on collision and a fusion. But not often enough to pay for the energy used in accelerating the beams! Believe me, many proposals for using beams for fusion have been tried and have failed. Here is an analogy to illustrate how plasma fusion works. Imagine a friction-free pool table which has no pockets at the edge. However, there are pockets all over the middle of the table, and each pocket is surrounded by a hill, like a deep crater at the center of a volcano. The hills represent Coulomb repulsion. A pool player then adds billiard balls randomly, shooting them with insufficient accuracy and speed to climb the hills and get into the hole. Since there is no friction, the numerous balls keep bouncing around at random until one is lost by chance by jumping off the table, whereupon it is replaced by another shot. Since the balls bounce against one another, once in a while, one will undergo several favorable bounces in a row and end up with more

than the average energy. If it has enough energy and is going right toward a crater, it will be able to climb the hill and get into the pocket at the top. This represents a fusion reaction yielding 17.6 MeV of energy. You might have to wait a long time for this to happen, but after the initial energy used to shoot the balls, no more energy is needed other than to replace those lost over the edge. This is the idea of plasma-induced fusion. A small amount of energy is invested in shooting the balls in, and then one waits for a long time before a ball by chance climbs a hill and gets into the pocket. But the payoff in energy is so huge that there is a large energy gain even if it takes many collisions to get one fusion.

The major instabilities encountered in early toroidal confinement research have been controlled. The remaining microinstabilities are of the drift-wave type, which we described in some detail in Chap. 6. They differ only in the energy source that

feeds them and in the collisional process that allows guiding centers to be unglued from magnetic lines. The effect of these instabilities on how long a plasma can remain trapped depends on the type of turbulence that the waves grow into — their nonlinear behavior, as physicists would say. In fluids like water or air, turbulence can the form of swirling eddies. For instance, in the picture of the surface of Jupiter shown in Fig. 7.21a, turbulence driven by winds is visible in the cloud patterns, including the largest eddy, the famous Great Red Spot. In water or air, flows are driven by pressure differences. In a magnetized plasma, flows across the magnetic field are driven instead by electric fields (the aforementioned E x B drift), but can also give rise to turbulent eddies. However, in a tokamak, Mother Nature reveals another of her helpful tricks: these eddies are self-limiting in their sizes! This means that large eddies like the Great Red Spot cannot occur — eddies that could otherwise bring plasma toward the wall rapidly across their diameters.

Referring back to Fig. 6.17, we see that drift waves create poloidal electric fields by the bunching of alternately positive and negative charges. These E-fields cause inward or outward flow of plasma in the radial direction, and the net loss of plasma comes about because the E-fields are phased so that the drift is always outward where the density is high and inward where the density is low. A better picture of these eddies is shown in Fig. 7.22. The distribution of “+”and “-” charges is, as shown in Fig. 6.17, generating the alternating electric field shown by the short red arrows. Together with the toroidal magnetic field, this E-field causes an E x B drift of the plasma in the closed loops or eddies, also called convective cells. The density pattern of the drift wave is displaced with respect to these eddies in such a way that the density is higher (blue) where the drift is outward and lower (red) where the drift is inward. Thus, the net motion of the plasma is outward. The danger is that these convective cells could be long “streamers” in the radial direction, as drawn here, so that the plasma can move a long way toward the wall in each cycle of the wave.

Fortunately, this does not happen because the turbulence takes on a different form as it grows. Alternating drifts in each radial layer automatically arise,

as shown in Fig. 7.23. These are the zonal flows. The flows are E x B drifts driven by “+”and charges on the boundaries of each zone. They break up the large convective cells into small ones, only about a centimeter wide, the size of an ion Larmor radius, so that the rapid convection in each cell can move the plasma only a short distance. The flows themselves cannot remove plasma, since they are parallel to the wall. In the picture of Jupiter taken by the Hubble Space Telescope shown in Fig. 7.21b, one can see zonal flows clearly in the upper half of the picture. In those stripes, the wind blows in alternating directions. The shear in the wind speed at the

zone boundaries causes the turbulence seen more clearly in the bottom half of the picture. The zonal flows in a toroidal plasma, however, are fundamentally different. In the plasma, the zonal flows do not create the turbulence. It is the turbulence that creates the zonal flows! In other words, a zonal flow is an instability that is driven by another instability! Since a zonal flow is the same all around the torus in both the toroidal and the poloidal directions, it takes little energy to set it into motion. There is no need to add angular momentum to spin the flows around the poloidal direction, since the flows are in opposite directions in adjacent layers, so that the net angular momentum is zero. Microinstabilities in a torus develop into a turbulent state that incorporates zonal flows, a type of turbulence that is self-limiting in its eddy sizes. In principle, this should cause anomalous diffusion to be slower than theoretically expected, though this has not yet been shown experimentally.

Zonal flows were seen in many computer simulations of the nonlinear state of microinstabilities and have received extensive treatment by theorists [7]. The tool of computer simulation has greatly advanced progress in fusion in the past decade; this subject will be described shortly. Theories have been proposed on many details of zonal flows, including how a drift-wave instability can drive zonal flows through what is called a modulational instability. Such details have not been verified by experiment, but the existence of plasma flows that do not vary in either the poloidal or toroidal direction has been established experimentally [8]. In two Japanese labo­ratories, one with a tokamak and the other with a compact helical system (a type of stellarator), a sophisticated diagnostic called a heavy ion beam probe was used for this purpose. A beam of ions, usually cesium (Cs+), is accelerated to such high energy that it has a Larmor radius larger than the plasma radius, and so it can be aimed at any part of the plasma. When it gets ionized to a doubly charged state (Cs2+), its Larmor radius gets smaller and its orbit changes. By catching the Cs2+ ions at a particular part of the periphery, it is possible to tell the exact spot inside the plasma where this re-ionization occurred. Then the number and energy of the Cs2+ ions can tell the electron density and electric field at that spot, even if these are fluctuating at a high frequency. With this tool, fluctuations matching the charac­teristics of zonal flows have been detected. However, the predicted connection between the existence of zonal flows and an improvement in confinement time has yet to be quantified in the laboratory.

In principle, what is done to the ions can also be done to the electrons, but the technology is entirely different. The electrons’ cyclotron frequency is in the giga­hertz range, and huge microwave generators are required. The power or current input can be deposited accurately at specific places inside the torus by adjusting the microwave frequency to match the magnetic field at those places. Since micro­waves are carried through waveguides, which are specially sized and shaped pipes, they can be injected through holes in the first wall and do not require an antenna inside the vacuum chamber. The bad news is that electron cyclotron waves cannot penetrate into the plasma from the outside of the torus. A property of these waves is that they must be injected from a high magnetic field into a lower magnetic field. Since the magnetic field is highest in the hole of the torus, the launching waveguide must be located in the cramped space also occupied by the central solenoid and the inside blankets. Waves at twice the cyclotron frequency, which also resonate with the electrons’ gyrations, can get in from the outer, weak-field side; but the higher frequency is more difficult to generate.

The electron cyclotron heating system in ITER calls for 20 MW of power at 170 GHz. This frequency corresponds to the cyclotron frequency at 6.0 T (60,000 G), high enough to cover ITER’s magnetic field of 5.5 T at the inside radius. Although we use microwaves in everyday life, 20 MW at 170 GHz is an entirely different mat­ter. A microwave oven puts out 1 kW at 2.45 GHz using a magnetron so small that we are not aware of its presence. Powerful microwaves are generated by gyrotrons, which work by running ECRH in reverse. In a gyrotron, an energetic electron beam is first produced. It is then injected into a magnetic field, so that the electrons undergo cyclotron gyrations. In doing so, they emit microwaves at harmonics of the cyclotron frequency which are then channeled into a waveguide leading to the toka — mak. The microwaves get their energies from the electron beam, which loses part of its energy. In experiment, the remaining energy is captured in a beam dump as heat. In advanced gyrotrons, the beam can, in principle, be re-injected so that its remain­ing energy can be re-used. Note that the electron beam in a gyrotron cannot be injected directly into a tokamak to heat it because the electrons cannot get through the magnetic field. In a gyrotron, the electrons are injected into the magnetic field from the ends of the field lines. A tokamak, of course, has no such ends; hence the need to convert kinetic energy into microwave radiation and then injecting the radia­tion instead of kinetic energy directly.

High-power gyrotron research began in St. Petersburg, Russia, decades ago. Those that can operate continuously for ITER are being developed in Japan, Germany, and the USA. So far, 1 MW at 170 GHz in a long pulse has been shown to be possible. Figure 9.24 shows the size of such a gyrotron. ITER will need 24 of these to produce the required ECRH power. Figure 9.25 shows a design of a 2-MW gyrotron with superconducting magnets.

Since the gyrotron has to be under vacuum and the waveguide is at atmo­spheric pressure, windows have to be used to isolate the waveguide from the vacuums at both ends. At present, the only material that can transmit the wave power at that frequency is synthetic diamond. Windows 10 cm (4 in.) in diameter have been made and tested for proper cooling. In a reactor, gyrotrons and their windows have to run continuously without failure for months or years between maintenance shutdowns. This constitutes a large step in engineering that has yet to be done.

This interesting device is not really a pinch; it has characteristics of spheromaks, pinches, inertial confinement, and even mirrors. A simple diagram is shown in Fig. 10.33. If you rotate the diagram 90°, it looks like a spheromak (Fig. 10.18), but it has one essential difference. There is no toroidal magnetic field. The toroidal direction is indicated by the ellipses for the current and an ion Larmor orbit. Toroidal coils on the outside create a magnetic field (B-field) going from right to left in the diagram. A toroidal current driven in the plasma creates a B-field oppo­site to the external field. The current is in the same direction as the electron diamag­netic current (Chap. 6), which adds to it. When the current is large enough to cancel the external field, there is a radius R at which the B-field is zero. This is the center of the tubular plasma. It is confined by a purely poloidal B-field. Inside of R, the B-field is opposite to that which was applied. Outside of R, the B-fields from the internal current and the external coils are squeezed up to the vacuum wall, which, being conducting, is a flux conserver. The field lines are divided into two types divided by a separatrix, shown by the dashed line, which represents a field line which leads to a B = 0 point on the axis. The field there has to be zero because it cannot point in two directions at the same time. Plasma inside the separatrix is confined in closed magnetic surfaces; those diffusing outside the separatrix are lost out the ends of the machine. There is therefore a natural divertor; and mirror coils, of which one is shown, can be designed to treat the escaping plasma the same way as in a mirror machine (Fig. 10.27), including the possibility of direct conversion.

Although the field lines on which the plasma lies are closed, this should be better than a mirror machine, but the FRC configuration is highly unstable. There are no helical field lines to link regions of good and bad curvatures, as there are in a spherical tokamak (Fig. 10.12). In fact, there is no good curvature anywhere. The curvature is especially bad at the ends of the machine, as shown in Fig. 10.33. How can an FRC plasma be stable against the main hydromagnetic instabilities? The FRC depends on finite-Larmor-radius effects (Chap. 6). The Larmor radius rLi of the ions at the bad — curvature regions is not negligible compared with the size of, say, the Rayleigh-Taylor instability (Chap. 5). That means that ions can travel across field lines far enough to short-circuit the voltages that the instability generates, keeping it from growing. Electrons, with much smaller Larmor radii, cannot do that; they are tied tightly to the field lines.

How large does rLi have to be? It has to be a sizable fraction of the plasma width, which can be measured by the distance between the center of the plasma and the last closed surface at r. This is R — r. The number of Larmor radii in that width is

s s

then s = (R — rs)/rLi. The parameter s has to be small to keep the plasma stable. In early FRC experiments, s was only 2 or less. However, plasma diffuses at a rate proportional to rLi via electron-ion collisions (Chap. 6), even if it is stable. So s has to be large to get long confinement times, and there is always this struggle to get stability at as large an s as possible.

If instabilities can be controlled, FRCs could have advantages as reactors [17]. They are small and do not require large B-fields. They naturally have high beta, since beta actually goes to infinity at the field null. Longer machines are predicted to be more stable, giving an easy way to get more plasma volume. FRCs have natu­ral divertors and the possibility of direct conversion. Once created, an FRC plasma can be moved into a compression chambers, where pulsed coils can pinch them to higher density and temperature. Research on FRCs has always been on the back burner, so they have not had the support of large computing efforts that tokamaks and laser fusion have had. Expensive equipment like neutral-beam heating has also

not been available. There is precious little information on how the early plasmas were created, but recent success in using rotating magnetic field (RMF) current drive has given the program new impetus. Invented more than 30 years ago by Ieuan Jones and Lance McCarthy at the University of Adelaide in Australia, this method applies a transverse magnetic field that rotates at radiofrequencies in the toroidal direction. Fig. 10.34 shows an end-on view of the RMF lines as they are affected by the plasma. Electrons are entrained by these field lines and rotate with them to the best of their ability, but they are slowed down by collisions with the ions. The rotating field has to have enough power to overcome this drag. There is also a radiofrequency skin depth so that the field does not penetrate all the way into the plasma. In the original Rotomak, the field lines were not closed, so confinement could not be good; but RMF works well in an FRC.

Experiments on the science of FRCs have been carried out in a series of machines in the Redmond Plasma Physics Laboratory of the University of Washington. The most troublesome instability has been the tilt mode, shown in Fig. 10.35. By 1995, stability had been obtained up to s=5 [17]. It was found that energy was lost mainly by radiation due to impurities coming off the walls. Conditions were greatly improved with a new vacuum system in the TCSU machine.

The reduced drag on RMF current drive allowed it to produce denser and hotter plas­mas. The total temperature (T+T) increased about a factor of 4 to »200 eV, the plasma

density about a factor of 3, and the plasma pressure about 50%. Diagnostics are still rudimentary. The plasma pressure can be expressed as a magnetic field Be which has the same pressure. Compared with the RMF amplitude Bw, Be is 4.9 times larger. RMF cur­rent drive in principle allows steady-state operation. These are encouraging results, but the plasma parameters are still very modest. It may be a long time before the conditions of an old reactor study [34] can be realized.

The high betas in FRCs make them suitable for advanced fuels, which require hotter and denser plasmas to ignite. This is being pursued in private industry with a FRC-type machine in which hydrogen ions are injected into a boron plasma for the p-B11 reaction. Tri-Alpha Energy in Irvine, California, was named for the three alpha particles which result from that reaction. The innovation involves adding rotation to the plasma in an FRC and is based on a theory by renowned plasma theo­rist Norman Rostoker [35].