Category Archives: An Indispensable Truth

Benefits of Nonaxisymmetry

Tokamak plasmas are basically symmetric around the major axis. They may have D-shaped rather than circular cross sections, but they still look the same from any direction. The figures here show that stellarators are far from symmetric. Instead of using the plasma current to shape the plasma, external coils are used, and these can produce shapes that cannot be formed by plasma current alone in a self-organized tokamak. It is precisely the lack of self-organization that gives stellarators their advantage [11]. Nonaxisymmetric shaping can be used to improve plasma stability, control ELMs, and eliminate disruptions. Indeed, the ELM coils being added to ITER to suppress ELM instabilities do so by spoiling the axisymmetry. In DEMO, the bootstrap current is relied on to supply at least 80% of the plasma current. This is extremely difficult to produce and control when self-organization is strong. In stellarators, a large plasma current is not at all necessary, since the rotational trans­form is generated by external coils.

In addition to their suitability for steady-state operation, stellarators have some unexpected advantages as reactors. Very small errors in the magnetic field (0.01%) have been found to cause problems with plasma confinement. Originally, stellara — tors’ problems were believed to be due to magnetic errors, but it has been found that once axisymmetry is broken, the wild shapes shown above are actually less sensi­tive to magnetic errors. Data from all stellarators have been found to follow a scal­ing law and fall on the same curve, as shown in Fig. 8.21 for tokamaks, so that extrapolation can be used to design larger machines. In addition, higher density and beta values have been achieved in stellarators. A purported benefit [11] of higher density is the formation of a MARFE (Multifaceted Asymmetric Radiation From the Edge), a “detached” layer which forms when plasma recombines before reach­ing the divertor. The energy is then radiated away before it reaches the divertor, sparing the divertor of the large heat load. The energy, however, has then to be taken up by the first wall. The advantages of stellarators come at a price: the dif­ficulty of making and assembling the weirdly shaped coils and vacuum chambers; but this technology has already been demonstrated.

How to Carry Hydrogen [29]

Pound for pound, hydrogen carries three times the energy of gasoline, and fuel cells can use this energy much more efficiently than can an automobile engine. However, if we carry hydrogen as a gas in a 20-gallon gasoline tank, there is only enough energy to drive the car 500 feet. There are two ways to carry more hydrogen: liq­uefy it or compress it. Hydrogen turns into a liquid at -253°C or just 20° above absolute zero. Needless to say, it takes a lot of energy to run the cryogenic equip­ment to cool to this temperature. Even if the tank in the car is very well insulated, the hydrogen will boil off slowly overnight. In use, it has to be heated rapidly to feed the fuel cell at a rate depending on the speed of the car. On top of this, each liter or gallon of liquid hydrogen has only 30% the energy of an equal volume of gasoline. It makes more sense to compress the hydrogen.

Scuba tanks and laboratory gas cylinders are heavy. For cars, light-weight tanks made of carbon fiber composites have been developed to hold pressures as high as 10,000 psi (pounds per square inch) or 69,000 kilopascals, which is 700 times atmospheric pressure. Normal would be about 5,000 psi, which is higher than in scuba tanks. The cost of such a tank would be at least ten times higher than for a gasoline tank of equal volume. Regardless of this, can the tank be large enough to power a car for 300 miles (480 km)? A back-of-the-envelope calculation of this is given in Box. 3.6. Squeezing the hydrogen takes energy, most of which shows up as heat of compression. The compressing has to be done beforehand, since the hydrogen has to cool. Otherwise, not enough can fit into the tank. When the hydro­gen is released for use, it will be too cold for the fuel cell and has to be heated up.

Under development are ways to store hydrogen in solids. Metal hydrides can absorb hydrogen like a sponge under pressure and then release it under heat when the pressure is relieved. As shown in Fig. 3.50a, the hydrogen molecules go between the atoms of the solid, so it can hold 150% more hydrogen than an equal volume of liquid hydrogen [29]. Unfortunately, the chemicals found so far are either too heavy, react too slowly, or require too high a temperature. Some can absorb only 2% of their own weight in hydrogen, even without the pressurized container. The fuel stored this way for a 300-mile trip would weigh half a ton [29]. Magnesium hydride can store 7.6% of its weight, but needs an inconvenient tem­perature of 300°C. The most promising ones are complex hydrides combined with a “destabilizer.” For instance, lithium and magnesium borohydrides (LiBH4 + MgBH4) will combine into two other hydrides and release hydrogen at a low temperature [30]. This can hold 8.4% of hydrogen by weight (Box 3.6). The reaction is reversed when hydrogen is added under pressure at a filling station. Unfortunately,

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Fig. 3.50 Schematics of (a) a destabilized hydride [30] and (b) a metal-organic framework [31] for trapping and storing hydrogen

Box 3.6 Carrying Compressed Hydrogen in a “Gas” Tank

The energy content of a gallon of gasoline is about the same as that of 1 kg of hydrogen, so 1 gallon » 1 kg H2. (In metric units, it is not as convenient: 1 L » 0.12 kg H2.) Say it takes 20 gallons of gasoline to go 300 miles. Since fuel cells are more efficient, it would take not 20 kg but only, say, 8 kg of H2 to drive a car that far. From high-school chemistry, we remember that a mole of gas occupies 22.4 L, so there are 2 g of H2 in 22.4 L. The density at stan­dard conditions is then 2/22.4 = 0.089 g/L. At 10,000 psi (700 atm) com­pressed hydrogen at room temperature would have a density 700 times higher or 63 g/L. Eight kilograms would then occupy 8,000/63 = 128 L or about 34 gallons. So to go as far as a normal car, a hydrogen car would need a 70% bigger tank, not including the mechanisms for handling the compressed gas.

There is also the question of weight. The US Department of Energy has set a goal that the weight of a tank should weigh no more than 17 times the weight of the fuel. (The fuel weight is more than 6% of the tank weight.) Hydrogen tanks so far are 25-50 times as heavy as the fuel.

the reaction rate is too slow to be useful even though the material is in the form of a fine powder to expose large surface area and reduce the path for heat conduction.

A promising new material called metal-organic frameworks (MOFs) has been invented by Yaghi [31]. These are extremely light-weight chemical structures that act as nets to trap larger molecules, as illustrated in Fig. 3.50b. Just like a net, a MOF has struts linked together with strong bonds, forming a scaffold to enclose a large space.

image147This atomic net has the largest area per unit weight ever obtained: 4,500 m2/g. That means that a paper clip’s weight of material can cover a football field. With consider­able chemical derring-do, hundreds of different kinds of MOFs have been created for different purposes. For storing hydrogen in cars, one liter of the compound MOF-177 can store 62 g of H2, exceeding the 6%-by-weight rule in Box 3.6. However, this has been done so far only at 77 K (kelvin: degrees centigrade above absolute zero). This is liquid-nitrogen temperature, easy to get in the laboratory but hard to maintain in a car, though much easier than the 20 K of liquid H2. A MOF that works for hydrogen at room temperature could get to 5% H2 by weight, but it is not easy to manufacture on a large scale. Another type of compound called COFs is suitable for that, and research is proceeding to make those work at room temperature. COFs can also help with carbon capture in coal plants. A tank filled with MOFs can hold nine times as much CO2 as one without MOFs [31]. Other compounds called ZIFs can actually selectively capture the CO2 going up a smoke stack.

Chemical storage of hydrogen is an active research area in laboratories, but noth­ing works well enough so far to proceed to the next step of engineering large-scale production.

Plasma, the Shining Gas

At this point, we should define what “hot” means. When a gas like air or steam has a temperature, it means that the velocities of the molecules are spread out in a particular way, known as a Maxwellian distribution. This is the same bell-shaped curve, called a Gaussian, that teachers use to grade exams. Gaussian and Maxwellian mean the same thing. Physicists tend to use Maxwellian while mathematicians use Gaussian. Figure 4.4 shows such a curve representing the relative number of hydrogen ions having different velocities in a gas at about 10,000 K.2 When a material is in thermal equilibrium, it has such a “Maxwellian” distribution. The temperature is proportional to the width of this curve, so the velocities are higher at higher temperature. By raising the temperature, we can assure that there will be enough D and T ions in the “tail” of the distribution with enough energy to fuse. The “tail” is either end of the Gaussian curve, far from the center, where there are few particles of very high velocity. The ones that collide without fusing go back into the body of the distribution. In our billiard ball analogy, those would be the balls that go up a hill and come down again without falling into the hole. Multiple collisions

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automatically maintain the shape of this most probable distribution. That means that the energetic particles in the tail which are lost in fusion reactions are replen­ished by successive favorable collisions. The collisions are random, so a particle can gain or lose energy each time. Only a fortuitous sequence of energy-gaining collisions can get a particle to high energy; that is why there are so few of them in the tail. Fusion reactors will require gas temperatures over 100,000,000 K!

At these temperatures, or even at 20,000 K, which is the temperature of the electrons inside a fluorescent light bulb, the gas no longer resembles the gases that we are familiar with, like air, helium, or CO2. Molecules become dissociated, and atoms become ionized. An oxygen molecule O2, for instance, first becomes dissoci­ated into two O atoms, and then each O is ionized into an ion (O+) and an electron (e-). Normally, an oxygen nucleus with charge +8 is surrounded by eight electrons, so that the atom as a whole is neutral. When one of the electrons is stripped off by colliding with a free electron, it becomes free, and the nucleus is left with an excess charge of +1. The gas is now a gas of ions thoroughly mixed with a gas of electrons, the way NaCl molecules are mixed with H2O molecules in a saline solution. But there is a big difference: this gas mixture is electrically charged. The ion fluid is positive, and the electron fluid is negative, so there can be electric fields inside the mixture. This type of electrically charged fluid is called a plasma. A plasma as a whole is neutral, with the same number of positive and negative charges. It is not exactly neutral, however, because there are electric fields inside a plasma. These fields are created by a very small charge imbalance of the order of one part in a million. If these fields were not there, nuclear fusion would not be a problem. So we call these gases “quasineutral” plasmas. Figure 4.5 shows what this new kind of gas is like. The ions are the small (blue) dots. They are given tails to show that they are moving in random directions. The big, fuzzy objects are the electrons, which provide the negative charges to make the plasma quasineutral. They are fuzzy

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because you can never tell exactly where a given electron is. These particles move around at their thermal velocities and bump into one another, preserving the Maxwellian distribution. At the temperatures we are dealing with, the electrons and ions move too fast to stick to each other and recombine into an atom.

Often called the fourth state of matter, plasma is what you get when you heat a solid into a liquid, then into a gas, and finally into an ionized gas. Plasma emits light when electrons collide with atoms, kicking one of the orbiting electrons into a higher orbit. Light is emitted when that bound electron goes back to its original orbit. Although 85% of the matter in the universe is believed to be dark matter, the part that we see can be seen because it is in the plasma state. That includes all the stars, galaxies, and nebulae. On earth, plasmas cannot survive in our dense atmo­sphere, but we can see them in the Aurora Borealis and in fluorescent lights. You may have encountered plasmas without knowing it. Sparks are plasmas at atmo­spheric pressure. When there is a high voltage, electrons can jump across and make a transient plasma. This happens when you touch a doorknob on a cold day or plug in the power brick of a laptop computer. Lightning is a huge spark between a cloud and the earth or another cloud. These breakdowns are uncontrolled; but the steady, voluminous plasmas that we create on purpose are well behaved. They cannot spark because they are already completely broken down!

Plasma behavior is extremely complicated, and a whole new science of plasma physics has grown up from the effort to produce fusion energy. This science has now permeated into other fields. Computer chips cannot be made without plasmas. Plasma TVs are commonplace. Chaos theory and supercomputers were spawned by plasma research. How did we get to this subject? We found that particle beams cannot create fusion with a net energy gain. We had to heat a whole gas up to an extreme temperature so that, in a thermal equilibrium with a Gaussian velocity distribution, there are ions in the tail of the distribution with enough energy to fuse together. This is, then, a thermally generated nuclear reaction or thermonuclear reaction. This word has bad connotations and is no longer used by fusion researchers. Nonetheless, this clever method underlies the hydrogen bomb.

It is obvious that no solid material can withstand temperatures of millions of degrees, so we cannot hold the plasma with walls. We can hope to hold it with invisible forces, such as gravity, electricity, or magnetism. The sun produces fusion energy by holding plasma in its core with a large gravitational field. We cannot do this on earth because our gravity is much too weak, and we cannot shape it. That leaves electricity and magnetism. We can make strong electric fields, but these would not do it. The real proof is subtle, but basically you can see that an electric field will pull ions one way and push electrons the other way. The field will pull a plasma apart rather than confine it. That leaves magnetic fields. The name of the game is to make a magnetic bottle to hold plasma. That is the main subject of this book. All magnetic bottles leak. It is like holding Jello(R) with rubber bands. A plasma has a mind of its own. Fixing one leak reveals another one that you didn’t see before. Nobel Laureate Irving Langmuir chose the unfortunate name plasma, which had already been adopted by the blood people. It means something that can be shaped or molded. Nothing can be further from the truth! But the problem has been solved, and the end is in sight.

Time Scales

At this point, you may wonder how the complicated picture of banana orbits and magnetic islands jibes with the seemingly unrelated picture of convective cells and zonal flows in turbulence. These phenomena have different time scales. Hot electrons move almost at the speed of light, which is about one foot per nanoscecond. One trip around a large tokamak may be 20 feet, taking 20 ns. If it takes 100 trips to describe a banana orbit, that amounts to 2,000 ns or 2 ms. These individual particle motions therefore occur on microsecond time scales. Microinstabilities, on the other hand, have typical frequencies of 10 kHz, corresponding to a wave period of 100 ps. Growing into turbulence takes several periods, so the time scale is of the order of 1 ms. On this time scale, the plasma can be described as a fluid, but the fluid is not like water or air, in which the particles move randomly. The fluid that participates in microinstabilities and turbulence in a tokamak consists of particles moving in the very peculiar orbits existing in toruses.

There are two longer time scales. With a steady level of turbulence, the plasma settles into a steady state, arranging the distribution of toroidal current to give a stable q profile, possibly with magnetic islands. The radial distributions of density and of ion and electron temperatures arrange themselves so that everything is con­sistent. If these profiles become untenable, there are sawtooth crashes once in a while to rearrange them. All this happens in many milliseconds. Meanwhile, the plasma and its energy are leaking out slowly at rates described by the particle and energy confinement times. As discussed in Chap. 5, this time scale is of the order of seconds, possibly longer in a reactor-size machine.

To keep a discharge going in a reactor, DT fuel in the form of pellets is injected, and the helium “ash” is removed by the divertors. Before it is removed, the helium deposits its energy in the plasma to keep it hot. The length of a pulse in current tokamaks is determined by the transformer action needed to drive the toroidal current, since transformers cannot run DC-wise. Pulse lengths of the order of an hour are already possible. Reactors have to operate continuously, so the part of their current not generated by “bootstrap” will have to be driven “noninductively,” by waves, for instance. Or else, reactors will have to be stellarators, which do not need a current to produce the twist of the field lines. A practical power plant will have to be designed to run continuously for months or years between maintenance shut­downs. That is the longest time scale.

Lower-Hybrid Heating (LHH)

A third type of wave that can be used for heating and current drive is the so-called lower — hybrid wave. This wave is particularly useful for current drive because it can control the current profile near the outside of the plasma. The lower-hybrid frequency lies between the cyclotron frequencies of the ions and electrons, or about 5 GHz in ITER. Klystrons are used to generate frequencies in this range. The wave has a long wavelength in the direction of the magnetic field, so to launch it requires a large “grill,” meters in size, as shown in Fig. 9.26. Each of the openings is a waveguide fed by one or several klystrons, each with its own vacuum window. The phase of the wave emanating from each wave­guide is set so that the total grill, including some dummy waveguides, forms the wave that deposits its energy in the right place. Since the launcher lies close to the plasma surface, its materials must sustain the heat and neutron damage that that implies.

In summary, the physics of auxiliary heating and current drive is well under­stood, but the engineering of the power supplies and the wave launchers present some difficult problems.

Z-Pinches

A Z-pinch, called a Zed-pinch in England, is the simplest of all fusion approaches. It involves no more than pulsing a large current between two electrodes immersed in deuterium or DT. A column of plasma is ionized by the current and is confined by the magnetic field generated by the current itself, with no need for external coils. The B-field is very strong, since it surrounds the plasma closely, and it compresses the plasma until its density and temperature are high enough for fusion. It is very unstable, of course, because of the kink instability (Fig. 6.2). Since Z-pinches are so easy to make, much effort had been spent in trying to stabilize the pinch or to make it so fast that fusion occurs before the instability breaks it apart. These unsuc­cessful efforts became outmoded with the invention of wire arrays.

Starting with a current through a tungsten wire was found to improve Z-pinches because of the initial straight path and the slower motion of the heavy ions. A ring of tungsten wires, as shown in Fig. 10.36, was found to be qualitatively better because of the blending of their magnetic fields. If the wires are close enough together, the B-fields outside the circle form an overall azimuthal field that com­presses all the plasma into the center without kink instabilities because the current through each wire is comparatively small.

Figure 10.37a is a photograph of a 4-cm diameter array of 240 tungsten wires, each 7.5 pm (0.0075 mm) in diameter, at Sandia National Laboratories in New Mexico. In the Z-machine (described later), some 20 MA of current was pushed through the wires, forming a dense Z-pinch in the center. The aim was to generate X-rays, and about 200 TW (200 trillion watts) of these were generated [36]. This is a spectacular result, since the total electrical generating capacity of the USA is only about 1 TW. Of course, the X-ray pulse lasts only a nanosecond or so. Figure 10.37b is the same pinch fitted with an inner array of 120 wires. The plasma from the inner wires creates a plasma that smoothes out the instabilities that start to develop in the outer plasma, and the X-ray power is increased to 280 TW [37]. However, these pinches cannot produce continuous energy for primary power.

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Fig. 10.36 (a) Diagram of a circular array of wires for a Z-pinch (Sandia National Laboratories, Albuquerque, NM. www. sandia. gov). (b) The magnetic field around each wire

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Fig. 10.37 Single (a) and double (b) wire arrays for Z-pinches at Sandia [36, 37]. The wires are about 2 cm long

The Magpie Project of Imperial College, London, conducts innovative research on wire-array Z-pinches in which the wires point radially outward from the center [38]. External magnetic fields can also be imbedded in the pinch. Though the work is interesting, it is done for other purposes than energy production.

Energy Storage

Since wind is so variable, one problem is how to smooth out the fluctuations. This means storing the energy. The method depends on how long the energy has to be stored. The capacitors in the nacelles and the turbine’s transmission station need to store energy only from one AC cycle to the next, and those capacitors are already very large. Storing enough energy to last an hour would do a lot of smoothing.22 Batteries can do this, but they are too expensive. The best batteries are lithium-ion (as in laptop computers) and sodium-sulfide (NaS). Enough Li-ion batteries to service a large turbine would cost as much as the turbine itself. A 1-MW bank of NaS batteries would be the size of three shipping containers. A 34-MW NaS dem­onstration plant in Rokkasho, Japan, occupies 16 large buildings.22 This does not seem practical either. Storing mechanically in large flywheels is not yet taken seriously.

There is also day-night storage for 8 hours or longer. If there is a hill, pumped hydro can be used. The excess energy is used to pump water into a reservoir uphill. The energy is then regained quite efficiently by hydroelectric power. A scheme that is being taken seriously is compressed-air storage. Excess wind energy is used to pump air into underground salt domes or porous sandstone topped by shale. These sites, also usable for CO2 storage, can be found over 85% of the USA.23 The energy is recovered by bringing the compressed-air backup to help spin a natural-gas tur­bine driving an electric generator. The scheme is shown in Fig. 3.17. The turbines there are gas turbines, not wind turbines. A gas turbine is shown in Fig. 3.18. When natural gas is burned, the expanding air blows through the fan blades and turns the shaft, which then turns an electric generator. The compressed air from underground can add to this push, increasing the efficiency of the turbine by 60% or more. However, there is a heat cycle involved. When the air is first compressed, it heats up, and that heat is lost to the rock. Then when the air is decompressed, it cools down and has to be reheated to help drive the turbine. If you examine Fig. 3.17 closely, you will see that the heat for this is recovered from the hot air leaving the turbines after it has done its work. The loss in efficiency is more than 50%.22 Nonetheless, large projects for such storage are planned in Iowa, Minnesota, Texas, and the Dakotas.23

Nuclear Power Importance of Nuclear Power

Both fission and fusion involve nuclear reactions, but the term “nuclear” usually applies to fission, and we shall use it with that connotation here. Nuclear energy is a mature technology. It is the only time-tested, continuous, dependable source of base-load electricity that does not emit GHGs and can be conveniently located. It has three well-known disadvantages: danger of nuclear accidents, danger of prolif­eration, and storage of radioactive wastes. We shall treat these one by one. Nuclear power is important for the world’s energy needs, but it has been impugned — indeed, attacked — by the press and environmentalists who have not done their homework and studied the risks and costs of the alternatives.7172

France has set an example. It generates 75% of its electricity from nuclear and 15% from hydro, both of which have no CO2 emissions.73 There have been no reported deaths. France has led in research on next generation reactors and has begun building them. Other countries which do not have coal have a high percentage of their electricity from nuclear: Belgium (54%), Ukraine (47%), Sweden (42%), S. Korea (36%), Germany (28%), and Japan (25%).74 Worldwide, the percentage is 15%. Because of its size, the USA’s 20% constitutes one-third of the world’s total. The supply of uranium will outlast that of oil and gas, and future breeder reactors will generate their own fuel. Fusion reactors will take time to develop, and fission can supply “green” power in the interim. The nuclear waste problem will become more acceptable when the public realizes that fission will eventually be phased out by fusion, so the problem will last only for a few human generations.

Stabilization by Sheared Fields

The Princeton Gun Club was a small shack on the side of the runway of the Princeton airport and was purportedly used for skeet shooting at one time. It was an ideal location for a classified meeting of Project Sherwood in 1955. The Robin Hood connection came from one of the participants, James Tuck (Friar Tuck) of Los Alamos. Representatives of the four US laboratories working on fusion (Livermore, Oak Ridge, Los Alamos, and Princeton) fit into the small room. Edward Teller was there. After hearing about our trying to hold a plasma with a magnetic field, he exclaimed, “It’s like holding jello with rubber bands!” Indeed, the jello would squeeze out between rubber bands, exchanging places with an equal volume of rubber, so that the rubber bands were on the inside and the jello on the outside.

A solution to the basic interchange instability was formulated: weave the rubber bands into a mesh. In a toroidal magnetic field, this is done by magnetic shear. Figure 5.9 shows several magnetic surfaces in a torus, each containing magnetic field lines that are twisted. The twist angle, however, changes from surface to sur­face, so if a ripple starts on one surface and is aligned with the field lines there, as in Fig. 5.8, it finds itself misaligned with the field on the next surface. The differ­ence in pitch angle from one surface to another has been greatly exaggerated. It does not take a very fine mesh of field lines to kill the interchange instability; in fact, we will see later that the amount of twist is limited by another instability.

A graphic picture of how shear stabilization works was provided by an experi­ment by Mosher and Chen [4]. The plasma in Fig. 5.10 was in a straight cylinder with a magnetic field up out of the page. The shaded circle in the center represents a thick rod inside the plasma carrying a current into the page and creating a “poloidal” magnetic field that gives the field lines a helical twist. At the left, a bump on a magnetic surface is shown which might represent an instability getting started.3 In successive views to the right, the current in the rod is increased, twisting

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Fig. 5.9 A torus with a sheared helical field

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Fig. 5.10 Effect of shear on a bump in a plasma

the field lines more and more. Finally, at the right, the measurements show that the bump has been twisted into a thin spiral, so thin that the charges that create the electric field in the Rayleigh-Taylor instability (Fig. 5.8) can leak across the spiral, short-circuiting the electric field and killing the instability. In addition, short-circuiting by electrons moving in the toroidal direction (perpendicular to the page) also happens, and in fact is the main stabilizing effect of shear on the inter­change instability.

To summarize this first of many instabilities, we saw that a plasma cannot fall out of its magnetic container the way water falls out of a bottle because a plasma weighs practically nothing. Its gas pressure, however, is always pushing against the magnetic field. With the slightest perturbation, the plasma organizes itself to create an electric field that causes a tongue of plasma to leak out and a bubble of field to leak in. Being wise to the plasma’s tricks, we can thwart the plasma’s moves by short-circuiting its self-generated electric fields with magnetic shear.

Big Q and Little q

As we now turn our attention from fusion physics to fusion energy, we have to introduce Big Q, as distinct from little q. Little q, as you remember, is the “quality”

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Fig. 8.19 Dependence of В on I/aB in various tokamaks [25]

factor in toruses like tokamaks and stellarators. It is the reciprocal of the rotational transform, which is the number of times a helical field line encircles the minor axis each time it goes around the whole torus. The variation of q with radius r, or q(r), is perhaps the most important feature in the design of toroidal magnetic bottles. Big Q, on the other hand, has to do with how much energy a fusion reactor will produce. It is the ratio of the fusion energy produced to the energy required to make the plasma:

q _ Fusion energy Input energy

In Chap. 3, we showed this equation for the DT reaction:

D + T ® a + n +17.6 MeV,

where a is an alpha particle (a helium nucleus) and n is a neutron. Most of the 17.6 MeV of energy released is carried by a 14.1 MeV neutron, and the other 3.5 MeV is carried by the alpha particle.11 The neutron energy is the part used to produce the electrical output of the power plant, and the alpha energy is used to keep the plasma hot. Since the a’s are charged, they are confined by the magnetic field, and the hope is to hold them long enough that they can transfer their energies to the DT plasma, keeping it at a steady temperature. But since the a’s have only one-fifth of the fusion energy, Q has to be at least 5 for this to happen. This is called ignition. The plasma is “burning” by itself. The reaction cannot run away as in fission because some instability will quench the plasma as soon as the operational limits are exceeded.

Подпись: Fig. 8.20 Lawson diagram showing progress toward breakeven and ignition [31]
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The first milestone is to achieve Q = 1, which is called scientific breakeven, which assumes that the whole 17.6 MeV is equal to the input energy. The next milestone is to get to ignition at Q=5. To produce net energy, you have to count also the energy needed to make the magnetic fields and the plasma currents, as well as all the electric­ity needed to run the power plant (even the lights!) and the energy used to transmit the power to where it is used. This means that Q has to be at least 10. Figure 8.20 is a Lawson diagram (Chap. 5) plotting nrE vs. T and showing what different tokamaks have achieved in DD and DT plasmas. The heavy curve is for Q = 1 in DT, and we see that this has been reached in JET. The yellow region is ignition at Q greater than 5. The diagonal dashed lines are for constant values of the triple product. The obvious next significant step is to get to ignition, and that is the story of ITER.