Industry is not interested in these technical details; it is concerned with the bottom line. RAMI is the acronym for four important criteria: reliability, availability, main­tainability, and inspectability. The Electric Power Research Institute puts it in even more basic terms: economics, public acceptance, and regulatory simplicity. It is of course too soon to know how these will turn out; but designers of fusion power plants as well as fusion technology researchers are well aware of these criteria, which are always kept in mind. The fusion core is only a part of a whole power plant, a cartoon of which is shown in Fig. 9.34. The remote handling system is essen­tial for maintainability and inspectability. The heating, current drive, and fueling systems affect reliability. The complicated fuel cycle system has to be completely

safe in regard to tritium release. The balance of plant, the equipment that generates and transmits the electricity, is a larger part of the power plant than the power core, though it is shown deceptively as a small addition in Fig. 9.34. These are the steam turbines that drive the electric generators and the transformers and capacitors that condition the output for delivery to the transmission lines. All power stations that convert heat into electricity have this equipment, whether the fuel be coal, oil, gas, or uranium. Hydroelectric plants do not need steam; water drives the generators. Wind and solar plants produce electricity directly. Fusion plants can use the same generators and transmission lines that already exist in fossil or nuclear plants; only the power core has to be replaced. However, tokamaks are so complicated and include such temperature extremes that they will require a higher portion of the capital cost than other power cores.

Availability is an important aspect of a fusion reactor that is hard to assess. How often will leaks occur, and how long will it take to do the re-welding? How often do blankets have to be replaced, and how long will the shutdowns be?

Re-circulating power

Fig. 9.34 Main parts of a fusion power plant [37]

How often will disruptions occur, and how long will it take to reassemble the machine? What percentage of the time will the machine be running during a year? During a shutdown, where will the power come from? Will we need a backup tokamak or new transmission lines from other power plants? Educated guesses are made by those who design fusion power plants based on available knowledge.

There has been much ado about almost nothing following the 1989 announcement by Fleischmann and Pons that they had produced energy in a flask of heavy water. The experiment consisted of electrolyzing the D2O into gaseous products by apply­ing a DC voltage between an anode and a cathode, the latter made of palladium. The energy input and output from the apparatus had to be carefully measured.

There was energy balance for several weeks, but then they found that the output was a few watts larger. Since then, the experiment has been repeated hundreds of times by reputed scientists without similar success. There have also been many believers in cold fusion who accuse the scientific community of snobbish exclusiv­ity, and who occasionally report observations of excess energy generation. The American Physical Society has held conference sessions and panel discussions on cold fusion with the conclusion that it is impossible.

Electrochemical potentials are sometimes surprisingly strong. The hydrogen car fuel cell (Fig. 3.51), for instance, uses a platinum or palladium catalyst to dissociate and ionize hydrogen magically before it has been heated. There is, how­ever, a huge difference between the 10 eV in ionization and the 10 keV in overcoming the Coulomb barrier in fusion. In cold fusion perhaps the deuterium seeps into the palladium after some time, and eventually two D’s get very close together and somehow the applied voltage can cause them to fuse. Sometimes a few neutrons are observed, but these could be due to cosmic rays. There is interest­ing physics in these infrequent events, and the International Conference on Cold Fusion has been meeting annually since 1990. Institutes for cold fusion have been established in some countries. However, cold fusion power is so miniscule that it would not pay for the palladium, much less a whole power plant. And it is only thermal power, not direct electrical power. Cold fusion may have interesting sci­entific aspects, but it has no relation to power production.

The uproar over cold fusion has had one benefit, however. It shows that the public is not disinterested in controlled fusion power, as long as it is cheap. It sim­ply does not understand why it is so hard to achieve, and why there are no shortcuts leading to the gold at the end of the rainbow. This book attempts to explain why.

A solar cell is an electronic device made of semiconductors in layers, just as com­puter chips are, but much larger and simpler. Since each cell produces less than 1 V, cells have to be connected in a series to give a useful voltage, like 12 V. Flashlight batteries generate 1.5 V, and we use two of them in series to get the 3 V required

by the bulb. Solar panels, about half a square meter in size, contain many cells connected together by transparent wires. The difference among conductors (like metals), insulators (like glass), and semiconductors arises from quantum mechanics, which mandates that energy levels in a solid are quantized. That means that electrons cannot have any old energy but must have an energy on one of the allowed levels. Furthermore, no two electrons can be on the same level. This situa­tion is shown in Fig. 3.30. Energy levels occur in bands, two of which are shown, each containing seven energy levels. There are, of course, zillions of levels in actuality. In an insulator, the levels in the lower band are all filled, one electron in each level. This material cannot conduct electricity, because the electrons cannot move. To move, they would have to gain a little energy, but there is no level close enough for them to move up to. In a conductor, the lower band is filled, but the material has some electrons in the upper band, which is not full. Those electrons can conduct electricity because there are levels above that they can move up to. In a semiconductor, the lower band is full, but the bandgap is small, so if the topmost electron gets a big enough kick (from sunlight, for instance), it can jump up to the upper band, where it can move. So a semiconductor conducts sometimes.

The most common semiconductor is silicon. The bandgap in silicon is 1.1 eV. It is not important at this point to know how much energy an eV is; it will be explained amply in Chap. 4. The “kick” that the electrons get from sunlight to cross the bandgap depends on the color of the light that hits it. Sunlight contains a range of colors, as we know by separating them with a prism (Fig. 3.31), giving rise to the proverbial sequence violet, indigo, blue, green, yellow, orange, and red. Light can be considered as a stream of photons, which are particles with energy but no mass. No, they do not follow E=mc2! Each color corresponds to photons of a certain energy. Those at the blue end of the spectrum have more energy, and those at the red end have less. For a photon to make a semiconductor conduct, it must have an energy of at least 1.1 eV. That means that the part of sunlight redder than that will be lost. For silicon PV, the idea is to add semiconductors with other bandgaps that can capture the other parts of the solar spectrum.

After a photon kicks an electron into the conduction band, what happens next? This is shown in Fig. 3.32. This is the semiconductor part of Fig. 3.30, but showing only the electrons on the top level. After an electron is kicked into the conduction band, it leaves a hole in the valence band. What we have not shown is that the electrons actually belong to atoms consisting of a positive nucleus surrounded by enough electrons to make the whole atom uncharged. These atoms are locked into a crystal lattice. In Fig. 3.32a, an electron has been knocked out of one atom into the conduction band. It leaves behind an atom with a missing electron and therefore

has a charge +1. That atom, shown in white, has a “hole” in it; that is, a place where an electron should fit but is missing. An electron can then jump from a neighboring atom, thus filling the hole but leaving a hole in the neighboring atom. As shown in B, the hole can move like a positive electron! If an electric field is applied, the electron in the conduction band will move one way, and the hole in the valence band will move the opposite way. These electron-hole pairs will conduct electricity, and now we have to see how the current is collected.

The electrons and holes cannot be collected directly with a copper plate con­nected to a wire because these charges cannot cross the interface between these very different materials. A buffer layer has to be added. These buffer layers are made of “doped” silicon. Here, doping is legal. By adding a few “impurities,” which are specially chosen atoms with one more or one less electron than silicon has, we can make n-type or p-type highly conductive semiconductors. The former has a net nega­tive charge, and the latter a net positive charge. We can then make a sandwich of three layers to form the basic unit of a solar cell (Fig. 3.33). Opposite charges attract, so when solar photons create electron-hole pairs in the silicon, the electrons are attracted to the p-type layer at the bottom, and the holes to the n-type layer at the top. Since they are negative, the electrons carry a current in the opposite direction to their motion. The buffer layer allows them to flow into wires carrying the current to the load (the appliance or battery that uses the juice). When the electrons reach the n-type layer, they fill the holes that had migrated there. The voltage generated is the bandgap voltage. The larger the bandgap, the higher the voltage. This makes sense, since only the energetic photons can push an electron across a large bandgap.

This subject is logically treated here because of the radioactive waste problem of fission reactors. However, fusion reactors have not yet been described. This section can be best understood if Chap. 9 on fusion engineering is read first. The reason for combining fusion with fission is that it could benefit both systems. Fission reactors can be run subcritically for better safety, and their high-level wastes can be trans­muted into fuel and a much smaller amount to be sequestered. Fusion reactors, on the other hand, can be run subcritically also, without producing all the energy of the reactor, greatly accelerating the time for their development. Many plasma theorists have advocated fission-fusion hybrids, notably Jeffrey Freidberg at M. I.T. and Wallace Manheimer at the Naval Research Laboratory in the USA. The idea was first proposed by none other than Hans Bethe. However, their arguments do not include specifics on how a hybrid reactor might be designed. A group at the University of Texas has proposed a reactor based on a spherical torus (see Chap. 10), a new fusion device that has not been extensively tested. The most detailed engi­neering design has been done by a group at the Georgia Institute of Technology (Georgia Tech) under the leadership of W. M. Stacey. Their subcritical advanced burner reactor [45] will be described here. A diagram of it appears in Fig. 3.61.

Within the D-shaped toroidal-field coils is the plasma of a fusion reactor, shown in yellow. Surrounding that is the fission fuel core, which is divided into four

Central solenoid Vacuum vessel Blanket and shield Reactor core Plasma

Plasma first wall Toroidal field magnets

concentric rings (gray). Surrounding both is a neutron absorbing blanket which breeds tritium from Li4SiO4 for DT fuel. The fission part is an LMFBR designed at Argonne National Laboratory. The fuel is 36 tons of transuranic waste from LWRs consisting of 40% Zr, 10% Am, 10% Np, and 40% Pu. It is in the shape of 7.3 mm diameter fuel pins, 271 of which form a fuel assembly. The fuel pins include a channel for the liquid sodium coolant. Their complete design and manufacturing process have been specified [46]. The fuel rings (batches) contain 918 assemblies. The tokamak part is a scaled-down ITER operating with conservative parameters lower than the maximum values needed for energy production. These include factors which will be explained in Chap. 9: the Greenwald limit, normalized beta, big Q, and the bootstrap current fraction.

The operating characteristics of this reactor have been extensively calculated. The fission part will generate 3 GWth (gigawatts thermal). It runs subcritically, generating fewer neutrons than is necessary to maintain a chain reaction. The missing neutrons are generated by the fusion part. Since its mission is not to generate power, it can be designed to contribute only 250-500 MWth of energy. The fission fuel is burned in 750-day cycles. Each batch spends one cycle in each position, for a total exposure of four cycles or 3,000 days. After that, it is removed to storage, and its decay heat over the next million years has been reduced by a factor of 2, and thus the storage facility requirements have been halved. The total time of exposure is limited by the life of the fuel cladding under neutron bombardment, set at 200 dpa (displacements per atom).

This amount of burnup of actinides can be greatly improved by reprocessing. If the fuel from the hybrid after four burn cycles is reprocessed, then mixed with
“fresh” waste from LWRs and sent through the hybrid again, the decay heat of the ultimate product can be reduced by 99%. High-level storage facilities can be reduced by a factor of 100. If the 200-dpa limit on neutron damage can be relaxed so that the fuel can be burned for four 3,000-day burn cycles for a total of 12,000 days (25 years), 91.2% of the transuranic waste can be removed after only once through the hybrid reactor. Such a fission-fusion hybrid can treat the waste from four 1,000-MW LWRs.

e

It is possible for the fission reactor to go critical. Zirconium is added to the fuel so that there is negative feedback: when the temperature rises; the reaction slows down. However, if this does not work and there is a runaway reaction, there is less time available for control rods to be inserted than in a normal LWR. Fortunately, there is a simple solution. The reaction cannot run without neutrons from the fusion reactor. The plasma producing these neutrons can be shut off within a second or so by a massive injection of gas.

Proponents of hybrids see that they can make fission safer and at the same time let fusion get online faster. Skeptics see that these would be extremely expensive and difficult reactors to design and construct and would detract from the main objective of developing pure fusion. In any case, this subject is still in its infancy compared with Generation III fission reactors or with tokamak fusion reactors.

In every tokamak discharge, there is a magnetic surface where q = 1. Inside that surface, where q is less than 1, the plasma is unstable to kinks, according to the Kruskal-Shafranov limit. Therefore, it is turbulent and a jumble of oscillations, and

there is no magnetic confinement. Only when plasma gets outside the q = 1 surface and enters the nested magnetic surface and island structure, does it get restrained by the magnetic field and diffuse slowly to the wall.

Very early in tokamak research, experimenters using a synchrotron-radiation method to detect changes in electron temperature observed regular oscillations near the q = 1 surface. These were observed in all tokamaks and always had a sawtooth shape, rising slowly and falling sharply each time, as seen in Fig. 7.5. Since the current is largest inside the q = 1 surface, near the center, the plasma gets hotter there. Higher temperature means less resistivity, and that makes the current even larger and more peaked. When the shape of the current profile changes, so does the whole island structure, as seen in Fig. 7.3. Finally, the magnetic structure is so disturbed that the steady state can no longer be maintained, and the plasma has to change. What the tokamak does is to eject the overly hot plasma in outward bursts, thus cooling the center back to normal. This explanation was for a long time only a conjecture, but recent advances in instrumentation have enabled actual movies of these sawtooth bursts to be taken in real time. These movies show that the tempera­ture actually oscillates several times before the big crash, when hot plasma is shot out and replaced by cooler plasma. Still frames from the movie by H. K. Park of the Princeton Plasma Physics Laboratory are shown in Fig. 7.6, but they do not do justice to the actual product [3].

As doubly heavy hydrogen, tritium has two extra neutrons, which do not sit well with a single proton. So tritium decays by emitting an electron, a process known as beta-decay. This loss of a negative charge changes one of the neutrons into a
positively charged proton and converts tritium into helium-3, a helium isotope with two protons and a single neutron instead of the usual two. This decay makes tritium radioactive, and it has to be handled carefully in a fusion plant.

Fortunately, the radioactivity is mild. The electron that is emitted has very low energy, about 19 keV. It cannot penetrate the skin, and even in air can go only 6 mm (1/4 in.) [12]. However, it can be harmful if ingested and must be carefully kept out of the water supply. Unlike fission products, tritium has a short half-life of only 12.3 years. This means that 5.47% of it decays into harmless helium each year. Because of its short life, very little tritium exists naturally. Cosmic rays make about 200 g of tritium a year, and there are only about 4 kg of natural tritium at any one time in the earth’s atmosphere. Man-made tritium raises this to about 40 kg. Compared with this, it will take 1 kg of tritium just to get ITER running on DT, and a reactor may use up 100 kg per year.

Stellarators like the Wendelsteins are large machines with large aspect ratios R/a, where R is the major radius of the ring and a is the radius of the cross section. There is a movement to build smaller, more economical machines by shrinking R to get aspect ratios of 3-5 instead of 10 or more. Proposed compact stellarators have been designed with different magnetic-field configurations to see which would work better. This freedom of design is not available for tokamaks, but it also means that it is harder to converge on the optimal design. The National Compact Stellarator Experiment (NCSX) was funded and under construction at the Princeton Plasma Physics Laboratory, but the project was canceled during the 2009 worldwide eco­nomic depression. Figure 10.8 shows the NCSX and its coil structure. There are only 18 coils of three different shapes. Although this machine was well designed and would have complemented the Wendelstein 7-X nicely, its discontinuation was reasonable. Tokamaks are far ahead in development, and to get a fusion reactor working the fastest way is to give them the highest priority.

Stellarators are second-generation confinement devices. They are probably better suited for reactors than tokamaks, but we need much more experience with how they run. An obvious question is: Where do you put the blankets in a DT stellarator

reactor? The problem is that the magnet coils are not circular but have small twists and bends. The coils have to be close to the plasma for these fine features to be felt; too far, and the details will be smeared out. That’s why the vacuum chamber has to be shaped to fit the coils. In a reactor, one still has to leave room for the tritium­breeding blanket, and the only way to do this is to scale the whole machine larger. There have been several reactor studies from Germany, Japan, and the USA. The ARIES-CS design is shown in Fig. 10.9 and the overall view in Fig. 10.10. It was found possible to place the blanket modules between the plasma and the vacuum wall and superconducting coils.

The heart of a hydrogen car is the fuel cell, whose parts are illustrated in Fig. 3.51. Hydrogen is forced into the channels in the anode plate and is then spread out uniformly in the diffusion layer. This layer has been described as a wet rag whose moisture content must be carefully controlled to keep the proton exchange

ANODE BIPOLAR PLATE

HYDROGEN IN

CHANNELS

OXYGEN IN

CHANNELS

CATHODE BIPOLAR PLATE

Fig. 3.51 Schematic of a fuel cell. It is not to scale. The catalyst layers and the PEM are only 10’s of microns thick, while the diffusion layers are 100’s of microns thick. The bipolar plates are of macroscopic dimensions
membrane (PEM) from drying out without dripping. The PEM is a plastic layer like plastic wrap made of a special material called Nafion® made by Dupont Chemical. It has the magical property of allowing hydrogen ions (H+) to pass through but not electrons. It is the platinum catalyst layer that dissociates hydrogen gas (H2) and ionizes it into two hydrogen ions (H+). This is an even more magical property. The catalyst layer consists of platinum nanoparticles thinly deposited on carbon paper which has to be rough to present a large surface area and porous to let the water through. The electrons, being blocked by the PEM, are drained off into a wire to form the electric current that is the output of the cell. When the H+ ions reach the other side, they encounter another catalyst layer, which could be platinum or iridium. Meanwhile, oxygen (O2) from air is pushed into the cathode plate and diffusion layer to meet the hydrogen ions in the catalyst layer. Therefore, the O2 is dissociated into atoms (O) and picks up electrons from the wire that has gone through the load to become negative ions (O-). Each O — then combines with two H+s to form H2O. Hydrogen and oxygen have been combined to form water and electricity. All in all, the fuel cell is a serendipitous invention, but it has problems.

Each fuel cell generates only 0.6-0.7 V, so as many as 100 of them have to be connected in a series to form a stack with a useful voltage output. Platinum is a precious metal used in jewelry and in catalytic converters. Its price drives the price of fuel cells to about $73/kW, twice the commercially viable value.49 Cyclic opera­tion of PEMs degrades their performance. PEMs have to be heated to at least 60°C from a battery before they can even start, and they need about 100°C to operate reliably. The water in the cell must not boil or freeze under all driving conditions. Corrosion of the bipolar plates is a problem; they cannot be made of a metal that can corrode and contaminate the system with iron or chromium. A carbon com­pound has to be used. Besides the electric motor, the car has to have a system to pressurize the gases. And the fuel cell has to last for 300,000 miles.

Currently, the whole shebang is too large to fit inside a car but can be used in trucks. No large-scale production and testing has been done. What can be gained is a fuel-cell efficiency of 80% times another 80% efficiency of the electric motor, giving a maximum efficiency of 64% in the conversion of hydrogen energy to mechanical energy. This compares favorably with the efficiency of gasoline-driven cars, about 15%, but the energy in producing the hydrogen has not yet been counted. If that part is 40% efficient, the net efficiency is 64 x 40= 26%, still higher than burning natural gas in a gas engine. However, the real gain will be when hydrogen is pro­duced in fission or fusion plants with no use of fossil fuels or emission of GHGs.

So we have found that the best way to produce fusion reactions in a continuous manner is to make a very hot plasma, so hot that it cannot be held in place by any material container. We also decided that of all the forces that we can use to make a wall-less container, only the magnetic force would work. What would a magnetic bottle look like? Actually, it looks like a bagel; but before we get to this, we have to review what we know about magnetic fields. Most people know that the earth has a magnetic field, as shown in Fig. 4.6. The lines with arrows show the direction of the field. A compass needle aligns itself with the field line that passes through it on the earth’s surface, and therefore points toward the magnetic pole, which is close to the geographic pole. The earth’s field is already a magnetic bottle, but an imperfect one. Protons and electrons coming from the sun in the solar wind3 get trapped in this field because charged particles tend to move along field lines, not across them. But the trap has large leaks at the north and south poles where the field lines run into the ionosphere, bringing the particles with them. When electrons strike oxygen atoms in our atmosphere, visible light is emitted which we call the Aurora Borealis. Since the plasma particles can travel in either direction, the same thing happens in the southern hemisphere. The Aurora Australis is not as well known because few people stay out on a winter’s night in Antarctica to watch it, and penguins have other agenda.

Magnetic field lines are, of course, only a mathematical construct. Electric or magnetic fields can be detected only by the forces that they exert. It was the great Scottish physicist James Clerk Maxwell4 who invented the concept of a “field” to describe action at a distance. Once a field at a given position is known, one can calculate the forces which that field would exert on an object there. To depict the shape of a field, one can draw any number of lines. A visual display of magnetic field lines is commonly given in textbooks, where the pattern of iron filings traces the field lines around a horseshoe magnet, as in Fig. 4.7.

Magnetic field lines are sometimes called “lines of force,” but this is a misnomer. The magnetic force is actually perpendicular to the lines! A compass needle points north-south because, when it is not aligned, the north pole of the needle is pushed one way by the magnetic field of the earth, and the south pole the other way, until the needle is aligned with it. Similarly, each elongated iron filing in the horseshoe demonstration acts like a miniature compass needle and points in the direction of the field at its location. It is important to understand what a field line represents, because how a magnetic bottle works depends critically on how these lines are shaped.

The problem with permanent magnets is that the strongest magnetic field it generates is inside the iron of the magnet, where we cannot put any plasma. Fortunately, we can create magnetic fields with electromagnets. In Fig. 4.8a, we show the field around a bar magnet, which is a magnetized iron cylinder; it has basically the same shape as the earth’s field. In Fig. 4.8b, we have replaced the iron bar with a glass tube of the same length and diameter, and we have wound many turns of wire around the tube. When we hook the wire up to a DC voltage source, such as a battery, the current in the wire generates a magnetic field of the same shape as that of the bar magnet! But now we can put plasma inside the glass tube, where the field is much stronger, as you can tell because the lines are closer together.

Fig. 4.8 The magnetic field around (a) a bar magnet and (b) an electromagnet of the same size

Now we can move on to see how to make a leak-proof magnetic bottle for plasma using cleverly shaped wire coils to produce field shapes that will plug all the leaks.

When neutral-beam heating was installed and turned on in the ASDEX tokamak in Garching, Germany [9] in 1982, Mother Nature came up with a major surprise that no one could have predicted. When the heating power was increased slightly from 1.6 to 1.9 MW, the plasma snapped into a new mode. Its temperature went up; its density went up; and the confinement times of both the plasma energy and the plasma particles went up, as dramatically shown by a sudden drop in the measured flux of escaping ions. It was as if a wall or dam, called a transport barrier, had formed, as depicted in the cartoon of Fig. 7.24a. The plasma would diffuse as it normally does up to this barrier, and then it would be held up by the barrier and leak out slowly in small bursts. This high-confinement mode, called the H-mode, came about from two innovations: the increase in heating power possible using neutral beams and the use of a single divertor of the type shown in Fig. 7.13. When the

Fig. 7.25

neutral beams are turned on below 1.6 MW, the confinement time actually gets a little worse because the beam disturbs the plasma equilibrium that was set up by ohmic heating. This is called the low-confinement L-mode. Once the power is increased beyond the H-mode threshold, the L — to H-transition occurs and a pres­sure pedestal forms.

Figure 7.25 shows what is meant by the pedestal. This is a graph of the plasma pressure as it varies across the minor radius; that is, from the center of the toka — mak’s cross section to the outside. Up to the pedestal, the plasma density and temperature (whose product is the pressure) fall gently from their maxima as in normal diffusion; but they do not fall all the way to zero. They hang up at a high value, so that the average pressure inside is higher than in the L-mode. At the ped­estal, the pressure falls rapidly to nearly zero as the plasma is drained off to the
divertor, where it recombines into gas and is pumped out. What happens inside the barrier is illustrated in Fig. 7.24b. Large electric fields in the direction of the minor radius are set up, and these cause perpendicular E x B drifts in the toroidal direc­tion, as shown in Fig. 5.6. These drifts are not uniform but are highly sheared. Apparently, this sheared motion stabilizes the microinstabilities and slows down the diffusion from the instability-controlled diffusion in the interior. Note that this is electric shear stabilization, as opposed to the magnetic shear stabilization used in elementary forms of toroidal confinement devices.

The H-mode barrier layer is very thin, about 1-2 cm in a large tokamak with meter-sized cross sections. The H-mode is not a peculiarity of the tokamak, since it has been seen in stellarators and other toroidal devices. It is also not a phenom­enon of neutral beam heating. It seems to have only two requirements: (1) that the input power be high enough and (2) that the plasma be led out by a divertor into an external chamber rather than be allowed to strike the wall. The latter requirement is due to the fact that impurity atoms or neutral atoms prevent the pedestal from forming. In the H-mode, the confinement time improves by about a factor of 2 (see Fig. 7.26a), and the plasma pressure by about 60%. A factor of 2 does not seem a lot, considering that confinement times have increased a million-fold since fusion research began; but we are now talking about a machine that is almost ready to be designed into a reactor. A factor of 2 can turn a 1-GW reactor into a 2-GW reactor, serving 1,000,000 homes instead of 500,000. All current designs for fusion reactors assume H-mode operation. The power produced by a reactor depends critically on the density and temperature of the pedestal.

How can we understand this freak of nature that we have stumbled on? There are two main problems: (1) How do the sheared fields in the barrier layer reduce the diffusion rate and (2) what causes this layer to form and how can we control that?

These have occupied the thoughts of a large fraction of fusion physicists for over two decades. One annual conference devoted to this topic has been going on for over 20 years. Sheared flows have good and bad effects. On the one hand, they can cause an instability, called the Kelvin-Helmholtz instability, which is well known in hydrodynamics. It is the instability that causes wind to ripple the surface of water. On the other hand, shear can quench an instability or at least limit its growth. In hydrodynamics, there is a simple theorem that tells what shape of shear is stable or unstable. In plasma physics, no such simple result is possible because so many kinds of waves can exist in a magnetized plasma. It is also difficult to make measurements in such a thin layer. The physics of the transport barrier — “edge physics” — is an ongoing study. The transport task force, a conference devoted to this topic, has been meeting yearly since 1988. More important, however, is to know how to turn on the H-mode. The threshold power depends on magnetic field, plasma density, and machine size. Since the H-mode threshold has been observed in so many machines, it was possible to formulate a scaling law that tells how the threshold depends on these various parameters. This is shown in Fig. 7.26b.

The H-mode has benefited not only our ability to confine plasma, but it has also improved our knowledge of plasma physics. Even the way in which the plasma’s energy escapes from the barrier has turned out to be a considerable problem. It escapes by means of yet another instability, call an ELM. This is described in the next chapter.