The figure showing a sawtooth crash was generated with modern measurement techniques and brings up the question, “How does one measure anything inside a fusion plasma?” At temperatures over a million degrees, nothing put into the plasma will survive. Plasma diagnostics is a whole field in itself, but here is a brief summary. There have to be enough windows, or “ports” to get light or other beams

After

Fig. 7.6 ‘erature distribution before, during, and after a sawtooth crash (top right and

colored squares). Yellow or light color is hot, and blue or dark color is cold. The pictured region at the q = 1 surface of the tokamak cross section is shown at the left. The small graph at the bottom shows the temperature distribution before and after the crash, showing that hot plasma has been moved out of the q = 1 surface [3] into and out of the plasma. The scattering of a laser beam can give information about the electron temperature and density of the plasma. Crossed laser beams can be used to measure the ion temperature. The transmission or emission of electro­magnetic radiation in the microwave, X-ray, or infrared range can show oscilla­tions inside the plasma. Sawteeth were first observed from the fluctuations in the soft X-ray radiation emitted by electrons at twice their cyclotron frequencies. Since the frequency depends on the magnetic field, and the field varies with position, this also tells where the radiation is coming from. Diagnostic beams of neutral atoms or heavy ions can be injected into the plasma since they can penetrate the magnetic field. In beam emission spectroscopy (BES), a beam of neutral hydrogen atoms is injected and reaches the plasma interior. There, it col­lides with the ions and is ionized by the electrons. In the process, it emits light whose spectrum can be analyzed by computer. This light carries information about the density and velocities of the ions and even the strength and direction of the local magnetic field. Heavy ion beam probes (HIBPs) work even better and can
even measure the internal electric fields. These are the main ways, developed over many years, to probe inside a fusion plasma and get the knowledge we now have on how a magnetized plasma behaves.

One of the most complex technological tasks is to manage the supply of tritium. Tritium is injected into the plasma as fuel. It leaves the plasma through the vacuum pumps, most of it going through the divertor. It is generated in the breeding blankets and has to be captured and purified. It is also a contaminant in the liquids and other materials that leave the reactor and has to be removed from them. Excess tritium has to be stored safely for future use in raising the power of the reactor or starting up other reactors. Figure 9.20 shows a simplified diagram of these paths.

To new

Inventory

Fig. 9.20

Tritium leaves the tokamak in two paths — either through the vacuum pumps, including those pumping the divertor, or through the first wall (FW) and the blanket. The vacuum exhaust goes directly to an isotope separation system which saves the T2, D2, and He and removes the impurities. Pure T2 is sent directly to Tritium Storage and Management. The tritium generated in the blanket goes first to a tritium processing plant to remove it from the breeder materials, and then to iso­tope separation. Material contaminated with irremovable tritium from both streams then goes the Tritium Waste Management. The fueling system receives recovered tritium from the two paths as well as from storage or from external sources. The fueling system then injects tritium and deuterium into the plasma. Deuterium is cheap and safe and does not have to be parsimoniously recovered.

The vacuum in the torus is maintained by cryo-pumps [13]. These are porous carbon surfaces cooled by liquid helium to 5 K; that is, 5° above absolute zero, the latter being -273°C or -459°F. At that temperature, all gases except helium are condensed and stuck to the cryogenic surfaces. To release hydrogen, including tri­tium, the cryo-pumps are periodically heated to about 90°K, and this gas is sent to the isotope separation system. To release all the captured gases, the pumps are raised to room temperature.

Fueling is done by injecting frozen pellets of tritium and deuterium at suf­ficient velocity to reach the center of the plasma. This is much more efficient than injecting DT gas at the boundary, since the gas will be ionized at the surface and will not reach the interior. There is some loss of tritium in the process, and this will appear in the pumping system. The plasma is heated mainly by neutral beam injection (NBI), the beams consisting of deuterium and tritium. This system will have its own system of tritium management.

Isotope separation is done by freezing the gases to liquid helium temperatures and selective warming in four interlinked distillation columns [13]. The tritium process­ing plant in ITER is a large seven-story building [12]. In addition, all water in the ITER installation and all air from buildings have to pass through a detritiation plant to remove the tritium. Water released back into the environment is pure H2O, and hydrogen released into the air is pure protium (H2). Tritium has to be stored until it is used. This is done in metal-hydride getter beds, each capable of holding 100 g of tritium [13]. Zirconium-cobalt (ZrCo) absorbs T2 to form ZrCoT3. The reaction is reversible upon heating to release the T2. Although techniques for tritium containment are well established in the fission industry, the amount of tritium in fusion is orders of magnitude larger. There has been no experience so far on such a large scale.

In Chap. 3, we carefully showed that a magnetic bottle has to be doubly connected and not a sphere; hence tokamaks are toruses.1 How, then, can a tokamak be spheri­cal? No, spherical tokamak is not an oxymoron. A tokamak can be spherical as long as there is still a hole in the middle. This is shown in Fig. 10.11. These small, fat tokamaks have typical aspect ratios A between 1 and 2. There are many advantages to having small A, but the problem is how to fit all the necessary equipment into the small hole. Spherical tokamaks (STs) are so attractive that many clever ideas have been proposed for treating the small hole, and there are over two dozen STs all over the world testing these ideas.2 In fact, one can eliminate the hole in the vacuum chamber altogether as long as the magnetic field is still toroidal.

Aside from the small size and the consequent cost savings, STs have a large advantage in plasma stability. This is explained in Fig. 10.12, which shows the magnetic-field structure in an ST. The field lines behave very differently from those in a normal tokamak (Fig. 6.1). A particle following a field line spirals around the central column before returning to the outside of the plasma. Good and bad curva­tures are shown in Fig. 7.10. In good curvature, the bend is toward the plasma, and in bad curvature, it is away from the plasma. We see that there is a lot of good curvature around the central column, and a region of weaker bad curvature when the field line returns to the top. Since particles spend more time in good curvature than in bad, there are strong forces pushing the plasma inwards. Much smaller magnetic fields are needed in STs because of the good confinement.

In a 1986 paper [16], Martin Peng and D. J. Strickler noted that the vertical field needed in tokamaks (Fig. 6.19) had a natural tendency to elongate the plasma, and they laid out the basics for the design of STs. Elongation is the vertical length of the plasma compared with its minor diameter, and it has good consequences for STs. As the aspect ratio goes down from 2.5 to 1.2, the elongation increases from 1.1 to 2, and the magnetic field that gives the needed quality factor q for a given

^bar. qg aspect ratio
(conventTSnaL tokamak)

Small aspect
ratio (spherical
tokamak)

Aspect Ratio = Major radius / minor radius

A= R / a

Fig. 10.11 A spherical tokamak has an aspect ratio much smaller than a normal tokamak [15]

plasma current falls by a factor of 20! [15] The value of beta (ratio of plasma pressure to magnetic-field pressure) is therefore very high in STs.

The British machines START (Small Tight Aspect Ratio Tokamak) and its successor MAST (MegAmpere Spherical Tokamak) have given the most informa­tion on STs. A photograph of the spherical plasma in START is shown in Fig. 10.13. The graph of beta values obtained in START (Fig. 10.14) shows the great improve­ment over normal tokamaks. In that graph, BT is the toroidal beta (that calculated with the toroidal magnetic field), and BN is the normalized beta, as defined in Chap. 8 under Troyon Limit. The recent data (red dots) show that the density limit can be exceeded in a spherical torus.

In spite of their physical appearance, STs exhibit the same phenomena observed in large-A tokamaks; the H-mode and ELMs, for instance. MAST is suitable for studies of ELMs and was used for the design of ELM-suppression coils. The shape of the field lines also gives STs a natural divertor.

Now we tackle the question of how to minimize the width of the central column. The toroidal magnetic field in a tokamak is generated by coils that thread through the hole, as shown in Fig. 6.1. All the coil legs that go through the hole can be combined into a single copper bar carrying all the current, as shown in Fig. 10.13.

This is possible because the B-field is small in an ST, so the coil currents are reduced. To drive the toroidal plasma current, the brute force way is to put an iron core through the hole and drive the current by transformer action, as shown in Fig. 7.14. Most tokamaks use air-core transformers that have no iron. These consist of toroidal coils around the plasma, including some inside the hole. This is shown in Fig. 7.15. These methods are called inductive drive. The disadvantage is that the current has to be increasing to excite the current; and since it cannot increase for­ever, the tokamak has to be pulsed. Modern tokamaks use noninductive drive,

which consists of bootstrap current and wave-driven currents (Chap. 9). This would eliminate the need for toroidal coils inside the hole.

The problem is that you can’t launch a wave unless there’s a plasma, and you can’t confine a plasma unless there is already a rotational transform. So it seems that at least some small toroidal coils have to be crammed into the hole, but there may be a solution. Neutral-beam injection is the usual way to heat a large tokamak. Currently, there has been some success (in MAST [15]) in ramping up the NBI in such a way that it drives a current also. It is also possible to create plasmas in cor­ners of the chamber where poloidal coils can be inserted, and to have these plasmas drift and merge into the center. This is illustrated in Fig. 10.15.

While experimentation on STs is being conducted intensely worldwide, reactor studies have been made both in Europe and the USA. The ARIES-ST design of 1999 is shown in Fig. 10.16. The central column is made to be slid out and replaced easily. All blanket modules are on the outside. Note the natural divertors at the top and bottom.

Only minute quantities of hydrogen occur naturally in the atmosphere, but it can be produced efficiently in a process called steam reforming. When methane (CH4), the main constituent of natural gas, is heated up to 700-1100°C in the presence of water (H2O), two reactions occur. First, CH4 and H2O combine to form hydrogen (H2) and carbon monoxide (CO). Then, the CO reacts with more H2O to form CO2 and more H2. The net result is that methane and water are made into hydrogen and carbon dioxide. The second reaction is exothermic (it gives off heat), so that heat can be used for part of the heat needed to drive the first reaction. The rest of the heat comes from burning some of the methane. The CO2 has to be sequestered using one of the methods discussed in Chap. 2.

Large factories for steam reforming already exist in the petroleum industry because hydrogen is needed for taking the sulfur out of gasoline and for producing ammonia and fertilizers. These sources supply the hydrogen for initial tests of hydrogen cars. There are other possible ways to produce hydrogen. The classical way is direct hydrolysis of water. An electrolyte is added to the water to make it conduct electric current. Two electrodes45 in the form of plates are then put into the solution, and a DC voltage is applied between then. Water molecules are bro­ken up into hydrogen and oxygen, and they bubble out separately at each elec­trode. The efficiency of the process depends on the electrolyte and electrode design, but in any case is quite low. If the energy used to produce the electricity is counted, the energy content of the hydrogen is perhaps a third of the energy used to produce it by electrolysis. Even that may be worth it if the original energy source is nonpolluting, such as a fission or fusion power plant. Pricewise, it is estimated that 1 kg of hydrogen costs $7-$9 to make by hydrolysis, compared with $4-$5 by steam reforming. The nuclear industry has plans to demonstrate hydro­gen production at $1.50/kg by 2015.50 One kilogram of hydrogen has about the same energy as 1 gallon of gasoline, but these prices cannot be compared directly with the price of gasoline because cars use and carry hydrogen and gasoline in completely different ways.

There are several new ideas on hydrogen generation without producing CO2 also. One is to use dye-sensitized solar cells plus a catalyst to get hydrogen directly from sunlight. Another is to perform artificial photosynthesis by growing algae. The most advanced is a system to run a hydrogen fuel cell backwards, using solar electricity to make hydrogen rather than using hydrogen to make electricity. In the Compagnie Europeenne des Technologies de l’Hydrogene (CETH) in France, a machine called the GenHy5000 Water Electrolyzer has successfully done this [32]. About the size of a refrigerator, the hydrolyzer produces H2 at the rate of 5,000 L/h at atmospheric pressure using electricity with 62% efficiency. It has run continu­ously for 5,000 h, but efficiency will drop with intermittent use. When powered by rooftop solar cells, the hydrogen can be generated and stored at 10-atm pressure for later use. For automobile refueling stations, higher pressures will be required. The hydrogen can be allowed to build up pressure as it is generated. A smaller model has run at 30 atm for a total of 10,000 h. Its other data are: voltage 1.7 V, current 1 A/ cm2, temperature 90°C, and power consumption 4 kWh/m3 of H2. The noble-metal content in the catalysts is 1.5-3 mg/cm2, and the hydrogen is 99.99% pure. Though this is a fuel cell run backwards, years of research have yielded valuable data on fuel cells in general: what materials to use, how to make them, how long they will last, and how they can be contaminated. In particular, it was found that the catalyst layers are best deposited directly on the membrane, and a method was devised to do this using frequency-modulated electric pulses.51

In spite of the problems with the fuel cell, prototype hydrogen cars costing millions of dollars have been made. The Honda FCX, for instance, is sleek, normal­looking passenger car with a 100-kW fuel cell stack weighing 148 lbs (67 kg) and occupying 57 L (2 cu feet). Four kilos of hydrogen are stored at 5,000 psi in a 170-L (6 cu feet) tank. A matching 100-kW (134 HP) electric motor runs on a lithium-ion battery charged by the fuel cell. The relation between kilowatts and horsepower (HP) will be found in Box 3.7. The mileage is stated to be 60 miles/kg of H2, and the range is 240 miles (386 km). The car could be leased at $600/month, but full production is not expected before 2020.

Box 3.7 Kilowatts and Horsepower

Kilowatts and horsepower are both units of energy relevant to electric cars. A kilowatt (kW) is approximately four-thirds of a horsepower (HP), and 1 HP is about three-fourths of a kW. The exact values are as follows:

1 kW = 1.341 HP 1 HP = 0.746 kW 1 W-hr=4.8 HP-sec 50 W-hrs = 241 HP-sec

When one puts a note on the refrigerator door with a magnet, one gets the impression that the attractive force is in the direction of the magnetic field. On the other hand, we said that the magnetic force is perpendicular to the field lines. Before we resolve this apparent contradiction, let’s see what the magnetic force on a particle (an ion or electron) is supposed to be. The force is called the Lorentz force,5 and it has five main features. (1) It acts only on particles with an electric charge. (2) It is propor­tional to the strength of the magnetic field, as one would expect. (3) It does not affect a particle that is stationary nor one that moves only along a field line. Only the perpendicular motion of a particle — that which takes it from one field line to an adjacent one — counts. (4) The force is perpendicular to both the particle velocity and the field line. (5) The force depends on the electric charge on the particle and is in opposite directions for positive and negative charges. This is a mouthful, but here is what it means. If a proton, say, is stationary, it feels no force. If the proton moves strictly along a field line, it also feels no force. If it moves across field lines, however, the magnetic field will push it, not backwards, but in a perpendicular direction. An ion and an electron both have the same charge, but of opposite signs, so the Lorentz force on them is in opposite directions. As we shall see, this will cause the protons and electrons to revolve in small circles around a field line. Refrigerator magnets seem to pull along the field, though. This is because permanent magnets are more complicated.6

A cartoon of the orbits of an ion and an electron in a magnetic field is shown in Fig. 4.9. The X in the center indicates that the magnetic field, labeled B, points into the page. The arrows indicate the Lorentz force, which is everywhere perpendicular to both the particle velocity and the magnetic field. If the velocity is constant, the force is inward everywhere with the same strength, so the orbits are circles. Note that the motions are in opposite directions because the charges have opposite signs. Imagine taking a yo-yo, stretching it out, and swinging it with a steady motion in a circle over your head. The string pulls the yo-yo inward with the same force at all times, so the yo-yo moves in a circle. Here, the magnetic field applies a force just like that of the string. This gyration orbit is called a cyclotron orbit, since the first cyclo­trons used this principle to keep the protons inside a circular chamber. It is also called a Larmor orbit because in science you can get something named after you without paying a huge endowment. The radius of the circle is called its Larmor radius.

Since the magnetic force is always perpendicular to the field’s direction, particles move in the parallel direction without being influenced by the magnetic field. A magnetized plasma, then, doesn’t look like Fig. 4.4, where ions and electrons are free to move in any direction. Instead, it would look like Fig. 4.10, where the charged particles gyrate in their Larmor orbits and move unimpeded in the direction of the magnetic field B. Field lines are like invisible railroad tracks that guide the motion of charged particles.

How big is a Larmor orbit? In a cyclotron, the orbit is the size of a large labora­tory because the protons have very large energies. In a fusion reactor, a deuteron has a Larmor radius of about 1 cm, when compared with a plasma radius of about a meter. An electron’s orbit is much smaller than a deuteron’s, even if it has the same energy. This is the result of two effects. With the same energy, an electron would move much faster because it is much less massive than a deuteron. So you would think that its orbit would be larger than a deuteron’s. However, the Lorentz force that curves the orbit is stronger with higher velocity. The upshot is

that the electron’s orbit is smaller by the square root of the mass ratio, or about 60 in this case. In Fig. 4.10, the electron orbit was greatly enlarged in order to be visible.

Since these gyration orbits are so much smaller than the plasma that they are immersed in, we don’t have to track the particle motions in such detail. We only have to track the motion of the centers of the circles, which are called guiding centers. In the future, when we talk about the motion of plasma particles, we will mean the motion of the guiding centers.

We can now return to the question, “How can a magnetic field hold a plasma?” We have seen that a magnetic field does not apply a force to a particle that will stop it from following field lines, so field lines that end on a boundary somewhere cannot prevent a plasma from hitting a wall.7 On the other hand, plasma cannot go across field lines because the magnetic force simply keeps charged particles spinning in small Larmor orbits around the same field line. Obviously, the solution is to make a field with lines that close on themselves and do not end. That’s the very first step in designing a magnetic bottle!

The q(r) profile of a tokamak discharge is perhaps its most important characteristic. It controls the stability of the plasma, where the magnetic islands form, and other essential features. An example of how the quality factor q varies with minor radius is shown in Fig. 7.2. It typically increases from 1 at the core to some number between 3 and 9 at the edge. Remember that q is the reciprocal of the rotational transform, so the twist of the magnetic field lines decreases gradually from the center to the edge of the plasma’s cross section. The changing degree of twist pro­vides the shear stabilization of instabilities. To increase the amount of shear would require q(r) to change over a wider range than 1-9. However, q cannot be too large, because then the twist would be too weak to cancel the particles’ vertical drifts; and q cannot be smaller than the Kruskal-Shafranov limit of 1, because, as we saw in Chap. 6, kink instabilities would occur. An obvious solution to this dilemma would be to make the twist change its angle several times, which would increase the shear without exceeding the bounds on q. This idea was never taken seriously earlier because there was no way to produce tokamak currents that would have to vary with radius in a screwy way. But now, all the large tokamaks have been able to produce “hollow” current profiles that are not peaked at the center but at some radius half­way out, as shown in Fig. 7.27. This generates a q(r) that is large at the center, falls to a minimum somewhere inside, and then rises again to a normal value at the edge.

Physically, the twist of the magnetic lines is very small near the center, gets tighter halfway out, and then gets gentle again near the edge. The twist angle changes more rapidly with radius, thus increasing the shear. A lower turbulence level is observed as well as a corresponding increase in confinement time.

Initially, hollow current profiles were produced transiently by a combination of ramped neutral beam heating (increasing the power in a prescribed way) and aux­iliary heating. This would not work for a reactor, which has to run in steady state; but by a fortuitous circumstance, bootstrap current can create hollow current profiles. This is yet another of Mother Nature’s gifts. With the large bootstrap fractions in reactor-level machines, it is theoretically possible to design an “Advanced Tokamak” scenario in which the pressure profile leads to a bootstrap current profile that produces reversed shear, and the resulting reduced diffusion rate is consistent with the pressure profile! This sounds like a pipedream, but, as we shall see, much of this has already been accomplished in experiment.

Edge-localized modes (ELMs) were described in Chap. 8. They are instabilities of the H-mode pedestal which can release plasma suddenly to the wall. Although most of these particles should flow to the divertor, the sudden burst of heat can erode and damage the divertor’s surfaces. The H-mode pedestal constrains one-third of the plasma’s energy, and 20% of this or as much as 20 MJ can be dumped into the divertor in a fraction of a second [16]. The preferred method to suppress ELMs is to impose a rippled magnetic field at the surface of the plasma, near the pedestal. The idea is to break up instabilities that tend to be aligned with the magnetic field. The pattern of currents in the ELM coils can be varied slowly to follow changes in the magnetic field lines. This method has been tested in the DIII-D tokamak in San Diego, California, and thorough calculations have been made to design the sizes and spacings of the coils for ITER [17]. A panel of ELM coils is shown in Fig. 9.27. Figure 9.28 shows what the surface of ITER will look like with these coils installed. It will take 2.6 MW of power to drive these coils. Being in-vessel components, the coils have to withstand intense heat and neutron bombardment. In ITER, the coils are protected from the plasma by a 50-cm thick, water-cooled, nonbreeding blanket whose only function is to attenuate the neutrons.4

In DEMO, there would be no place for ELM coils, since breeding blankets have to cover the machine to capture as many neutrons as possible. Locating the coils behind the blanket would probably be too far. ELM coils are ad hoc, temporary

solutions not included in the original design of ITER since the problem had not yet arisen. The physics of ELMs has to be understood better to find passive methods for their control, but there is time to do this.

Once the ELM coils have been installed, they can also be used for other purposes. By applying a small current at a low frequency like 50 Hz, a weak insta­bility called the RWM can be controlled. A differently spaced DC current can also be added to help prevent disruptions (described in detail in the next section).

When high-intensity lasers became available around 1970, people like Ray Kidder at Livermore and Keith Brueckner at the University of California, San Diego, began to think about inertial fusion. If it’s so hard to hold a plasma with a magnetic field, what about heating a plasma so fast with a laser that it fuses before it can fly apart? The idea was to fill a very small glass sphere with deuterium or DT fuel and zap it with lasers from all sides. The glass would evaporate and expand outwards, and the reaction would push the fuel inwards into a small hotspot where it would fuse before it could turn around and blow out. They worked out the numbers and made a proposal to the Atomic Energy Commission to start a laser-fusion program at Livermore. This proposal was reviewed by a committee, chaired by Lawrence Hafstad, which included the author. The proposal was accepted, and the rest is history.

Starting with a budget much smaller than that for magnetic fusion, the laser program was very successful, and a series of larger and larger lasers was built, with names like Janus, Argus, Shiva, Nova, and now NIF, the National Ignition Facility. The success depended in large part on an intricate computer program by John Nuckolls, the first of its kind, which could predict what would happen in the implosions. At $458M, the budget for inertial confinement has overtaken that for magnetic confinement ($426M) [29]. However, inertial fusion is not primarily funded for energy. Although some scientific support comes from Fusion Energy Sciences, the main support is from the National Nuclear Security Administration. That’s because the miniexplosions that lasers can create are powerful enough to mimic the effects of hydrogen bombs on materials. Data needed to maintain the nuclear stockpile and develop new weapons can be obtained without underground testing with real explosions. In addition, the study of the behavior of matter under extreme pressure and temperature conditions is vital to our understanding of astrophysical objects in our universe.

One might object to spending more money on the military part of fusion rather than on the energy part, but that expenditure is essential. National security must come first. Without freedom, we can’t do anything. Laser fusion is sold to the public as an energy source because of its glamorous achievements. It will reach ignition decades before ITER can. However, it is a pulsed system like the pinches in the previous section and is difficult to make into a steady power source.

The main problem is the lack of a suitable driver. The term inertial confinement fusion was coined to include drivers that are not lasers. To have a steady power output, a laser-fusion power plant has to implode a pellet at least ten times a second. A car runs smoothly with 3,200 explosions a second (four cylinders at 800 rpm), but 10 explosions per second would be enough for a power plant. However, lasers can’t pulse that fast. The most powerful ones use neodymium-doped glass disks a couple of feet in diameter. As much light as possible is passed through the glass for amplification. This heats up the glass almost to the point of cracking. It takes hours for the glass to cool. With earlier lasers, two shots a day were all that could be expected. There are thousands of these disks in a megajoule laser. If one of them cracks, the whole system shuts down.

The main task, then, is to find a better driver. Ion beams have been tried, but they are hard to focus down to a small target and also have to be pulsed. Krypton — fluoride (KrF) lasers use no glass and can be pulsed more rapidly. They have some promise, but pulsing at five times a second has been proved possible only at low power. Systems based on pulsed power (discussed later) are also pulsed infre­quently. Laser fusion should be considered as the fantastic technological achieve­ment that it is, but not as a promising base-load energy source.

Wind is an attractive source of free energy. It generates electricity directly. It does not pollute, and it can generate enough energy to cover itself in half a year. The technology is well developed and is actually rather interesting. But wind can never be a primary source of power. It is too variable, and the problems of energy storage, transmission, and load leveling are overwhelming. Wind power is suited for islands such as the Galapagos25 and Hawaii,26 where all other energy must be imported. Wind is the best of the renewable sources of auxiliary power, but it cannot supply backbone power.

When a U235 nucleus is joined by a slow neutron, it can split into two nuclei further down in the periodic table, plus two or three neutrons, as shown in Fig. 3.59. In this case, the fragments are Ba144 and Kr89. Adding the mass numbers will show that three neutrons are released in this case. A chain reaction occurs when one, and only one, of these neutrons splits another U235 nucleus to make more neutrons to keep the chain of reactions going. If two neutrons cause further fissions, the reaction will run away. Figure 3.59 shows another way to continue the chain. As we shall see, there are many more U238 nuclei in the fuel than U235s, so a neutron can enter a U238 nucleus to form U239, which then beta-decays into Pu239, which is fissionable. A neutron hitting the Pu239 will cause fission and keep the chain going.

Moderation is the Key

Of course, things are not this simple. The neutrons from a fission have energies around 2 MeV (about 20 billion°K). (Definition of electron-volt units is given in Chap. 5). They have to be slowed down to normal temperatures before a nucleus will accept them. Room temperature is about 0.025 eV. A moderator is used to do this. Here, a moderator is not the chair of a panel discussion; it is an element that slows down neutrons efficiently without absorbing them. The most common mod­erators are light water [ordinary H2O, heavy water (D2O), and graphite (very pure carbon)]. Only light elements (those with low atomic masses) can be moderators. The reason is that neutrons are light, and they will bounce off a large nucleus with­out losing much energy. A marble striking a billiard ball will just bounce off. A cue ball striking an 8-ball can come to a complete stop, losing all its energy to the 8-ball, because it has the same mass. Light water is a better moderator than heavy water because the H is closer to the neutron in mass than the D, but it’s not twice as good because the H can capture the neutron to make a D. A deuteron is less likely to capture yet another neutron to make triply heavy tritium. Carbon has mass 12, so graphite is a weaker moderator than water, but it has other properties, like staying solid at high temperature. Moderators are so important that nuclear reactors are classified according to their moderators.