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Plasmas and Fluids (1986)
Commission on Physical Sciences, Mathematics, and Applications (CPSMA)

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4 Fusion Plasma Confinement en cl Heating SCOPE AND OBJECTIVES OF FUSION PLASMA RESEARCH Introduction Thermonuclear fusion is one of the very few options available that can provide for mankind's energy needs in the very long term. Based on essentially inexhaustible (billion-year) fuel reserves of near-zero cost, fusion power is perceived to offer many advantages over alter- natives, such as solar power or the breeder reactor. Environmentally, fusion has the potential to provide a much safer system than the breeder reactor, with respect both to the safety of the plant itself and to all aspects of its fuel cycle: fissionable materials are not involved; fusion's "ashes" are inert; and radioactivity associated with plant operation can be minimized and made to be short lived. Recognition of the major advantages of fusion is reflected in the fact that fusion has become a major international research effort. There are large fusion programs in Western Europe, in the Soviet Union, and in Japan (where fusion has been declared to be a national goal). The U.S. fusion program is recognized worldwide as being preeminent, largely as a result of a foresighted expansion of the program about a decade ago. If the present momentum can be maintained, the United States could also become the world leader in the construction and deployment of fusion power systems. 144

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FUSION PLASMA CONFINEMENT AND HEATING 145 Although the study of naturally occurring high-temperature plasmas is of considerable scientific interest of itself, it has been the quest for controlled fusion power that has been the dominant influence on research in plasma confinement and heating for three decades. Fusion plasmas require very high temperatures, higher even than the center of the Sun, and must be confined either by very strong magnetic fields or by compression to ultra-high particle densities. The basic theoretical properties of a magnetized plasma, and the conditions under which thermonuclear power can be released, were fairly well understood at the outset of fusion research in the early l950s. In retrospect, however, it is clear that the experimental diffi- culties, as well as the vicissitudes of plasma behavior, were greatly underestimated. By the late-19SOs, it became clear that more basic research would be required before any practical, large-scale fusion device would be possible. Theoretical efforts directed toward the fundamental understanding of plasma confinement and heating re- ceived high priority, and these efforts were reinforced by many experiments directed more toward the development of plasma physics than toward the immediate objective of fusion power. By the late- 1960s, the theoretical understanding of magnetically confined plasmas had advanced impressively, but there was still no firm experimental basis for the extrapolation of any magnetic-confinement scheme to the plasma conditions regarded as being necessary for a practical fusion reactor. The prospects for success in fusion research turned dramatically better toward the end of the 1960s and have improved steadily throughout the 1970s and early 1980s as a result of the experimental demonstration of high-temperature, well-confined plasmas in a number of devices in several different countries. Plasma parameters in some of today's fusion devices are within reach of those required in an actual reactor. However, while empirical scalings deduced from these exper- iments may perhaps prove adequate to bridge the remaining gap to the reactor regime, the improvement in predictive capabilities that would result from a more thorough theoretical understanding of the behavior of confined plasmas an understanding that has tended to lag behind the experimental achievements would greatly enhance confidence in detailed reactor projections and would aid in the design of the most advantageous fusion systems. Progress in the much younger discipline of inertial confinement- which had its origins in the weapons programs of the 1950s but became a serious candidate for power production and other civilian applica- tions only in the late 1960s has been sustained by the remarkable advances that have occurred in recent years in the development of

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146 PLASMAS AND FLUIDS very-high-power lasers and intense beams of energetic particles. In inertial confinement, these lasers or particle beams are used to com- press a tiny pellet of fusion fuel to ultra-high density; magnetic fields are not involved. Progress in the science of inertial confinement has been greatly facilitated by the development of highly sophisticated diagnostic methods, which can make measurements of physical quan- tities in microscopic regions of space in times as short as a trillionth of a second. Whether useful net energy gain can be achieved by inertial confinement remains uncertain, but the techniques have other impor- tant civilian applications, such as the production of fissile fuel. The experimental science of plasma confinement now rests on a solid theoretical understanding of the macroscopic dynamics of nonuniform plasmas. Indeed, to an ever-increasing extent, important experimental advances in plasma confinement are the result of some new insight into the theoretical properties of some particular confinement configura- tion. This close link between the physical processes of importance and the geometry of the confinement configuration is intrinsic to fusion research and implies that any discussion of progress in fusion must be organized by confinement concept; such is the approach adopted in this chapter. Progress in the experimental science of plasma heating has been the result both of technological advances and of greatly improved under- standing of the microscopic processes underlying the propagation and deposition of energy in nonuniform plasmas; plasma-heating tech- niques are relatively insensitive to geometrical configuration and can often be applied to a number of different confinement concepts. Plasma confinement and heating are not the only issues to be resolved before a practical fusion reactor can be built. However, for the first time in the history of fusion research, there seems now to be a substantial and reliable experimental basis for the detailed descrip- tion of the fundamental scientific requirements of such a reactor-at least in the case of the magnetic-confinement approaches. The Fusion Process The reaction most likely to be used in a first-generation fusion reactor brings together the charged nuclei of deuterium (D) and tritium (T), which react to form an energetic charged nucleus of helium (4He, sometimes called an alpha particle) and an ultra-energetic neutron (n), according to the relationship D + T > 4He (3.5 MeV) + n (14.1 MeV). Creation of fusion reactor fuel a plasma of positively charged deute

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FUSION PLASMA CONFINEMENT AND HEATING 147 lo-23 -24 10 b lO ' ' ' ' "'1 ' ' ' ' ~ 'l' - (a ) ~ ~ DT/ \ D - He / -26 -27 0 -28 _~ IQ 1( )' IQ2 1( 3 ION ENERGY (KeV) : T-T/// , ., ., ,.1 10 -17 - -18 he's 1 0 - lb -19 0 -2 0 lo-15 (b) ~ ' "2 lo-16- D-T/D-3H~ :/ D-D lo-21 . 1 . . 1 . . e 10° 101 lo2 103 ION TEMPERATURE ( rev) FIGURE 4.1 (a) The cross section cr for various fusion reactions as a function of the relative energy of the colliding ions. (b) The quantity rev that is a measure of the fusion reaction rate averaged over thermal distributions of colliding ions, as a function of ion temperature. rium and tritium nuclei and neutralizing electrons-is facilitated by the dissociation of atoms into their electrically charged constituents at temperatures above 1 electron volt [eV (1 electron volt equals about 104 degrees Celsius)~. However, before the positively charged deute- rium and tritium nuclei can fuse, the electrostatic forces of repulsion between them must be overcome. Figure 4.1(a) shows that, for the cross section of the D-T reaction to be at its maximum, the relative kinetic energy of the colliding nuclei (ions) must be about 100 kiloelectron volts EkeV (109 degrees Celsius)~. In a thermal distribution of ion energies, fusion reactions occur predominantly among the most energetic (suprathermal) particles; Figure 4.1(b) shows that the reac- tion rate reaches a broad maximum for ion temperatures in the range 20 to 100 keV. In terms of the potential overall energetics of the fusion process, an energy investment even of 100 keV in each reacting nucleus is quite modest, since the fusion energy released by each reaction is almost 200 times greater, namely 17.6 million eV [MeV (10~2 degrees Celsius)~. In terms of the actual realization of fusion condi- tions, however, the requirements are formidable, since the plasma must not only be heated to a temperature in excess of 10 keV (about 108

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148 PLASMAS AND FLUIDS degrees Celsius), but the energy must also be confined (that is, contained within the plasma, without being carried to the walls of the containing vessel) for times long enough for the relatively infrequent fusion reactions to occur. Eventually, it seems possible that the deuterium-tritium reaction might be replaced by fusion processes that are more difficult to achieve but have even more desirable environmental features. For example, use of the deuterium-deuterium reaction would eliminate the need for regeneration of tritium fuel in the fusion reactor by means of a process using lithium compounds that is well understood, in principle, but that complicates the design of the heat-producing fusion-reactor "blanket." Another reaction that between deuterium and helium-3- is an example of a fusion reaction that releases its energy entirely in the form of charged particles, rather than neutrons, thereby offering the possibility, at least in principle, of direct conversion of the fusion energy into electrical energy. However, Figure 4.1 shows that the cross sections and reaction rates for these reactions are as much as a factor of 10 lower than those for the deuterium-tritium reaction. An important figure of merit for an experimental fusion reactor is the ratio of the output power derived from the fusion reactions to the input required to heat the plasma. This ratio, called the energy multiplication factor Q. depends on the fraction of the hot nuclei that are able to fuse during the time it would take for the plasma to lose its energy. Since fusion reactions are two-particle reactions, the Q-value is found to depend on a confinement parameter (sometimes called the Lawson parameter), the product of the plasma (electron) density and the energy confinement time; the Q-value depends, of course, also on the ion temperature. Figure 4.2 shows the requirements for thermalized break- even (a Q-value of unity for a thermal distribution of reacting particle energies) in a deuterium-tritium plasma, as a function of the spatially averaged ion temperature and the confinement parameter. For exam- ple, thermalized breakeven in a plasma with an average ion tempera- ture of 10 keV requires that the confinement parameter exceed 6 x 10~3 particles per cubic centimeter seconds. Approaches to fusion that utilize magnetic confinement divide into two main classes: (i) those whose goal is a plasma with a density of somewhat more than 10~4 particles per cubic centimeter and a confine- ment time of about a second (tokamaks, stellarators, mirrors, and bumpy tori) and (ii) those that have the potential for much higher- density plasma, typically 1O~s particles per cubic centimeter or more, with correspondingly reduced requirements on confinement time, typically a tenth of a second or less (reversed-field pinches, compact toroids).

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FUSION PLASMA CONFINEMENT AND HEATING 149 One . - Cal ~ 10 AL LLI an to _' Iqnit ions / : . : : ' Therma lized Breakeven tTe=Tj~ / Beam Driven Breakeven (Eb= 200 keV ) 1 1 2 1013 1014 CONE I NEMENT PARAMETER nT (cm3s) FIGURE 4.2 The ion temperature Ti and confinement parameter no required for D-T ignition, for breakeven in a thermal plasma, and for breakeven in a beam-driven plasma (beam energy 200 keV). Here, n is the electron density and ~ the energy confinement time. Approaches to fusion that utilize inertial confinement seek to com- press a deuterium-tritium pellet to a density of about 1025 particles per cubic centimeter and to maintain a thermonuclear "burn" at fusion temperatures for about 10-9 S before the pellet disassembles. In the case of the lower-density magnetic approaches, where the plasma can be penetrated by beams of energetic particles, a significant improvement in the confinement requirement-by almost a factor of 10-can be realized by using reacting beams of very high energy to heat the plasma. Figure 4.2 also shows the requirements for this kind of beam-driven breakeven, for the case where a tritium plasma is heated by a 200-keV deuterium beam. On the other hand, the Q-value of a plasma increases rapidly after the confinement parameter exceeds the break-even threshold, because 20 percent of the energy produced in fusion reactions between deute- rium and tritium is released in the form of energetic helium nuclei (alpha particles), which can be retained in the plasma, thereby ampli- fying the input power available for heating. Eventually, the fusion reactions become able to maintain the temperature of the plasma without any input of heating power, and the Q-value becomes infinite; at that point, the plasma is said to be ignited. Figure 4.2 shows that

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150 PLASMAS AND FLUIDS ignition of a deuterium-tritium plasma with an average ion temperature of 10 keV requires that the confinement parameter reach 3 x 10~4 particles per cubic centimeter seconds. At temperatures below 5 keV the fusion reactions are unable to sustain the plasma temperature against losses of energy by radiation, with a result that ignition becomes impossible even if the energy carried from the plasma by conduction and convection is negligible. From a practical viewpoint, taking into account the efficiency for conversion of fusion energy into electrical energy and the efficiency of plasma heating, a fusion reactor can produce useful net power if the Q-value lies in the range 10-20. (In inertial confinement fusion, a pellet-plasma Q-value of a hundred or more is needed to compensate for driver and implosion inefficiencies.) The principal approaches to fusion magnetic confinement utilizing either toroidal or mirror magnetic fields and inertial confinement are illustrated in Figure 4.3. Magnetic Confinement The most successful approach to the confinement of plasma at fusion temperatures makes use of the fact that charged particles tend to gyrate in tight spirals along the lines of force in a magnetic field. The radius of gyration of a deuterium ion with an energy of 10 keV in a magnetic field of strength 20 kilogauss (kG) is only 1 centimeter (cm), implying that the particles of a fusion plasma can be readily confined in a suitably shaped "magnetic bottle" of modest size and modest field strength. However, a plasma at fusion densities and fusion temperatures has a kinetic pressure (density times temperature) that is large enough to depress the magnetic pressure of the confining magnetic field by a significant factor, called beta, as illustrated in Figure 4.4. The plasma beta-value that is attainable depends mainly on the shape of the magnetic bottle. For a magnetic field strength of 50 kG-typical of that proposed in many reactor designs-the realization of a beta-value of 6 percent would provide a plasma with a pressure of about 6 atmospheres. This would correspond, for example, to an average plasma density of 2 x 10~4 particles per cubic centimeter and an average ion and electron temperature of 10 keV, requiring an energy confinement time of about 1.5 s for ignition. The fusion power density in a deuterium-tritium plasma would be about 5 megawatts per cubic meter (MW/m3) a practical value from an engineering viewpoint. Fusion-reactor con- cepts involving substantially higher beta-values offer greatly improved

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FUSION PLASMA CONFINEMENT AND HEATING 151 (a) Magnet ic Field LinesElectrical \,~Conductors it_ MagneticE lectrica I (b) Field LinesConductors Rae ~ ~ ~ / ^ V V OF V V V ~ v v v v v (c) Laser Light ...... . . . r. _ ·.-. . . _ . .......... id: :.:.:~Blow-Off ~ · . . . _. .~ . - A.. .. ~ ` ~ ...... - ---------I Compressed Igniteld Fuel _,85 ~,{:: ~i;::::: :: ~ . : Implosion ~ Neutrons FIGURE 4.3 (a) Toroidal magnetic confinement. Charged particles gyrate in tight spirals about closed magnetic field lines, passing time and time again around the doughnut-shaped containment vessel. (b) Mirror magnetic confinement. The magnetic field lines are open, but charged particles are reflected at high-field regions at the ends of the device and thus remain trapped within the containment vessel. (c) Inertial confine- ment. A tiny D-T pellet is imploded by high-power laser light to a density high enough for thermonuclear burn to occur.

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152 PLASMAS AND FLUIDS MAGNETIC ~ PRESSURE ~\ B2 \ 87r 87rnT if= 2 B \'PLasMA \ PR ESSU RE nT FIGURE 4.4 Illustration of the depression in the magnetic pressure B218r caused by the kinetic pressure nT of a confined plasma. Here, B is the field strength, n the density of electrons and ions, and T the plasma temperature. The ratio of the two pressures is ,B = 8rnTlB2 reactor economics by better utilization of the magnetic energy, which can result either in reduced requirements on field strength or in a more compact reactor configuration; in the latter case, however, the higher fusion power density can represent a formidable engineering problem. The various magnetic bottles that are possible candidates for con- fining a fusion plasma divide into two main classes: toroidal (doughnut- shaped) configurations, illustrated in Figure 4.3(a), and mirror (linear, narrowing at the ends) configurations, illustrated in Figure 4.3(b). Toroidal magnetic configurations have the special advantage that charged particles cannot escape by simply moving along the magnetic field lines. Moreover, when ions collide with each other, they are deflected only one radius of gyration across the confining field. Many such collisions will, of course, lead to a slow migration (diffusion) of ion energy to the walls of the containing vessel. In order to minimize the importance of this particular energy-diffusion process as an obsta- cle to the achievement of fusion conditions, it is sufficient that the minor radius of the plasma torus should be more than a hundred times larger than the radius of gyration, that is, about 1 m or greater. One of the simplest of the toroidal configurations the tokamak- has been by far the most successful of all fusion concepts in realizing reactorlike plasma conditions in laboratory-size experiments and has already come within a factor of 4-5 of meeting minimum break-even requirments. The tokamak, and its close cousin the stellarator, are discussed later in this chapter. The principal alternative approach to a fusion reactor based on magnetic confinement is the mirror machine, an open-ended magnetic

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FUSION PLASMA CONFINEMENT AND HEATING 153 bottle in which most, but not all, ions are prevented from escaping along field lines by an increase in the magnetic intensity at the ends of the device. The energy confinement times are then determined by particle collisions, which scatter the ion velocity vectors into the loss regions. Mirror-confinement concepts are also discussed later in this chapter. A number of alternative toroidal configurations the bumpy torus, which adds high-energy mirror-confined electrons to produce a mod- erate-beta steady-state toroidal plasma; the reversed-field pinch, which produces a very-high-beta pulsed toroidal plasma; and the compact torus, which produces a moderate-beta plasma without any external magnetic coils linking the plasma have become important elements in the U.S. program and are also discussed below. In striving to attain the prescribed range of reactorlike parameters, experiments on magnetically confined plasmas have encountered four main energy-loss processes, listed here in order of increasing severity, that must be kept under control: (i) particle collisions, which disrupt the orbits of confined particles and give rise to an irreducible rate of diffusive energy loss; (ii) radiative cooling of the plasma, mainly in the form of ultraviolet radiation from impurity ions; (iii) fine-scale plasma instabilities, in effect tiny stepwise particle migrations that allow plasma energy to diffuse gradually across the magnetic field lines to the walls of the containing vessel; and (iv) large-scale plasma instabilities, that is, spontaneous deformations of the confining field that cause the plasma to escape abruptly out of the magnetic bottle. Although these four energy-loss processes take different forms in different magnetic configurations, progress in research on both toroidal and mirror- confinement concepts has been paced by a gradual improvement in the understanding of the fundamental physical mechanisms underlying all four processes and by the development of effective techniques to minimize them. However, the quest for a more complete, fundamental understanding of these processes still presents the science of plasma confinement with its most difficult and challenging problems. Although the stability and transport of magnetically confined plas- mas tend to be quite sensitive to the shape of the magnetic bottle, the various techniques that have been developed for heating a confined plasma tend to be applicable in a wide variety of magnetic configura- tions. A number of confined plasmas notably tokamaks are subject to one intrinsic type of heating, which arises from the resistive dissipation of the plasma currents that are needed to maintain plasma equilibrium. Because of the rapid decrease in plasma resistivity with increasing electron temperature, this type of intrinsic heating is gener

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154 PLASMAS AND FLUIDS ally inadequate to heat a plasma to fusion temperatures, except in some high-current-density toroidal pinch configurations. The auxiliary heat- ing power (that is, the power in addition to the intrinsic heating by the plasma current) that will be required to heat a plasma to fusion conditions can be estimated by noting that a deuterium-tritium plasma with a pressure of 6 atmospheres produces a fusion power density of about 5 MW/m3, corresponding to an alpha-particle heating power density of about 1 MW/m3. An auxiliary-heating power density of about half this value is found to be needed to heat an initially cold plasma to temperatures at which self-heating by fusion reactions becomes important. Thus, to heat a reactor plasma with a volume of order 100 m3, a total heating power of order 50 MW will be needed. Present-day experiments operate with auxiliary heating powers typi- cally of up to about 10 MW. One of the most effective plasma-heating techniques has been the injection into the plasma of intense beams of energetic neutral atoms of hydrogen or deuterium. These freely cross the confining magnetic field until they are stripped of their electrons, by collisional ionization and charge exchange, and are then retained in the plasma as energetic ions, gradually transferring their energy to background plasma particles by collisions. As an alternative to this type of neutral-beam heating, a variety of radio-frequency electromagnetic waves can be launched into a magnetically confined plasma, and there are a number of resonant frequencies at which such waves are strongly absorbed by the plasma, their energy being converted into thermal energy of the plasma particles. These radio-frequency heating processes have been known theoretically since the earliest days of plasma research, but only in recent years have they been applied successfully to heat plasmas to fusion temperatures. Plasma heating techniques both neutral-beam and radio-frequency are discussed later in this chapter. Inertial Confinement Separate from all the magnetic-confinement concepts, there are a number of entirely different inertial-confinement schemes, in which intense beams of laser light or accelerated particles are focused onto the surface of a tiny pellet filled with deuterium-tritium fuel Esee Figure 4.3(c)~. The pellet implodes because of the rocketlike reaction to the blow-off of the surface material of the pellet by deposition of the beam energy; as a consequence, the density rises to extremely high values (1025 particles per cubic centimeter, about a thousand times solid densities). The fuel heats up because of compression and shock waves,

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232 PLASMAS AND FLUIDS addition, the flow of electrons can be markedly reduced by self- generated magnetic fields created by anisotropies in the energy depo- sition. Fortunately, the effects of such fields are much reduced when targets are more uniformly irradiated. The heat flow has been investigated in laser plasma experiments under a wide variety of conditions. Often, the experiments have indicated a heat flow below the classical level. Empirical heat-flow models, normalized to experiments, are often used in design calcula- tions. Since electron heat transport has a marked effect on plasma conditions, hydrodynamic efficiency, preheat, and implosion symme- try, this remains a key area for further research. The efficiency by which absorbed energy reaches the ablation surface and the resulting blow-off velocity of the ablating materials determine the hydrodynamic efficiency of the pellet, that is, the kinetic energy delivered to the fuel divided by the absorbed driver energy. The most efficient transfer of momentum to the pellet shell occurs when the blow-off plasma velocity (the final ablation plasma velocity far from the target) is comparable with the final shell velocity. Shorter-wavelength lasers improve the hydrodynamic efficiency because the energy is absorbed at higher plasma density and closer to the ablation surface. For 0.25-m-wavelength light incident upon reactor-sized spherical pellets, calculated hydrodynamic efficiencies are as high as 15 percent, or about three times the minimum efficiency needed for high-gain applications. The distance between the driver energy-absorbing region and the ablation region is another important parameter affected by the heat transport. If nonuniformities in the energy absorbed are transmitted to the ablation surface, where the pressure is applied to the shell, the result will be an asymmetric implosion. Fortunately, such nonuniformi- ties will tend to be smoothed out between the energy-absorption and ablation regions, provided this separation exceeds the wavelength of the disturbance. This smoothing mechanism, called the cloudy-day effect, has been found experimentally to be quite effective at a 1-~m laser wavelength. However, for shorter-wavelength laser light, the very source of the improved absorption and greater hydrodynamic efficiency (higher-density absorption) aggravates the uniformity prob- lem.

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FUSION PLASMA CONFINEMENT AND HEATING 233 SHELL ACCELERATION' UNIFORMITY' AND HYDRODYNAMIC INSTABILITIES · Experimental results on ablatively accelerated pellet implosions have been encouraging, with respect to both implosion velocities and compression factors achieved, but the uniformity of the implosion is not yet adequate for compression to fusion densities. Various techniques for improving the implosion uniformity appear promising. Hydrodynamic instabilities, which would aggravate the problem, do not seem to be so severe as initially predicted. Investigations of pellet-shell acceleration and hydrodynamic behav- ior have been accomplished by imploding actual pellets, using multiple- sided irradiation facilities, or by studying the acceleration of thin planar targets. Early implosion experiments worked in the "exploding pusher" regime. In these experiments, small glass microballoons containing gaseous D-T were irradiated with intense short-duration light pulses. The laser-heated electrons deposited energy so quickly in the glass that the shell exploded. Roughly half of the exploding shell (pusher) traveled inward, first driving a shock wave through the D-T gas and then compressing the postshock material. Copious thermonuclear neutrons were generated as the D-T fuel heated to temperatures of many kiloelectron volts. However, the preheat levels of these targets, and the exploding pusher behavior, limited their peak fuel densities to a few times liquid density, far below the densities required for high-gain pellets. Most present-day implosion work has advanced to the more relevant ablative mode. Ablation acceleration or implosion occurs as a result of the continuous acceleration of ablating material. These experiments either utilize thicker shells, to reduce hot electron preheat, or use lasers operating in a lower-irradiance or shorter-wavelength regime, where hot electrons are not dominant. This implosion mode is expected to scale successfully to large inertial-fusion devices. Multinanosecond 1-~m lasers operating below 10~4 W/cm2 have been used to produce well-behaved ablative accelerations. Planar targets have been ablatively accelerated to velocities of 160 km/s, with preheat below 10 eV and velocity uniformity to within 7 percent. Acceleration uniformities within 2.5 percent over almost a square millimeter have been achieved in other planar target experiments. Ablatively driven pellets have compressed D-T fuel to nearly a hundred times solid density, albeit with low temperature (about 400 eV). These experi

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234 PLASMAS AND FLUIDS meets are encouraging, but further progress is required to meet the critical-element physics requirements. The pellet implosion must proceed with shell velocity nonuniformi- ties below about 1 percent in order to compress the fuel properly. This requirement is aggravated by the fact that the pellet itself is susceptible to hydrodynamic instability at several phases during the implosion. Driver nonuniformity problems can be alleviated in three ways. Use of hohlraum targets with conversion of driver energy to x rays provides a promising method of smoothing without requiring the beams of the driver to be symmetrically arranged. In the direct illumination ap- proach, nonuniformities in absorption can be smoothed out by oper- ating in a regime where the cloudy-day effect is operative. In fact, nonuniformity reductions of an order of magnitude have been demon- strated in 1-~m laser light experiments. Finally, development of driver technologies that produce smoother beams should also be effective. All three methods are under active investigation. A recent innovation in laser technology, called induced spatial incoherence, provides a promising method to reduce laser-beam nonuniformities to acceptable levels. The method works by dividing a broad-bandwidth laser beam into many smaller beamlets, with a small relative time delay introduced into each beamlet's path. If these time delays are longer than the beam coherence time, the laser nonuniformi- ties will tend to cancel out statistically when the beamlets are over- lapped on the target. Hydrodynamic Rayleigh-Taylor instability can occur whenever a lighter fluid accelerates a heavy fluid. Inertial fusion analogs of the Rayleigh-Taylor instability occur when the low-density ablating plasma accelerates the dense shell, or later in the implosion when the dense shell decelerates on compressing the lighter fuel. Hydrodynamic instability causes two deleterious effects. First, the nonuniformities can prevent a central region of dense, hot D-T fuel from being created and cause the pellet to fail to ignite or even disassemble before full compression. Second, fuel can mix with the shell pusher material and spoil the ignition. There is an active growing theoretical program on the mechanisms, growth rates, and saturation levels for the Rayleigh- Taylor instability. A number of effects have been shown to reduce the growth rate below initial predictions. Experiments are beginning to make significant headway into the study of the hydrodynamic stability of laser-accelerated targets. The evolution of accelerated "structured" targets, in which regular mass variations are introduced, has been followed using x-ray backlighting and double-target diagnostics. First indications suggest that the Ray

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FUSION PLASMA CONFINEMENT AND HEATING 235 Leigh-Taylor instability growth rate may be less than classical, in agreement with the more recent theoretical predictions. Prospects for Future Advances · Two very large driver facilities are currently under contraction in the United States: the NOVA neodymium-glass laser and the PBFA-II light-ion-beam accelerator. Construction of the world's most powerful CO2 laser, ANTARES, was recently completed. These, and other smaller facilities, will be used to extend greatly our knowledge of the efficiency, symmetry, and stability of pellet implosions. In addition, heavy-ion-beam drivers have been pro- posed, and the search for efficient shorter-wavelength lasers continues. As indicated in Table 4.12, a new generation of drivers is being developed. The NOVA neodymium-glass laser will have an output of 100 kJ of 1.05-llm light (this will be frequency converted to shorter wavelengths, i.e., 0.53- and 0.35-~m light); the ANTARES CO2 laser has an output of 30 to 40 kJ of 10.6-~m light; and the PBFA-II light-ion-beam accelerator will have an output of about 2 MJ of 4-MeV protons. The new machines coming on line in the next few years will allow significant tests of key inertial-confinement fusion principles. For example, it is anticipated that the NOVA laser will be able to compress D-T fuel to about one thousand times liquid density, with fuel temper- atures in the central hot spot in the 1-2 keV range. Such experiments will significantly test and extend our knowledge of the efficiency, symmetry, and stability of pellet implosion. The ANTARES CO2 laser will test the suitability of long-wavelength laser light for inertial- confinement fusion. PBFA-II is anticipated to provide light-ion beams focused to sufficient intensity to test pellet implosions. The PHAROS, OMEGA, and CHROMA lasers will supplement the larger facilities by addressing important physics issues of inertial-confinement fusion. Driver technology will continue to advance toward a high-energy, high-repetition-rate, efficient driver suitable for inertial-confinement fusion application. One promising system under development is the krypton-Huoride laser, with a wavelength at 0.26 ,um, which may satisfy the requirements for an efficient short-wavelength laser. Mega- joule-class glass-based lasers are also under evaluation; these systems could be frequency converted to provide short-wavelength light. Finally, particle-beam drivers, such as heavy-ion-beam systems and

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236 PLASMAS AND FF UlDS light-ion accelerators, have the potential to offer high efficiency and repetition rates. Small, exploratory heavy-ion drivers are expected to operate in about 5 years. Inertial confinement continues to be an active and exciting field. Research in the next decade will provide scientific and technical information needed to determine the physics of inertial-confinement fusion. In turn, this information will provide the basis for a decision in the late 1980s regarding the next generation of experimental facilities. ADVANCED FUSION APPLICATIONS The discussion in this chapter has concentrated on the D-T fusion reactor, which would generate electricity by means of a conventional thermal conversion cycle, because the relatively large cross section of the D-T reaction makes it the easiest fusion process to achieve and apply. However, fusion processes offer a wide range of other possible applications, from production of fuel for light-water fission reactors to direct production of electricity using advanced fusion fuels. If achiev- able, advanced-fuel fusion reactors would produce almost no neutrons, thus reducing reactor activation by orders of magnitude, and would eliminate the need for tritium production. One promising recent innovation has been the realization that fusion reaction rates can be altered significantly by polarizing the spins of the fuel nuclei. (The nuclei can be thought of as small magnetized gyroscopes.) At first sight, it might appear that the use of polarized nuclei for fusion could not possibly work, because the energy associ- ated with polarization is approximately 10-3 kelvin (K) compared with a plasma temperature of about 108 K. However, because of the very weak interaction between the particle motion and the spin, the use of this technique does indeed appear to be possible. By aligning the spins of D-T ions, the fusion reaction rate can be increased by a factor of 1.5. A more exciting application of spin-polarized fusion would be to reduce fusion neutron production, relative to electrically charged reaction products, by using certain combinations of polarized fuels. The sim- plest fusion reaction that produces no neutrons is the reaction between deuterium and helium-3; parallel polarization of the deuterons and the helium-3 ions can increase this reaction rate by a factor of 1.5 and at the same time substantially suppress the neutron-producing deuterium- deuterium reactions. (However, to make practical use of this reaction, a source of helium-3 must be found; although helium-3 does not occur naturally, it can, of course, be bred in a fission reactor.)

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FUSION PLASMA CONFINEMENT AND HEATING 237 A fusion reactor could find many practical applications in addition to providing a heat source for conventional power generation. An exam- ple would be the use of radiation for chemical processing of synthetic fuels. Also, since the x rays and fast neutrons produced by a fusion plasma can pass through the walls of a reactor vessel and heat a blanket to almost any desired temperature, such reactors could find uses in high-temperature processing and in high-efficiency heat engines. Some attention has been given to the direct recovery of the energy of electrically charged fusion reaction products, but the possible applica- tions of such fusion reactors have not yet been explored in any depth. For example, a compact mirror fusion reactor that produces most of its energy in charged particles could, in principle, make an ideal propul- sion unit for large space missions. The successful development of a fusion reactor could lead to the production of a wide variety of isotopes for scientific, industrial, and medical use, just as modern fission reactors do. Moreover, since the energetic particles produced in fusion reactions (alpha particles, pro- tons, deuterons, tritons, as well as neutrons) are different from those produced in fission reactions, the range of possible isotope products should be much greater. Furthermore, the fluxes of energetic charged reaction products per unit surface area from a fusion reactor could be much larger than the flux of neutrons from a fission reactor. The existence of a working fusion reactor should also provide a valuable stimulus to several branches of fundamental science. Cer- tainly, a more profound understanding of plasma science itself will automatically result from the increased experience with hot, confined plasmas. In addition, fusion reactors should have a strongly beneficial impact on low-energy nuclear physics; specifically, they will provide the first large-scale terrestrial experience with stellar atomic processes. Another interesting aspect of fusion reactors is that they provide a totally new, unique type of energy source; in particular, they will produce copious microwaves and x rays, in addition to energetic particles. Just as neutrons from fission reactors have become powerful scientific tools, so should the versatile radiation from fusion reactors find numerous important scientific applications. These are just a few of the possible advanced applications of fusion reactors. Perhaps the most exciting ultimate applications of fusion have not yet been conceived, as has been the case in most previous human ventures across new scientific and technological frontiers.

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238 PLASMAS AND FLUIDS FUNDING OF FUSION PLASMA RESEARCH IN THE UNITED STATES Fusion plasma research in the United States is almost entirely funded by the federal government through the Department of Energy. (A very small fraction of fusion funding not more than 3 percent of the total is provided by the private sector and is mostly applied to nonmainstream magnetic-confinement approaches. In addition, the utility industry through the Electric Power Research Institute funds some fusion studies and small-scale developmental activities.) Fusion approaches based on magnetic confinement are funded through the Department of Energy's Office of Energy Research, Office of Fusion Energy; inertial confinement is funded primarily through the Division of Military Applications, Office of Inertial Fusion, with some funding from the Office of Energy Research for the heavy-ion-beam approach. The total appropriations for fusion research in each fiscal year since 1971 are shown in Figure 4.23. The appropriations are shown both in actual current dollars and, to remove the inflation element from funding growth, in equivalent constant 1984 dollars, using published official price indices. The appropriations for magnetic-confinement fusion are shown in Figure 4.23(a) and those for inertial-confinement fusion are shown in Figure 4.23(b). The tokamak program, and supporting technology, accounts for about 65 percent of the magnetic-confinement program. Within the total magnetic fusion program, activities that could be broadly categorized as relating to plasma research, i.e., including the construction of new experimental facilities but excluding engineering development and technology, account for about 75 percent of the total budget. The 1970s was a period of rapid growth in the magnetic fusion program prompted by early successes with tokamak confinement and sustained both by continued advances in tokamak parameters and by dramatic improvements in mirror concepts. The 1970s also saw the emergence of inertial confinement as a viable fusion-energy option. Figure 4.23 shows clearly that, when the inflation element is removed, fusion appropriations have leveled-off indeed declined in the late- 1970s and early-1980s. If the momentum of fusion research is to be maintained and, in particular, if the future advances in each of the confinement concepts described in the succeeding sections of this chapter are to be realized appropriations must increase markedly in the late-1980s.

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FUSION PLASMA CONFINEMENT AND HEATING 239 600 500 400 300 200 100 300 250 con c 200 150 -~ I 00 50 ) _ O ~ a ~ Megnetic Conf inement Actuel Current Dollars ~Constanlt1984) Dollars O L:~ 71 72 73 74 75 76 77 78 79 80 81 82 83 84 FISCAL YEAR ~ b ~ Inertial Conf i nement - 81 Actua I Current Do I I a rs ~ Constant (1984) Dollars 72 73 74 75 76 77 78 79 80 8 1 82 83 84 F I SCAL YEAR FIGURE 4.23 Federal appropriations for fusion research in actual and constant (1984) dollars. (a) Magnetic-confinement fusion. (b) Inertial-confinement fusion. Price indices obtained from Statistical Abstract of the United States, 103rd edition, page 452. Fiscal year 1976 contained 15 months. (Since the preparation of this chapter, the federal appropriation for magnetic-confinement fusion has decreased again to $440 million in fiscal year 1985.)

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240 PLASMAS AND FLUIDS PRINCIPAL FINDINGS AND RECOMMENDATIONS Magnetic Confinement In all the main approaches to the magnetic confinement of fusion plasmas, the principal measures of plasma performance-plasma den- sity, temperature, and confinement time improved by more than an order of magnitude as a result of intensified fusion research in the 1970s. One approach the tokamak has already come within a mod- est factor of meeting the minimum plasma requirements for energy breakeven in D-T plasmas. These achievements have been made possible by rapid advances in plasma science. The techniques used for plasma control and heating, the technology of high-power heating sources, and the precision of plasma measure- ments all improved dramatically during the past decade. There were equally rapid advances in plasma theory and numerical modeling, which are now able to explain much of the observed dynamical behavior of magnetically confined plasmas. The establishment of the National Magnetic Fusion Energy Computer Center (NMFECC) made possible many of these advances in theoretical modeling and data interpretation. A particular strength of the U.S. fusion program is its broad base, which includes research on several alternatives to the mainline con- finement concepts, to ensure that the maximum potential of fusion is realized. A new generation of magnetic fusion facilities, coming into operation worldwide, will in the mid-1980s extend experimental plasma parame- ters to reactorlike values of density, temperature, and confinement time. However, if the United States' pre-eminent position in the world- wide fusion program is to be maintained into the 1990s in the face of aggressive Japanese and European competition, the pace of new- device authorization that characterized the early 1970s must be re- stored soon. The science of plasma confinement and heating has reached a stage of development that fully justifies the recent recommendations of the Magnetic Fusion Advisory Committee-an advisory committee to the Director of Energy Research, U.S. Department of Energy-which proposed a strategy for the development of magnetic confinement fusion with the following principal features: · Initiation of a moderate-cost tokamak experimental facility (less

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FUSION PLASMA CONFINEMENT AND HEATING 241 than $1 billion plant and capital expenditures) designed to achieve ignition and long-pulse equilibrium burn; · Depending on future assessments of the tandem-mirror data base, potential utilization of upgraded mirror facilities to test fusion blanket and engineering components; · Vigorous pursuit of a broad-base program in magnetic-confine- ment research, encompassing tokamaks, mirrors, stellarators, bumpy tori, reversed-field pinches, and compact toroids. A vigorous base research program is essential to technical progress in mainline tokamak and mirror research. Moderate-size experimental facilities are the primary sources of the scientific and technological innovations required to develop fusion to its fullest potential. Continued research on alternate fusion concepts is essential to advance basic understanding of plasma confinement and to foster the development of approaches that show significant promise of improved reactor configurations. Intensive research must continue on the theoretical and computa- tional descriptions of magnetically confined plasmas and on supporting experiments in basic plasma physics. These have been a source of many promising new concepts in fusion research. Continued strong university involvement will be essential to fusion research for the foreseeable future. Universities augment fusion re- search in the national laboratories in several unique and important ways. They educate and train professional fusion researchers; they provide the fusion program access to a breadth of talent and intellect in the sciences and engineering; and their research is a major source of innovative ideas and scientific and technological advances. Inertial Confinement The United States has maintained world leadership in inertial- confinement fusion research since its inception in the late 1960s. Its near-term applications are military, with promising long-term applica- tions to energy production. An inertial-confinement fusion reactor would have a relatively small containment volume, and its operation, maintenance, and repair may be relatively simple. During the past decade, a vigorous international research effort was established to investigate the inertial-confinement approach to fusion. An impressive array of experimental facilities was developed, includ- ing neodymium-glass and CO2 lasers and light-ion accelerators, which led to considerable scientific progress. Investigations of laser-coupling

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242 PLASMAS AND FLUIDS physics over a wide range of intensities and wavelengths showed that lasers with wavelengths of a micrometer and less have good coupling. D-T fuel was heated to thermonuclear temperatures in laser-irradiated implosions. Shells were ablatively accelerated to above 107 calls, with velocity nonuniformities of less than 5 percent. In implosions, final fuel densities of 100 times the liquid density of D-T were achieved with fuel temperatures of about 5 million degrees. These fuel densities are within a factor of 10 of the compression needed for a high-gain target. On the basis of these findings, we recommend the following near- term emphasis and strategy for inertial-confinement fusion research: · Use present driver facilities to determine the physics and scaling of energy transport and fluid and plasma instabilities to regimes characteristic of high-gain targets. · Use the new generation of drivers under construction to implode D-T fuel mixtures to 1000 times liquid density required for high-gain targets and to implode scale models of high-gain targets to the density and temperature of the full-scale target. · Identify and develop cost-e~ective, multimegajoule driver ap- proaches. Timely execution of this strategy will provide the basis for a decision in the late 1980s on the next generation of experimental facilities. Drivers in excess of a megajoule would allow demonstration of high-gain targets for both military and energy applications. ACKNOWLEDGMENTS The authors gratefully acknowledge valuable contributions to this report from several of their colleagues, in particular S. E. Bodner (NRL), E. M. Campbell (LLNL), G. Cooperstein (NRL), J. C. Glowienka (ORNL), J. Holzrichter (LLNL), S. Kahalas (DOE), H. Kugel (PPPL), J. D. Lindl (LLNL), J. Mark (LLNL), R. S. Massey (LANL), J. H. Nuckolls (LLNL), R. R. Parker (MIT), M. Rosen (LLNL), R. L. Schriever (DOE), and L. D. Stewart (PPPL). The Chairman is grateful to R. Sheldon for providing information on inflation-adjusted fusion appropriations and especially to Barbara Sobel for her careful typing of the manuscript.

Representative terms from entire chapter:

plasma confinement