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Plasmas and Fluids (1986)

Chapter: 4. Fusion Plasma Confinement and Heating

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Suggested Citation:"4. Fusion Plasma Confinement and Heating." National Research Council. 1986. Plasmas and Fluids. Washington, DC: The National Academies Press. doi: 10.17226/632.
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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

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

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

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

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).

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

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

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.

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

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

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,

FUSION PLASMA CONFINEMENTAND HEATING 155 and fusion temperatures are produced in the center of the pellet; thermonuclear ignition then occurs. If the yield of this miniature thermonuclear explosion is high enough, the fusion energy can be used for several applications, including power generation. Inertial-confinement fusion diners from magnetic fusion in that plasma confinement is provided by the inertia of the exploding pellet, not by a magnetic bottle. A key parameter in inertial fusion, equivalent to the confinement (Lawson) parameter in magnetic fusion, is the product of the density and radius of the compressed pellet. For inertial fusion to work, this parameter must be large enough for the fusion products to be contained, thus allowing propagating thermonuclear burn. Density compression is required to increase the rate of fusion reactions during the brief instant (less than 10-9 s) that inertia holds the pellet together. Very stringent physics requirements must be satisfied in order to achieve the ultra-high-density compressions and thermonuclear tem- peratures needed for ignition with a reasonably sized beam driver. First, the incident beam energy must be absorbed efficiently at the pellet surface. Second, in order to achieve highly compressed fuel volumes, the symmetry of implosion must be excellent, and the fuel temperature must remain as low as possible until the instant of ignition. Finally, there must be satisfactory means of igniting the imploded pellet at the right moment implying a good pellet design. Research in inertial fusion is aimed at elucidating the physics that dominates the behavior of the driver-pellet interaction, especially for laser drivers. The physics of the coupling of driver energy to the pellet has been a preeminent issue, because the partition of beam energy in the pellet determines whether the physical requirements for fusion can be met. Lasers have been the drivers used for almost all inertial fusion research to date, because their high-power beams can be focused to the intensities needed for inertial fusion. [Both neodymium-glass lasers, which operate with a wavelength of 1 ~m, and CO2-gas lasers, with a 10-~m wavelength, with outputs of up to 100 kilojoules (kJ) have been developed for inertial-confinement fusion experiments.] As an alternative to lasers, intense particle beams can be used as drivers either light-ion beams or heavy-ion beams. The light ions are generated in high-current pulsed-power accelerators that provide megaamperes of ion current at a few megavolts energy; these genera- tors are highly efficient and relatively inexpensive but cannot as yet attain the power densities required for fusion, although the technology is rapidly improving. The heavy-ion-beam approach would use ions such as uranium accelerated to gigaelectron-volt energies in conven

156 PLASMAS AND FLUIDS tional accelerators; the accelerators needed to generate the heavy-ion beams would be expensive but would have many properties desirable for inertial fusion applications. Steady progress has been made toward the achievement of fusion by inertial confinement. Pellets have been compressed to a hundred times solid density, fusion temperatures have been reached, and remarkable advances have been made in driver technology. However, much further progress needs to be made to satisfy simultaneously all the requirements for the practical realization of fusion power. Inertial- confinement fusion is discussed toward the end of this chapter. TOKAMAK AND STELLARATOR MAGNETIC-CONFINEMENT SYSTEMS Introduction · Closed field-line magnetic-confinement systems of the tokamak and stellarator type have displayed a sustained favorable trend in experimental achievements, and tokamaks now occupy the dom- inant position in fusion research worldwide. The tokamak and stellarator are magnetic-confinement devices uti- lizing closed magnetic fields and toroidal (doughnut-shaped) plasmas. The main magnetic field is produced by external coils. Although the simplest toroidal magnetic field [Figure 4.5(a)] does not confine plasma, a twisted toroidal field does [Figures 4.5(b)-4.5(d)~. The tokamak, which has a symmetric toroidal plasma, has an additional magnetic field produced by a current flowing in the plasma. This additional field gives the required twist EFigure 4.5(b)~. The stellarator is not symmetric around the torus, which allows the twist in the magnetic field to be produced by external coils, with no plasma current [Figures 4.5(c) and 4.5(d)~. The early development of the tokamak took place in the Soviet Union, but the concept has played an increasingly important role in the U.S. and world fusion programs since the late 1960s. It was the simplicity of the tokamak, in which the plasma current provides not only good confinement but also creates and heats the plasma, that first led to its choice as the centerpiece of many fusion research programs worldwide. A sustained favorable trend in tokamak experimental results has led to the tokamak's becoming the largest element in the U.S. program and dominating the fusion programs of Europe and Japan.

FUSION PLASMA CONFINEMENT AND HEATING 157 z PU R E TO R O I DA L F I E LO it TOROIDAL COILS TOROIDAL Fl ELD (a) IN A PURE TOROIDAL FIELD UN Ll KE CHARG ES SEPARATE VERTICALLY AND THE PLASMA ROLLS OUT STELLARATOR H E Ll CA L - COILS i+ + THE EXTERNAL COI LS IN A STELLARATOR ALSO TWIST THE TOTAL FIELD AND LEAD TO CHARGE CANCELLATION TOKAMAK POLOIDAL Fl ELD p J PLASMA \ hi/ CURRENT P LASMA Bt (b) THE POLOIDAL FIELD OF THE PLASMA CURRENT IN A TOKAMAK TWISTS THE TOTAL FIELD AND LEADS TO CHARGE CANCELLATION MODU LAR STE LLARATO R ..... 17~ ~ (d) MODULAR EXTERNAL COI LS MAY BE USED TO PRODUCE A HELICAL FIELD FIGURE 4.5 Toroidal confinement systems pure toroidal field (unable to confine plasma), tokamak, stellarator, and modular stellarator.

158 PLASMAS AND FL UlDS Tokamak experiments have already obtained plasma parameters close to those required in a reactor. Indeed, experiments just coming into operation the Tokamak Fusion Test Reactor (TFTR) at Princeton, New Jersey, and the Joint European Torus (JET) in Europe, should produce more thermonuclear power than the power required to heat the plasma. The stellarator concept originated at Princeton in the early l950s, but stellarator research was almost totally displaced in the United States TABLE 4.1 Representative Tokamaksa Major Minor Field Plasma Pulse Radius Radiusb Strength Current Length Program Device Location (m) (cm) (kG) (MA)(s) ContributionsC DIII-D GA 1.7 82 22 3.5 10 (S,B,PD,RF) TFTR PPPL 2.5 85 52 2.5 2 C,DT,NB,PW,RF DIII GA 1.4 58d 40 2.sd 1 S,B,PD,NB ALCATOR C MIT 0.6 17 140 1.0 1 C,RF,CD PLT PPPL 1.3 45 35 0.6 3 C,NB,RF,CD PDX PPPL 1.4 45 24 0.5 1 PD,NB,S,B TEXT Texas 1.0 28 30 0.4 0.5 C,RF ISX-B ORNL 0.9 37 18 0.3 0.3 B,F,S,C Macrotor UCLA 0.9 40 4 0.1 0.1 RF,PW,C Torus II Columbia 0.2 9 5 0.1 10-5 B Tokapole Wisc. 0.5 22 1 0.1 10-2 C,RF,PD JET EEC 2.9 160 35 4.8 20 C,DT,NB,RF,PW JT-60 Japan 3.0 100 45 2.7 10 C,NB,RF,PD T-15 USSR 2.4 70 45 2.0 1 + (SC,C,NB,RF) ASDEX-U FRG 1.6 50 39 2.0 6 (PD,C,B,PW) Tore-Supra France 2.1 70 45 1.7 30 (SC,RF,CD) FT Italy 0.8 19 100 1.0 1 C,RF TFR-600 France 1.0 20 60 0.6 1 C,RF ASDEX FRG 1.6 40 28 0.5 10 PD,PW,C,B T-10 USSR 1.5 37 30 0.5 1 C,RF JFT-2M Japan 1.3 45 15 0.5 1 B,NB,RF TEXTOR FRG 1.7 50 26 0.5 3 PW JIPP T-II Japan 0.9 25 20 0.3 0.3 TS,RF,F DITE UK 1.2 28 27 0.3 0.5 BD,F,NB,PW T-7 USSR 1.2 31 24 0.2 1 SC,CD JFT-2 Japan 0.9 16 20 0.3 0.3 B,NB,RF a Listed in descending magnitude of plasma current, with U.S. devices listed first. b Average minor radius in the case of noncircular cross-section devices. c Program contributions in parentheses for devices still under construction. See Table 4.2 for key to program contribution codes. a' Parameters for a single lobe of the doublet configuration.

FUSION PLASMA CONFINEMENT AND HEATING 159 by the tokamak, starting in 1969. Recently, there has been a consider- able revival of interest in the stellarator. This is due, in large part, to exciting experimental results from stellarators in Germany and Japan. A larger stellarator effort is now under way in the United States, with the goal of demonstrating a conceptual improvement in toroidal systems. The parameters and research areas of representative tokamaks and stellarators are shown in Tables 4.1 and 4.2, respectively. These tables illustrate well the international character of, and contributions to, tokamak and stellarator research and the key part played by the U.S. program. In the United States, work is concentrated at GA Technol- ogies Inc. (formerly General Atomic), La Jolla, California; the Massa- chusetts Institute of Technology, Cambridge, Massachusetts; the Oak Ridge National Laboratory, Oak Ridge, Tennessee; and the Princeton Plasma Physics Laboratory, Princeton, New Jersey; with the Princeton laboratory playing a lead role in the program. Substantial supporting work is undertaken in universities such as the University of Texas at Austin; Columbia University; New York University; the University of California, Los Angeles; and the University of Wisconsin. TABLE 4.2 Representative Stellaratorsa Major Minor Field Pulse Radius Radiusb Strength Rotational Length Program Device Location (m) (cm) (kG) TransformC (s) Contributionsa' ATF-1 ORNL 2.1 30 20 0~95 5 (T,TS,C,B,NB,RF) IMS Wisc. 0.4 5 6 0.6 0.1 MST,C WVII-AS FRG 2.0 20 30 0.4 1 (MST,C,B,NB) Heliotron Japan 2.2 20 20 2.1 1 T,TS,C,NB,RF Uragan-3 USSR 1.0 16 30 0.7 0.5 T,C,RF L-2 USSR 1.0 12 20 0.7 0.3 S,TS,C,RF W VII-A FRG 2.0 10 25 0.2 1 S,TS,C,B,NB a Listed in descending magnitude of minor radius, with U.S. devices listed first. b Average minor radius. c Rotational transform is the number of times a field line circuits the poloidal circumference in one complete circuit of the toroidal circumference. ~ Program contribution codes for Tables 4.1 and 4.2 are as follows: confinement (C), high-beta (B), shaped plasma (S), neutral-beam heating (NB), radio-frequency heating (RF), poloidal divertor (PD), bundle divertor (BD), plasma-wall interactions (PW), fueling (F), operation with tritium (DT), superconducting coils (SC), stellarator (S), torsatron (T), tokamak-stellarator hybrid (TS), modular stellarator (MST).

160 o ~ or - US o ED ED ~ ~=' ~o~ =' ~i '=i~ o o C ~_ X 1 C~ 1 · 1 J ·_ ~ _, ~ - ~1 ~, o 1 a' =, CL. ·81 ~ ._ ~ . = X L~ I_ X Y _B cn I_ · ~ o . l ~D ~- o- (%) <§, Y _ ~o~,< _ · C~ . 11 1 1 C ~_ ~C~ o o (l\a)l) °!1 ( t\a~ ~aS£ cU3) !1 (1U ) '40 O C~ .' ~ ._ ~ _ C~ - Ct ~ >.0 3 ~ tv ~ .o U~ o C) s~ ,,, ~ _ ,~ .^ ~ 5 _ ,= ~ 1 .0 _ Ct ~ ~ Ct C) C) - Ct 4 -o.e O C) _ C~ Cd ·_ ~ ^ _ . C~ ~ ·= . _ o ~ O - ~> s: C~ ~ o V ~ _ Ct t4 ~: O C~ - ·- 43) C~ ~ ~ O Ct ~ C) C ~ C: ~ ~ s~ ~ -O ~ $- ~ ~ ,C (L) ~ o ~ . C~ . ~ c;5 ~0 0 E_4 C£L ~ -~ 04,:~ ~ ~ ~ _ r ~ c~ ~ ~r ~ ~ O _ L14 ~ ~ o s~ a~ -Ct: Ct O ~o ._ - ._ 04 ._ - o o C~ Ct 0 ~ a ~> .O - Cd o ~9 _ _ ~ o ;^ - Ct . - _~ Ct s~ - O Ct e~ cr) P. OD 1 U~ _ ~) ~ _ o

FUSION PLASMA CONFINEMENT AND HEATING 161 Major Advances · Tokamak plasma parameters are approaching reactor require- ments; stellarators behave as well as tokamaks of comparable size. For more than 30 years, the improvement in experimental capabili- ties and physical understanding of toroidal plasmas has been remark- ably steady. The advances of the last decade have brought us to a point at which ignited fusion experiments can be designed with confidence and have been based on the solid foundations of toroidal plasma physics built in the l950s and 1960s. The most impressive experimental achievements have been in tokamak research, where a number of critical plasma parameters have improved dramatically during the past decade. Possibly the most critical parameter is the product of density, ion temperature, and energy confinement time, which measures the approach to reactor conditions. This parameter has increased by a factor of more than a hundred in the past decade, although another factor of just less than a hundred is still required for ignition EFigure 4.6a. Reactorlike ion temperatures have already been achieved [Figure 4.6(b)l, and the plasma beta needed in an ignited reactor has been approached EFigure 4.6(c)~. The present experimental achievements are, however, mainly in separate devices, each with specialized characteristics. In the next phase of the program, experiments such as TFTR, JET, and other devices in the U.S. and world programs will work toward the goal of achieving simultaneously all the needed reactor-grade parameters. The stellarator has also made substantial progress, although stellara- tors generally lag behind tokamaks in size by a few years. Neverthe- less, stellarator plasmas are found to have characteristics comparable with those of tokamaks of similar size. OPTIMIZATION OF EXPERIMENTAL PERFORMANCE · The development of powerful auxiliary heating, coupled with improved techniques for plasma control, has been the key to the realization of reactorlike plasma parameters. Demonstrations of the efficacy of magnetic diverters for impurity control, and of steady-state transformer-free current drive, have further improved the prospects of the tokamak as a viable reactor candidate. The substantial improvements in the basic plasma parameters of tokamaks and stellarators have been partly due to increased plasma

162 PLASMAS AND FLUIDS size and partly due to the successful implementation of several auxiliary techniques for optimizing plasma performance. These tech- niques have taken a number of different forms: (i) magnetic shaping and feedback control of the plasma cross section; (ii) programmed density variation by controlled addition of gas (puffing) and by injection of solid hydrogen pellets; (iii) auxiliary plasma heating (additional to the intrinsic heating from the plasma current) by injection of intense beams of energetic neutral atoms, by radio-frequency electromagnetic waves, and by adiabatic compression; and (iv) control of the plasma edge conditions by specially designed mechanical "limiters," by suitable choices of limiter and wall materials, and by "magnetic diverters." In the early 1970s, the four main tokamaks in the United States were the ST and ATC devices at Princeton, ORMAK at Oak Ridge, and Doublet II at General Atomic, which had auxiliary heating powers up to a few hundred kilowatts (comparable with the heating by the plasma current) and pulse lengths of a few hundred milliseconds. The best plasma parameters achieved were as follows: central ion and electron temperatures of up to 2 keV; confinement parameter (product of density and confinement time) of up to 3 x 10~i particles per cubic centimeter seconds; and plasma beta as high as 1 percent. By the late 1970s, these devices had been replaced by larger experiments, with auxiliary heating powers in the multimegawatt range and pulse lengths typically of 1 s. These larger experiments, mostly still in operation, are the PLT and PDX tokamaks at Princeton, ISX at Oak Ridge, Doublet III at GA Technologies, and Alcator A and C at the Massachusetts Institute of Technology. These experiments also have better access for diagnostics and heating, improved plasma-shaping capability, and various types of active impurity and particle-control systems. The best plasma parameters achieved have been as follows: central ion temperature of up to 7 keV; central electron temperature of up to 4 keV (both in PLT); confinement parameter of up to 8 x 10~3 particles per cubic centimeter seconds (Alcator C); and plasma beta of up to 4.5 percent (Doublet III). In a tokamak, the plasma current is necessary for confinement, and it also provides the initial heating of the plasma. Technically, the simplest way to produce the required plasma current is to make the plasma the output circuit (secondary winding) of a transformer. Un- fortunately, a transformer can drive current in one direction for only a limited time. In a tokamak reactor, the transformer could drive the current for as long as a few hours in a single pulse. Nevertheless, it would be desirable to be able to operate for longer pulses, or even in steady state. Based on earlier theoretical studies, it has been shown

FUSION PLASMA CONFINEMENTAND HEATING 163 both in Alcator C and in PLT that substantial plasma currents may be driven using electromagnetic waves of appropriate frequency (see section on Radio-Frequency Current Drive). Part of the renewed interest in stellarators stems from their virtue of having no net plasma current. The pure stellarator, in which all the fields are supplied by currents in external coils, is therefore inherently steady state. The successful suppression of impurities has been a major factor in the success of tokamaks. Impurities are generated in a tokamak because of the interaction of the plasma edge with the walls of the confining vessel. Conventionally, the plasma edge in a tokamak is defined by a solid object, called a limiter; considerable advances have been made in choosing a material for the limiter that minimizes impurities. Alternatively, the plasma edge is defined by a diverter, which uses special magnetic fields to isolate the plasma from the vessel walls. Divertors reduce impurity contamination by (i) depositing heat from the plasma on a distant target plate, (ii) preventing the backflow of impurities to the plasma from the target plate, and (iii) shielding the plasma from wall-generated impurities. There have been a number of successful diverter experiments in the United States and abroad. A significant development for particle control has also been the extension of the intrinsically simpler limiter technique to provide pumping at the limiter a concept known as the pumped limiter. The understanding of tokamaks and stellarators has been improved by the development of an impressive battery of plasma diagnostics. These diagnostics, coupled with computer-aided data-acquisition and -analysis systems, have made it possible to make accurate tests of theoretical models and to establish well-tested empirical models of plasma behavior. These models have been used in computer codes that simulate plasma behavior in considerable detail and that can be used to predict results in future large tokamaks. CONFINEMENT · Toroidal systems have the potential for very favorable plasma confinement, if classical-like processes prevail. In tokamaks, anomalous processes of electron loss arise that, while not thor- oughly understood from a fundamental viewpoint, are found to obey empirical laws that scale favorably with increasing plasma size. Nearly classical ion confinement has been observed in many tokamak experiments. In stellarators, classical-like processes of

164 PLASMAS AND FLUIDS ion loss are more severe but are predicted to be manageable in a reactor-size device. The variation in magnetic-field strength on a surface of constant pressure in toroidal devices causes particles to drift across these surfaces. For particles moving parallel to the field, the projected orbit on a minor cross section of the plasma is a circle displaced slightly from a surface of constant pressure. Particles with greater perpendicular motion may be reflected from regions of higher magnetic-field strength. In tokamaks, this latter class of trapped particles has orbits that project onto the minor cross section into the characteristic "banana orbits" shown in Figure 4.7. Thus, the radial excursion of a particle exceeds the basic gyroradius with which particles spiral about a field line, and R - ~===~ ~ ~ Particle orbit /~ / ~ At\ Particle guiding-cenler orbit / Pro action of I,,,_ Ar particle Rt Projection of particle guiding-center orbit FIGURE 4.7 Trapped-particle orbits in a tokamak. A trapped particle gyrates in tight spirals about a magnetic field line, while bouncing back and forth along the field line and slowly processing around the torus. The projection of the particle's orbit onto a cross-sectional plane is a closed orbit in the shape of a banana.

FUSION PLASMA CONFINEMENTAND HEATING 165 this leads to an increased radial step following each interparticle collision and to increased diffusion and heat conduction. The theory of confinement that includes these orbit effects is termed "neoclassical." In a fusion-grade plasma, a typical particle will travel around the torus many thousands of times between collisions, with the consequence that neoclassical transport should be quite small. With the advent of substantial auxiliary heating in tokamaks, it has been possible to vary plasma parameters considerably and to measure the ion thermal conductivity over a wide range of collisionality. In almost all cases, the ion thermal conductivity is close to neoclassical predictions. This is particularly encouraging since, at low collisional- ity, it had been predicted theoretically that new types of plasma fluctuations could arise that would degrade ion confinement. The neoclassical confinement is degraded when the symmetry of the toroidal configuration is broken, since the banana orbits no longer have a closed projection as they do in Figure 4.7. This effect occurs in stellarators owing to the intrinsic lack of toroidal symmetry. Trapping of ions occurs in the helical troughs in the field strength and is predicted to lead to losses at low collisionality enhanced over those of a symmetric toroidal plasma. These losses may be substantially reduced by radial electric fields set up by the plasma to maintain charge neutrality. This is an active area of current research, and the theory of confinement in asymmetric plasmas has advanced considerably in the last decade. Codes based on the Monte Carlo method for following the dynamics of a large number of particles have allowed calculations to be made for magnetic-field configurations that are accurate representa- tions of actual experimental situations. The outlook for ion confine- ment in stellarators has improved considerably as a result of these recent more sophisticated calculations. In sharp contrast to the situation with ion confinement, electron confinement in tokamaks is found to be degraded from the neoclassical level, resulting in so-called anomalous transport. However, since electron neoclassical confinement would be substantially better than ion neoclassical confinement, quite large anomaly factors can be tolerated in electron losses before these exceed the ion losses. A key study of electron confinement was undertaken in the Alcator A tokamak. By virtue of the high toroidal-field capability of this device (up to 100 kG) and high plasma current density, it was possible to vary the plasma density over a wide range. It was found that the electron thermal diffusivity (the rate at which energy residing in the electron component diffuses to the vessel walls) was inversely proportional to the electron density. Similar behavior was found in other tokamaks

1 6 6 P LA SMA S. A ND FL UlD S heated by the plasma current alone. This led to an empirical confine- ment scaling that was diffusive in nature, that is, the confinement time increased with the square of the minor radius of the plasma and with the plasma density. This empirical scaling, coupled with the favorable ion-confinement scaling, indicates that ignited tokamak plasmas may be obtained in devices only slightly larger than the new generation of large tokamaks, namely TFTR and JET. More recent data from Alcator C, in which the plasma minor and major radii were varied, suggests a somewhat modified empirical scaling, but with an even more favorable dependence on overall plasma size, namely that the confinement increases only linearly with plasma minor radius, but also increases with the square of the major radius. When intense additional heating is applied to a tokamak plasma, the electron energy confinement is often degraded relative to the case with current heating alone. This degradation may be a direct result of differences in heating techniques, or it may be due to increases in plasma beta. The scaling of energy confinement is also quite different: confinement is found to be relatively insensitive to plasma density but increases with the strength of the poloidal magnetic field and with the square of the plasma minor or major radius. This scaling also predicts that ignition would be achievable in devices modestly larger than TFTR and JET. A possible explanation of the degraded electron confinement may lie in small-scale plasma fluctuations, so called microinstabilities. Density fluctuations have been measured whose wavelengths and frequencies correspond well to theoretical predictions. However, while theory can predict the possible existence of such fluctuations, a fully self- consistent theoretical treatment predicting fluctuation amplitudes and their relationship to confinement is beyond our present capabilities. In a stellarator, anomalous electron behavior occurs when a plasma current is used to initiate and maintain the plasma. Improved electron confinement, however, occurs in both the German (WVII-A) and Japanese (Heliotron E) stellarators when auxiliary heating is used and the current is turned off. STABILITY AND BETA LIMITS · Stable plasma betas approaching 5 percent have been demon- strated in tokamaks; detailed theoretical analyses of stability against current-driven kink modes and pressure-driven ballooning modes indicate that significant further advances in beta should be

FUSION PLASMA CONFINEMENT AND HEATING 167 possible. Stellarators are also predicted to have beta limits in the 5-10 percent range. On the macroscopic scale, a toroidal plasma may be treated as a perfectly conducting fluid. This model is used to establish self- consistent toroidal equilibria, plasma pressure profiles, and internal and external magnetic fields. The stability of these equilibria is examined by studying the growth of characteristic perturbations of the plasma. Lack of stability frequently means that the plasma merely assumes a small helical distortion usually seen as a rotating distortion in the experiments but, in a severe case, it can result in a catastrophic loss of confinement. In a perfectly conducting (ideal) plasma, the plasma and the magnetic field are locked together. The finite resistivity of a real plasma permits the plasma and magnetic fields to rearrange themselves. In practice, finite-resistivity effects are only important on pressure surfaces where a helical distortion of the plasma twists in resonance with the helical magnetic field, thereby facilitating this kind of field rearrangement. These resonances cause the constant-pressure surfaces to break up, leading to the formation of localized magnetic structures called mag- netic islands. Helical distortions of the plasma can be induced either by a gradient in the plasma current density, and are then usually called kink or tearing modes, or by the pressure gradient, in which case they are usually called interchange or ballooning modes. Tearing modes play an important role in the behavior of tokamak plasmas. The helical twist of the magnetic field is measured by the safety factor, which is the number of times a field line circles toroidally while encircling the plasma once the short way around. The safety factor in a tokamak increases from the center of the plasma to the plasma edge. If the safety factor is significantly less than unity in the center of a tokamak, there is always an unstable tearing mode. This mode is frequently seen as a variation of the x-ray emission from the plasma center; it limits the central density and temperature but is otherwise relatively harmless. If the current profile is not properly controlled, higher-order tearing modes can arise, which can interact with each other to give a sudden loss of plasma confinement, called a disruption. When careful control is exercised over the plasma, this phenomenon may be avoided. Pure stellarators have no current and are free of disruptions and other current-driven instabilities. Ballooning modes are small corrugations of the pressure surfaces that follow the twist of the field lines. These distortions are caused by the plasma pressure gradient and therefore occur when the plasma beta

168 PLASMAS AND FLUIDS is raised above a critical value. The effect of these distortions on confinement is not fully understood. However, the presumption is that if the confinement is sufficiently degraded that these modes set an upper limit on the obtainable value of beta. Theoretically, the ballooning-mode limit on beta for a circular cross-section plasma is about 3 percent. For elongated (in particular, D-shaped) cross-section plasmas, this limit may be increased to 7 percent for a plasma of aspect ratio (ratio of major to minor radius) of about 3. Current research indicates that even higher beta values may be possible with other plasma cross sections. In a number of experiments with circular plasmas (ISX-B, PDX, Doublet III, as well as several foreign tokamaks), beta has been raised to around 3 percent. In a noncircular plasma, Doublet III has achieved a beta of 4.5 percent. However, as beta is raised, these devices have generally experienced a degradation of electron confinement. Detailed fluctuation studies in ISX-B suggest that this degradation may result from finite-resistivity ballooning modes. Fortunately, such effects should diminish in larger, higher-electron-temperature plasmas. The theoretical understanding of ballooning and tearing modes has seen major improvements during the past decade. Large computer codes have been developed that provide the complete range of unstable modes and permit a detailed comparison between theoretical models and experimental measurements. In particular, these codes have provided definitive results on theoretical beta limits and, coupled with better diagnosed experiments, have given a detailed picture of the disruption phenomenon. Current Frontiers of Research · A new generation of tokamak facilities is coming into operation worldwide, with the capability of producing reactorlike confine- ment parameters and reactor-grade hydrogen and (deuterium- tritium)\D-T plasmas. Results from these devices, together with information on beta optimization, impurity control, current-drive, and long-pulse plasma technology from several moderate-size specialized devices, should enable the tokamak program to em- bark on a major next step-a long-pulse ignition experiment. A new generation of moderate-size stellarator experiments is dedi- cated to configuration optimization, with a view to realizing fundamental improvements in toroidal confinement concepts. The next phase of toroidal research will be centered around powerful

FUSION PLASMA CONFINEMENT AND HEATING 169 new facilities that are just now beginning operation or that are under construction for operation in the mid-1980s. New-generation tokamak devices such as TFTR, JET, the Japanese device JT-60, and an upgrade of the Doublet III device called DIII-D, have plasmas of about a meter in minor radius, multimegaampere current capability, pulse lengths of up to 10 s, and tens of megawatts of auxiliary heating. Moreover, TFTR and JET will eventually operate with D-T plasmas and should produce more thermonuclear power than is required to heat the plasma. In addition, several modest-scale devices will study improvements to toroidal confinement in the areas of steady-state operation, higher-beta operation, disruption control, and simplified impurity control. The goals of this phase of the program are the following: To study confinement at low collisionality and high beta in hydrogen and D-T reactor-grade plasmas, To study plasma behavior for longer pulse lengths, To develop advanced toroidal confinement concepts that can lead to more attractive reactor configurations. It is expected that this phase will provide the technical foundation for the next step in the tokamak program, namely a device that will operate with an ignited D-T plasma during a long-pulse equilibrium to provide for the study of a plasma heated by fusion alpha-particles. The key issue for tokamaks remains electron confinement. A vigor- ous program is under way to develop a predictive capability for anomalous transport, although the large plasmas of TFTR, DIII-D, JET, and JT-60 will be so close to reactor conditions as to require only a limited further extrapolation to reactor-scale plasmas. The diversity of configurations (circular, D-shaped, diverter) and heating techniques (neutral-beam and radio-frequency) to be found in this new generation of tokamaks offers the hope not only of optimization of experimental results but also of further progress toward an understanding of the underlying physics. TFTR and JET will also begin the study of fusion alpha-particle physics. In the stellarator area, improvements of existing experiments (Helio- tron-E, WVII-A) and new facilities that are under construction (WVII- AS in Germany and ATF-1 at Oak Ridge) will permit the study of high-beta and low-collisionality stellarator plasmas. The central issues are the role of the radial electric field, which maintains equal ion and electron losses, the effects of the helical magnetic ripple at low collisionality (high temperature), and possible degradation of confine- ment as beta is raised above a critical value.

170 PLASMAS AND FLUIDS In the past, most tokamak and stellarator reactor designs have been based on a plasma operating at a 3 to 7 percent beta level. Some years ago, it was predicted that, while unstable modes might set a limit on beta in a tokamak at about this levier, nevertheless there would be a regime at even higher beta that would be stable the so-called second stability regime. In a small tokamak, Torus II at Columbia University, transient plasmas have been set up with betas of around 12 percent using rapid heating. This augers well for the theory, but in larger devices the level of heating required to cross the unstable gap may be too large. Fortunately, some stable routes to the second stability regime have been identified. For tokamaks, the use of a kidney-bean- shaped plasma cross section, where the indentation of the bean is on the small major radius side of the plasma, can give direct access to the second stability regime. Studies of such a plasma will be undertaken in a modification of the PDX tokamak (PBX). Because the production of such a cross section in a reactor might be difficult, a second possible route has been identified, namely, stabilization of the plasma using an energetic electron component. For stellarators, a configuration (ATF-1) has been identified that also has a stable route, theoretically, to the second stability regime. Stellarators with a helically displaced plasma have also been shown theoretically to have a capability for very high stable betas. A substantial effort is under way to increase the pulse length of tokamaks by the application of long-pulse heating power and radio- frequency power for current drive. The present noninductive current- drive schemes in a tokamak have power efficiencies that are just adequate for a reactor. The first goal of the current-drive program is to test theoretical predictions in reactor-grade plasmas; the second goal is to explore improved current-drive schemes. Even at low efficiency, current drive may still make an important contribution. For example, it may be used to start and raise the plasma current, thereby freeing the transformer for use only in current maintenance. Initial tests of this idea are encouraging; it should enable a tokamak reactor to have a pulse length approaching a day. Stellarators have inherent steady-state capability, because the fields are all produced by external coils. The main issue for stellarators, once configurations with good confinement and beta have been established, is to find a coil set that is reactor relevant from the viewpoint of construction and maintenance. Tokamak-stellarator hybrids are also being studied that combine the good features of both devices, namely, the simplicity, good confinement, and satisfactory beta of a tokamak

FUSION PLASMA CONFINEMENT AND HEATING 171 and the disruption-free operation and reduced current-drive require- ments of a stellarator. The problem of maintaining a pure plasma for very long pulses involves the minimization of impurity production and the active removal both of wall-generated impurities and of alpha particles produced by the fusion reactions. In the next phase of the program, this will be studied by operating plasmas for progressively longer pulses, initially of about 10-s duration and ultimately in steady state. Control of the density will be achieved by using a mixture of gas puffing and pellet injection, coupled with either a pumped limiter or a magnetic diverter to remove excess particles. The control of impurities is a more difficult matter. There are some favorable conditions under which the plasma edge is predicted to operate at low temperature, in which case the production of impurities by sputtering would be low. If such conditions are found in reactor-grade plasmas, then the pumped limiter will be a reactor-relevant solution for particle and impurity control. If, on the other hand, a greater level of active control of the plasma edge is required, then a magnetic diverter will be necessary. Prospects for Future Advances · Improvements already demonstrated on smaller-scale experi- ments should greatly improve toroidal reactor attractiveness. The program described above should lead to the early test of an ignited long-pulse thermonuclear plasma in a new tokamak that is a modest scale-up from today's largest devices. Simultaneously, the program will be developing concepts for improved performance of toroidally confined plasmas in a wide range of areas: High beta operation with good confinement Current drive: assisted start-up, plasma profile control, steady-state operation; -Steady-state stellarator operation; Disruption-free operation; and Simplified particle and impurity control. Each of these improvements will depend on further advances in theoretical analysis, in computer modeling, and in the diagnosis and analysis of experimental data. The ability to model the complete toroidal plasma system, coupled with the development of more-reliable

172 PLASMAS AND FLUIDS input in each constituent area, will lead to the identification of optimized toroidal configurations that combine the best features of all the proven advances. Impurity control by means of poloidal diverters has been demon- strated successfully on PDX and will be pursued further in foreign tokamak programs. The advantages of high-beta bean-shaped plasmas are to be explored on the PBX modification of PDX. Techniques for quasi-steady-state operation, with emphasis on radio-frequency cur- rent drive, are being developed on Alcator C and PLT. Eventually, the program must address a variety of long-pulse physics, engineering, and technology issues in an integrated superconducting tokamak environ- ment. The improvement of stability against transients by means of stellarator-type shaping features will be addressed by the ATF- 1 torsatron device. The principal advanced reactor candidates are the ultra-long-pulse tokamak using radio-frequency-assisted start-up, the steady-state tokamak using current drive, and a variety of stellarators. A number of routes to the high-beta second-stability regime have been identified, both in tokamaks and in stellarators. High-beta operation, that is, at levels well above the minimum reactor requirement, coupled with long pulse or steady state, should lead to extremely attractive reactor economics. MAGNETIC MIRROR SYSTEMS Introduction . Fusion plasmas can be magnetically confined in an open-ended tube by strengthening the magnetic field at the ends of the tube to form magnetic mirrors. Open-ended systems possess some impor- tant advantages for fusion purposes. In the principal alternative approach to magnetic confinement, an open system, the magnetic field lines leave the plasma at each end of a tubular-shaped confinement volume. Plasma escape along the open lines is inhibited by strengthening the magnetic intensity at the ends, creating the so-called mirrors. These magnetic mirrors turn back those particles whose spiraling motion along the field lines is not too nearly directed along the field, i.e., those whose velocity vector (pitch) angle does not lie within the loss cone with respect to the magnetic field. Particles trapped between the mirrors in this way will continue to bounce back and forth until their pitch angle is deflected into the loss

FUSION PLASMA CONFINEMENTAND HEATING 173 Minimum-B m;: \ Field lines W \\~sma ~i: me' - ~Coil current FIGURE 4.8 A magnetic-well mirror cell that has the property that the field strength increases in all directions from the geometric center. cone by the cumulative effect of chance collisions with other trapped particles. This angle-dependent nature of the particle losses leads inevitably to trapped-particle distributions having empty loss cones, i.e., departing from the isotropic distribution in velocity angle that characterizes an ordinary gas, with the consequent negative implica- tions for the stability of mirror-confined plasmas discussed below in the section on Current Frontiers of Research. Mirror systems of the type described have confinement times that are low, bounded by the time required for an ion to be deflected through 90°. Such times would at best be marginal for a fusion reactor. However, mirror systems possess two major advantages for fusion purposes. First, a properly designed magnetic mirror field (with the field lines being convex toward the plasma surface) can form a deep magnetic well, a region in space surrounded by a magnetic field that increases outwardly in every direction (Figure 4.81. These magnetic wells have exceedingly high magnetic efficiency, having been shown to be capable of holding stable plasmas with pressures comparable to the energy density of the confining field (i.e., beta values approaching 100 percent). Second, because the confining fields are externally generated, mirror systems are inherently steady state. Mirror fusion research, begun in the early l950s, had by the mid-1970s reached a crucial turning point. A major triumph at that time was the control of high-frequency unstable fluctuations (called microinstabilities) to which the nonisotropic mirror plasmas can be subject. With this task accomplished, the rate of plasma loss slowed,

174 PLASMAS AND FLUIDS approaching the loss calculated to arise from the classical process of interparticle scattering. On the heels of this achievement came the demonstration of the generation and containment of high-beta plasmas at fusion temperatures. However, despite the encouragement from such an achievement, it was recognized that the single-cell mirror machine would have confinement too poor to satisfy the requirements for economic fusion power, i.e., too large a fraction of the fusion energy yield would have to be fed back to keep the system going. The challenge thus became to enhance the confinement in a mirror system to the point of engineering and economic practicality for a fusion power plant. Major Advance~the Tandem Mirror · A tandem-mirror system has mirror cells plugging the ends of a large-volume ignited plasma, resulting in a sharp improvement in overall confinement over the single-cell mirror. In response to the challenge for improved mirror confinement, the tandem-mirror idea was conceived independently in the Soviet Union and the United States. In the tandem mirror, small-volume, relatively lossy, mirror cells plug the ends of a central mirror cell of large volume. The overall confinement of the open system is thus much improved, while preserving much of its high magnetic efficiency. In this steady-state, linear fusion system, the fusion power is generated in a cylindrical chamber with solenoidal magnets (a linear assembly of simple circular magnet coils). The chamber is surrounded by a modularly constructed blanket for tritium breeding and neutron- energy recovery. At the ends, there are compact mirror end cells, followed by expansion chambers, where the field lines flare out. Within the expansion chambers are located special electrode arrays, forming a direct converter (resembling a Van de Graaff accelerator working backwards). These direct converters perform the dual function of spreading out the heat from the escaping plasma and of converting a large portion of the plasma's kinetic energy to direct-current electric- ity power that can be recycled to maintain the plug plasmas. The end-mirror cells serve two purposes: (i) to electrostatically plug the end losses from the central cell and (ii) to anchor the entire plasma against gross magnetohydrodynamic instabilities. In first-generation tandem-mirror devices, both of these purposes were served by shaping the end cells as magnetic wells and filling them with high-density plasma at high temperature, thereby creating a region of high positive

FUSION PLASMA CONFINEMENT AND HEATING 175 potential (as discussed in the following section), while at the same time providing a plasma "anchor" that stabilized the central plasma against gross motions. At this stage (circa 1977), the considerable progress achieved in mirror physics over the preceding decade was brought to bear in designing an entirely new type of confinement system from the ground up-one that actually performed very much as predicted. In this first generation of tandem mirror experiments in the United States (TMX and Phaedrus) and Japan (Gamma 10), several key elements of tandem confinement were established: (i) The higher-density end cells electrostatically plugged the center cell in agreement with theory, giving a confinement parameter approaching 10~ particles per cubic centimeter seconds; (ii) The higher-pressure end cells anchored the central cell gross motion for average beta values as high as 20 percent (in TMX); and (iii) The loss-cone-driven microinstabilities in the end cells behaved predictably and could be controlled in agreement with theory. For economically motivated reasons, there have now been devised better ways of generating the required plugging potentials than the simple method used in the first tandem-mirror experiments. These methods, involving the use of thermal barriers, are described in the following section. During recent years, the tandem-mirror program has benefited from a number of important theoretical advances, originating both in the United States and abroad. These include (i) theory of microinstabilities and their control; (ii) multiregion computer codes to calculate scatter- ing and radio-frequency heating; (iii) computational codes for the magnetic fields generated by complex-shaped magnet coils; (iv) three- dimensional pressure equilibria and their gross stability in mirror fields; and (v) description of particle transport processes within the magnetic fields of tandem mirrors. Turning to technological advances, mirror research has been respon- sible for some major contributions, including energetic neutral beams, high-field superconducting magnets of complex shape, and the devel- opment and application of microwave sources for plasma heating. The United States has by far the largest program in tandem-mirror research, concentrated at the Lawrence Livermore National Labora- tory, Livermore, California, with smaller programs at the Massachu- setts Institute of Technology and the University of Wisconsin. Tan- dem-mirror research is also under way in Japan and in the Soviet Union..

176 PLASMAS AND FLUIDS Current Frontiers of Research · Building on previous successes, future progress toward fusion in mirror research will come from an increasingly quantitative un- derstanding of the plasma processes that control the confinement of fusion plasmas in tandem-mirror systems. The current frontiers of research in mirror confinement reflect the present need for a quantitative understanding of the physics of plasma confinement in magnetic fields. This need stems, of course, from the ultimate goal of fusion research-to achieve net fusion power by the most direct and economical means possible. Central to the issue of achieving a net fusion power yield from any magnetic-confinement system is an understanding of the rate at which heat is lost from the confinement zone. In mirror systems, these losses are of two kinds: (i) axial losses, i.e., losses through the mirrors and out the ends, and (ii) radial losses, i.e., losses by diffusion across the confining field lines. The physical mechanisms involved in these two kinds of losses are not the same, with the result that their study involves different physics issues. In order to convey the nature of the issues that must yet be resolved, we will discuss them here in terms of four related conditions that must be met in order that confinement adequate for realizing a net positive fusion power balance can be achieved. These four conditions are as follows: -Microstability, referring to the control of high-frequency oscilla- tions, particularly as they might occur in, and interfere with the operation of, the end plugs; Axial confinement, pertaining to the need to achieve adequate control over any processes that lead to losses of particles that penetrate the electrostatic barriers created by the plug; Macrostability, referring to the maintenance of pressure equilib- rium and stability of the confined plasma against gross unstable motion across the magnetic field; and Radial confinement, not the same as the previous condition, but rather referring to maintaining adequate control (through config- uring the magnetic field and other means) over the rate of diffusion of the individual plasma particles across the confining field. The early years of mirror research, and first-generation tandem- mirror experiments, provided both fundamental understanding and a data base from which to start the investigation of the physics under

FUSION PLASMA CONFINEMENT AND HEATING 177 TABLE 4.3 Representative Tandem-Mirror Devicesa b Confinement Period of Parameter Thermal Device Location Operation (cm-3 s)c Barrier . . MFTF-B LLNL 1986- (10'3) Yes TMX-U LLNL 1982- (low) Yes TARA MIT 1984- (1011) Yes TMX LLNL 1978-1981 10 ~No Phaedrus Wisconsin 1978- 10~° No Gamma-10 Japan 1983- (low) Yes Ambal USSR 1984- (10'~) No Gamma-6 Japan 1978-1981 10~° No a Listed in descending device size, with U.S. devices listed first. b Supporting single and mult~cell devices are STM at TRW, Constance at MIT, LAMEX at UCLA, and MMX at U.C. Berkeley. c Projected parameters are in parentheses. lying the above conditions. It is now, however, necessary to be much more precise in this understanding, in order to gain confidence that third-generation experiments will achieve their goals of closing the gap between where we are now and a close approach to net fusion power. All the tandem-mirror devices operating or under construction are shown in Table 4.3. The values cited for the confinement parameter (product of plasma density and confinement time) are approximate and are given as indications of the performance level of the various devices. In what follows, we will discuss briefly the physics issues involved in meeting the four conditions outlined above. MICROSTABlLITY · Understanding of the properties of loss-cone-driven instabilities has led to their progressive suppression in a sequence of experi- mental steps and to their predicted elimination in a thermal-barrier tandem mirror. As noted in the section on Major Advances the Tandem Mirror, owing to their open-ended nature, mirror systems are vulnerable to high-frequency instabilities that can cause unacceptably high losses of particles through the mirrors. The degree to which a mirror cell is vulnerable depends on the degree of anisotropy of the species confined in the cell. In a tandem mirror, there is greater anisotropy in the end

178 PLASMAS AND FLUIDS plugs, where mirror action provides the dominant confinement force, than there is in the central cell, where electrostatic plugging predomi- nates. It follows that concern for loss-cone-driven microinstabilities applies almost exclusively to the plug region. The Livermore 2X-JIB experiment reduced the level and influence of microinstability by flowing warm ions through the hot, mirror-confined ion population. In TMX, the axial losses of ions from the central cell played the same function. This was described theoretically as a reduction of the destabilizing aspects of the mirror-confined ion energy distribution. A thermal-barrier plasma has this feature, without the need for additional flowing plasma. Validation of this theoretical picture will constitute a major step forward; early results from the new TMX-U experiment have been very favorable. Theory and past experiments have identified the plasma conditions and parameters for micros/ability. Current and future experiments should be able to demonstrate quiescent plasma behavior in theoreti- cally predicted stable conditions of higher temperatures and higher beta values, in this way delineating the constraints imposed on, and conditions required for, a mirror fusion power system. AXIAL CONFINEMENT: CONTROL OF THE POTENTIAL PROFILE AND THERMAL BARRIERS · Control of the axial potential profile is essential to tandem-mirror operation. The thermal-barrier end cell develops the plugging potential necessary for confining the central cell plasma with an end-cell density below that in the central cell, thereby reducing both the end-cell maintenance power and the required magnetic field. The central cell of a tandem mirror is essentially a large-volume mirror confinement cell with a moderately large mirror ratio (strength of mirror field divided by the strength of the central field), with its ion loss channel plugged by a positive potential provided by the plugs. Power, incident in the form of neutral beams or microwaves, is required to generate the plugging potentials in the small-volume, lossy end cells. However, because of the large volume ratio between the central cell and the plugs, and because of the effectiveness of electro- static plugging, the fusion power released from the central cell more than compensates for the power needed to maintain the plasmas in the plugs.

FUSION PLASMA CONFINEMENT AND HEATING 179 Jo14 jo13 ol2 C, ~ 1031 - x Solo 109 ¢.4,/t `/M FT F - B - ~ / Do/ _ /~*/ /~''~y ~/~ 8/TMX Upgrade ,`/ '/ GAMMA 10 l / P/EDR: G AMMA 6 _ loo 1 1 0.01 .~ it/ 2XI IS A// TMX Plug LITE Hi// 2X 2XI I _/ .: 2XI IB //-BB /47 BB I I ~ PRO // DECAIIB /~1 1, l l,,,ll ,, ,1, 0.1 1.0 10 100 E; (keV) FIGURE 4.9 Variation of the confinement parameter no with ion energy Ei for single-cell mirrors and the central cell of tandem mirrors, showing a strong improvement with increasing ion energy and a sharp increase due to electrostatic plugging. Here n is the plasma density, ~ the confinement time in the single cell or central cell, R the mirror ratio, and me the electrostatic plugging potential. The contrast between the confinement ability of a tandem mirror and that of a single-cell mirror is illustrated in Figure 4.9, which plots the confinement parameter against ion temperature in kiloelectron volts. The points lying along the lower lines show experimental results from a variety of single-cell mirror experiments and their approach to the ideal theoretical values (set by classical collision-induced losses). Some departures are evident, usually the result of inadequate suppres

180 PLASMAS AND FLUIDS sion of microinstabilities. The upper lines bracket the achieved and predicted confinement parameters for the central cell of various tandem-mirror devices. The dramatic improvement seen in the con- finement parameter for a given energy over that achievable in a single-cell mirror results from the much greater effectiveness of elec- trostatic-plus-mirror confinement relative to mirror-only confinement. Theory predicts, and experiment confirms, that the electrostatic con- finement depends exponentially on the ratio of the confining potential to ion temperature. Achieving confinement in a tandem mirror implies an ability to control the profile of the electric potentials within the plasma in the vicinity of the plugs. The way such potentials are generated and controlled in the plug plasmas rests on the exploitation of a fundamen- tal property of a plasma its strong tendency to maintain charge neutrality. Even slight local departures from charge neutrality can create substantial electric potentials. This fact is put to practical use in the tandem mirror as a means of creating electrodeless, i.e., nonmate- rial, potential-forming regions that control the containment of plasma particles. The single-cell mirror naturally develops a positive potential in operation for a simple reason: the intrinsic mirror-only confinement time of hot ions is much longer than that of the rapidly scattering electrons. Charge imbalance leads to the buildup of a restraining potential (equal to several times the electron temperature), large enough to hold back the electrons, so that the rates of loss come into balance. In the simplest embodiment of the tandem mirror, that tested first in Gamma 6 and TMX, the confining potentials were generated by just this means: high-density mirror cells at each end generated the potentials (named ambipolar potentials) that electrostatically confined the ions of a lower-density central cell. In this way, a property of the plasma its ambipolar potential was used to enhance its own con- finement. While the original tandem mirror idea worked well to enhance mirror confinement times, from a future economic standpoint it had several drawbacks that prompted a search for improvements. The density of the plug plasmas had to be substantially larger than that of the central plasma, in order to establish the required potential "hill" confining the central cell ions. Furthermore, since the electron temperature con- trolled the magnitude of the total potential, in order to increase the potential it would have been necessary to heat all the electrons plugs and central cell to enhance the potential. Since the volume of the central-cell plasma is much larger than that of the plugs, this was

FUSION PLASMA CONFINEMENT AND HEATING 181 deemed to be an unnecessarily expensive and wasteful process. Finally, because the plugs had both high density and high ion energy, this pressure required prohibitively high magnetic fields. It was reasoned that if the electrons in the plugs could be isolated from thermal contact with the central-cell electrons, a major econom- ically related benefit would occur. The plug electrons could then be heated to a much higher temperature than the central-cell electrons (with a now much-reduced heating power input), and the potential would rise correspondingly. It was in fact predicted that the required confining potentials would be generated even if the central-cell plasma density exceeded that of the plug plasma. The thermal barrier represents an improvement based on exploiting the possibility of controlling the relative charge-density profiles of electrons and ions in the end regions of a tandem mirror. It consists of a localized negative dip in potential between the central-cell plasma and the plugging potential. Such a potential dip serves to isolate the electrons trapped in the plugging potential from those in the central-cell plasma. It may be looked upon as a pair of back-to-back double layers of the type discussed in the physics of auroras. A comparison of typical potential/plasma-density profiles for conventional and thermal-barrier tandem-mirror systems is shown in Figure 4.10. The thermal barrier represents a further manipulation of the axial potential beyond the idea embodied in the original tandem mirror. To maintain it, external power input is required in the form of electron heating and in the power required to pump out ions from the thermal- barrier region. Theoretical calculations show that, compared to the original tandem, the decrease in power required to maintain the plug plasmas (using neutral beams) more than compensates for the power required to form and maintain the thermal barrier. The decrease in permitted plug-plasma density also lowers the magnetic field required in the plugs, resulting in an important simplification in magnet design. MACROSTABILITY: EQUILIBRIUM AND BETA LIMITS · With careful attention to design of the end-cell magnetic fields, the open system's high-beta capability can be realized in a tandem mirror, with calculated beta limits in the range of 35-50 percent. The requirement for a pressure equilibrium between the plasma and its confining field that is stable against gross plasma motion (magnetohydrodynamic instability) is common to all magnetic- confinement systems. The driving forces for such unstable motions are

182 PLASMAS AND FLUIDS Conventional n Thermal Barrier 0 n FIGURE 4.10 Axial profiles of tandem-mirror density n and potential ~ without (conventional) and with a thermal barrier, showing the sharply reduced end-cell density required when a thermal bamer is present. the plasma pressure gradients themselves, abetted by effects associ- ated with the curvature of the magnetic field lines and by centrifugal effects if the plasma is rotating. The field-line curvature enters in a fundamental way: regions where the field is convex toward the plasma are locally stabilizing; those concave are destabilizing. In a tandem mirror designed for gross stability, the good curvature regions are made to outweigh the bad, thereby achieving a favorable average. The plasma is also subject to unstable perturbations that localize in regions of unfavorable curvature. Magnetically induced localizations, leading to ballooning instabilities, require line bending and conse- quently lead to beta limits. Electrostatic localization, leading to trapped-particle instabilities, requires a population of fast-bouncing particles that are trapped in the unfavorable-curvature region. Achiev- ing stability sets a minimum for the fraction of particles that must visit both good and bad curvature regions. The challenge to magnet design- ers, blending together physics and engineering constraints, is to optimize the beta limits on stability and thereby optimize the magnetic efficiency. It appears that tandem-mirror systems can be designed that

FUSION PLASMA CONFINEMENT AND HEATING 183 exhibit average beta values that are substantial, of the order of 35-50 percent. Many of the features of equilibrium and macroscopic stability theory have already been tested in previous mirror and tandem-mirror exper- iments. Features of the theory having to do with rotation effects associated with the radial electric fields in the central cell of a tandem-mirror system have yet to be tested. However, using the existing theory, conceptual tandem-mirror fusion power systems have been designed that are predicted to be stable to all such effects. If the underlying theoretical models are validated in upcoming experiments, an important physics aspect of the design of tandem-mirror fusion power plants will be secure. RADIAL CONFINEMENT: PARTICLE TRANSPORT AND RADIAL POTENTIAL CONTROL · Control of cross-field particle transport in tandem-mirror systems involves taking into account the symmetry of the magnetic fields and the effects of radial electric fields. Experiments are providing checks of the theory of these effects, which predicts that they can be made satisfactorily small. In a tandem-mirror system, the end loss is plugged by an electro- static potential. Since this potential cannot be maintained constant radially all the way to the plasma surface, it follows that the outer surfaces of the plasma are less well plugged than the inner regions. In such a system, the radial transport of particles then implies only that they are transported to regions where they are less well confined axially than they are in inner regions; they still end up by being lost through the ends rather than directly to the chamber wall (which need not be close to the plasma surface). This feature, a natural diverter action, can be a great practical advantage for fusion power generation. Design of the magnetic-field configuration in tandem-mirror systems has a critically important bearing on the particle confinement in such systems. Typically, the end-mirror cells of a tandem mirror are designed with "quadrupolar magnetic well" type fields in order to ensure stability against gross (MHD) plasma instabilities. As a result of the essential azimuthal asymmetry of these fields, various complicated drift motions of the confined ions can occur that can cause these ions to diffuse radially across the confining field. This radial loss process is principally nonambipolar- ions escape across field lines, and electrons along field lines to the end walls. The problem of this so-called

184 PLASMAS AND FFUlDS "resonant transport," especially affecting the ions in nonaxisymmetric mirror fields, has been addressed theoretically, and scaling laws have been derived that can be used for comparison with experiment or for conceptual designs of tandem-mirror fusion power systems. In recent tandem-mirror experiments, the rates of radial ion trans- port have been measured and have been found to agree within a factor of 2 or 3 with theory. In addition, by using special electrodes at the ends of the apparatus to control the radial distribution of electric potential (thus influencing the particle drift motions), marked improve- ments in radial confinement have been observed, in general agreement with expectations. Currently, several approaches are under experimental and theoreti- cal investigation for replacing the highly asymmetric quadrupolar end-mirror fields by alternative shapes that should permit totally, or nearly totally, axisymmetric central-cell fields. Based on present theory, these changes in geometry should reduce the asymmetry- related radial transport to negligible levels. Prospects for Future Advances in Mirror Confinement · In the growing quest for the most practical avenues to fusion power, the inherent flexibility of the mirror approach may lead to advantageous systems that are new or simpler. One of the attractive features of mirror-based approaches to fusion power is the versatility and flexibility with respect to their design. The tandem-mirror idea is a prime example of these qualities, where the open-ended nature of tandem-mirror systems permits the manipulation and control of both the magnetic and the electrostatic aspects of its operation in a variety of ways. First steps in the evolution of the tandem-mirror idea are already being taken with the introduction of the thermal barrier idea, aimed at more effective control of the confining potentials with expected future economic gains. A coming challenge for tandem-mirror researchers will be to find ways to accomplish this and other objectives in simpler ways. Simplification, with its resulting engineering and economic advan- tages, may be sought in improved magnetic configurations and in simpler means of potential generation and control. With respect to the tandem-mirror magnetic configuration, there is hope, based on low-temperature results, that axially symmetric (or nearly so) versions of the tandem could be designed that would preserve the high-beta qualities of the present nonaxisymmetric con

FUSION PLASMA CONFINEMENT AND HEATING 185 figurations, while at the same time suffering less particle transport and being much simpler and cheaper to construct. With respect to simplified means of potential control, there exists the theoretical possibility that designs or operating modes for the tandem- mirror plugs can be found that retain the advantages of present thermal barrier ideas but achieve the equivalent result by much simpler means. One example would be the negative tandem mirror, operated at a net negative potential, with magnetically confined electrons plugging the ion leak channel. The above are intended to illustrate some of the possibilities that may arise when two fundamental ideas the magnetic-mirror effect and the control of plasma by self-generated electrostatic potentials- come together as they do in the tandem mirror. Increased understanding of basic mirror principles should advance the mirror approach to mag- netic confinement. The goal is a simple and effective fusion reactor. As the most prominent mirror-based approach, the tandem-mirror concept has been built on a series of innovative ideas, which have been verified in the first generation of experimental devices. The momentum created by these successes should carry us near a demonstration of fusion breakeven by the end of this decade. ELMO BUMPY TORUS Introduction · The Elmo Bumpy Torus (EBT) concept relies on superhot mirror- confined high-beta electron rings to stabilize a core plasma in a mechanically simple, steady-state toroidal configuration. Plasmas confined in toroidal or mirror magnetic geometries tend to be unstable in regions where the magnetic field lines bulge away from the plasma, i.e., regions of "bad curvature.?' A generic method for improving stability is to create a superhot component in the bad- curvature region. The diamagnetic current from a sufficient number of these hot particles produces a local minimum, or well, in the magnetic field (a minimum-B field). If the motion of the superhot component is dynamically decoupled from the remaining plasma, the minimum-B field will produce a stable confinement configuration. This principle is the basis of the EBT. The basic building block of an EBT is the single canted mirror sector shown in Figure 4.11. The mirror sectors (typically 24) are connected toroidally, forming a highly accessible and simple mechanical structure

186 PLASMAS AND FLUIDS SECON D-HARMON IC Rl NO H EATI NG (0.5 T ) 1 11 ~406- 1 ~ me, W/~ ~242 ''J N DAM ENTAL CORE PLASMA HEATING (~.0 T) FIGURE 4.11 A single canted mirror sector of a bumpy torus, showing field lines (dashed lines), contours of constant field strength (solid lines), and electron cyclotron resonance zones (hatched). that is operated steady state. The coil spacing causes the magnetic field lines to bulge out between magnets, creating a bumpy magnetic field and providing an absolute trap for charged particles. Stability of the equilibrium is provided by very hot, stable electron-ring plasmas (ring temperatures of 100-500 keV) generated by steady-state microwave power. The hot electron-ring plasmas are created in the annular region where the applied microwave frequency equals the second harmonic of the local electron cyclotron frequency. The stored energy density in the rings is found to be comparable with the local magnetic field energy density; hence, the ring-plasma beta can be high, up to 50 percent in some cases. These rings can be formed in the regions where the toroidal core plasma would otherwise be susceptible to the interchange instability. The essence of the EBT concept is the generation of a toroidal series of hot electron rings for the creation, stabilization, and buildup of the

FUSION PLASMA CONFINEMENT AND HEATING 187 fusion-relevant toroidal core plasma that threads through them. The objective of the EBT program is to demonstrate the viability of this concept, ultimately for a reactor. Key objectives are to demonstrate stable confinement of ring and core plasma and efficient microwave heating of ring electrons. EBT research in the United States is centered at the Oak Ridge National Laboratory, with smaller efforts at McDonnell Douglas, TRW, JAYCOR, SAI, and various universities. There is also a major program in Japan. Major Advances · In EBT experiments, the production and maintenance of superhot electron rings by microwave heating using 28-60 GHz gyrotrons obeys theoretical predictions and scales favorably to a reactor. The stability of the ring depends on dynamic decoupling from the core plasma, and sets a limit on the core-plasma beta, which has not yet been tested experimentally. Experiments in the Elmo linear mirror, and thereafter in the EBT-1 toroidal device, established that stable hot electron ring plasmas could be generated steady state and that the rings could stabilize a warm, moderately dense core plasma (plasma density of 10~2 particles per cubic centimeter and electron temperatures of 100-400 eV). The primary limit on particle and energy density was the applied frequency and the available electron cyclotron resonance heating (ECRH) power. The success of EBT-1 with 10.6- and 18-GHz heating prompted the development of higher-frequency, higher-power, steady-state micro wave sources. In 1978, the first EBT scaling experiments at higher magnetic field and microwave frequency were performed with a 28-GHz gyrotron at about 30 kW steady state. The power levels increased steadily, with routine plasma operation at 200 kW steady state achieved in 1981. Most recently, a prototype 60-GHz gyrotron was tested at 200 kW steady state. EBT experiments have shown that production of hot electrons by electron cyclotron heating is an efficient process. Data from EBT and other single-frequency ECH hot-electron experiments have indicated that the ring temperature obeys a simple scaling law, in which the hot-electron radius of gyration (which is proportional to the square root of its temperature) is limited to 5-6 percent of the magnetic-field curvature scale length. In addition, heating at several frequencies close

188 PLASMAS AND FF UlDS in value was shown to improve the heating efficiency (by increasing the density) an order of magnitude on the Symmetric Tandem Mirror (STM) experiment, a linear multicell mirror device with EBT-type hot-electron rings. Experimentally, ring losses appear to be classical, primarily deter- mined by collisional slowing down and scattering on the core plasma at low energies and by synchrotron radiation at high energies. Since the rings in an EBT reactor occupy only a small fraction of the plasma volume and their thickness is larger than the hot-electron gyroradius, the ring power loss would be fairly modest for 1-2 MeV electrons. The stabilization by the rings depends critically on whether the rings are rigid, i.e., dynamically decoupled from the behavior of the core plasma. Experimentally, ring decoupling is clearly achieved in certain regimes of operation. Because the usual theory of ideal fluids cannot explain this phenomenon, a new type of quasi-kinetic stability theory has recently been developed for instabilities in EBT caused by unfa- vorable curvature. This theory yields stability for certain parameter values, not inconsistent with experimental operation. However, it also predicts that, at a relatively low core-plasma pressure, coupling between ring and core plasma will occur and generate an unstable configuration. This beta limit cannot be tested on the present genera- tion of EBT devices. Current Frontiers of Research · The emphasis in current EBT research is on increasing the core plasma density and temperature, so as to test the beta limit, and on understanding and optimizing the confinement of the core plasma. Although EBT has made substantial progress in containing core plasma, to date the density is limited to a few times 10'2 particles per cubic centimeter, or about 10 percent of the ECRH cutoff density limit. There is a high priority to show that higher density can be achieved. One possible technique would be to launch the wave energy from the high-field region, as opposed to the conventional low-field launch, and to control the polarization of the wave. Another technique is slow- wave ion cyclotron resonance heating (ICRH), found to be elective in raising the plasma density in the Japanese Nagoya Bumpy Torus experiment (NBT). Ion cyclotron heating is being developed to heat the core plasma ions and to explore confinement of hot ions in EBT. Fast-wave ion heating is available on present experiments at power levels comparable with,

FUSION PLASMA CONFINEMENTAND HEATING 189 or greater than, that absorbed by the electrons. If the density can be raised, the applied ICRH power should heat the ions more efficiently. With higher density and hotter ions, it may become possible to check the plasma beta stability limit predicted by theory. The beta limit is important in determining the operating regime for future experiments and in assessing reactor feasibility. For instance, there is a trade-off between plasma-beta and ring-power economics, in that high beta would require thick rings, whereas thin rings are desirable for mini- mizing their energy investment. Even with ideal operation of the rings, the EBT configuration must be able to contain a core plasma long enough against the diffusive effects of particle collisions. An EBT system, taken to be dominated by classical collisions, would be marginally adequate for ignition in a modest 1000-MW reactor. However, there is concern that anomalous transport due to drift wave fluctuations may degrade confinement. Prospects for Future Advances · The next stage of the EBT program could involve a scaled-up experiment with improved confinement. Alternative configura- tions are under investigation, and aspects of the EBT concept have application also to advanced tokamaks and mirrors. The next evolutionary stage of the EBT program would be to test confinement in larger standard bumpy tori at parameter regimes of higher density (in the range of 5 x 10~3 particles per cubic centimeter range) and higher temperature (above 1 keV) for the toroidal core plasma. From theory have come a number of ideas for improved containment of particle orbits, such as advanced coil designs, reversing the ambipolar potential, reconfiguring the standard bumpy torus into bumpy straight sections with high-field corners, and hybrid combina- tions of an EBT with rotational transform. Recent theoretical work also suggests that the stability of tokamaks, stellarators, and mirrors can be enhanced by the introduction of energetic particles similar to those in EBT. In addition, EBT research has had other benefits. The desire to provide higher-frequency, more-powerful ECRH sources for EBT has resulted in a national program for microwave-source development. These gyrotrons are being used extensively in the tokamak program for local heating and assisted start-up and in the tandem-mirror program for thermal-barrier production.

PLASMAS AND FL UlDS REVERSED-FIELD PINCH Introduction · The reversed-field pinch is, like the tokamak, a toroidal confine- ment system. Its distinguishing features include high beta and the potential for a compact reactor in which the plasma currents themselves provide heating to ignition. The reversed-field pinch (RFP) is a close cousin of the tokamak confinement system. Like the tokamak, it is a toroidal device that combines a toroidal magnetic field with a poloidal magnetic field to confine a plasma. Figure 4.12 shows the direction that the magnetic fields point in different parts of the REP plasma. It is the reversal in the direction of the toroidal field near the wall that gives the reversed-field pinch its name. An important difference between the REP and the TRANSFORMER PRIMARY WINDINGS TOROIDAL FIELD / WINDINGS _ - MAY MAGNET I C FIELD ll ~ , / -METAL VESSEL /T OROI DAL F I ELD I WALL >a P O L Ol DAL Fl ELD ~ / \ I . ~ - - RADIUS it- M ET AL WA LL FIGURE 4.12 Magnetic fields in the reversed-field pinch. The plasma current is induced by the transformer primary windings, whereas the toroidal magnetic field is produced initially by the toroidal field windings. The direction of the magnetic field lines on surfaces at different radii is also shown. Notice that the pitch of the field-line helices reverses near the walls, because the toroidal magnetic field changes sign. Hence the name reversed-field pinch.

- FUSIONPLASMACONFINEMENTANDHEATING 191 TABLE 4.4 Representative Reversed-Field Pinches Major Minor Plasma Radius Radius Current Device Location (m) (cm) (MA) OHTEa GA 1.24 19 0.25-0.50 ZT-40 LANL 1.14 20 0.06-0.24 ETA BETA-2 Italy 0.65 12.5 0.05-0.20 HBTX 1-A UK 0.80 26 0.10-0.50 TPE-1R(M) Japan 0.50 9 0.13 REPUTEb Japan 0.80 20 (0.4) STP-3Mb Japan 0.50 9 (0 3) a Privately funded. b Under construction 1984. tokamak is that in a tokamak the dominant confining field is the toroidal field, produced by an external magnet winding, whereas in an RFP it is the poloidal field produced by the plasma current that is responsible for plasma confinement. To maintain stability in a tokamak, the poloidal field, and hence the plasma current, must be kept small compared with the toroidal confining field. In an RFP, the toroidal and poloidal magnetic fields are of comparable magnitude, so for a given toroidal magnetic field much higher plasma currents are carried in an RFP. These differences can be exploited in a reactor. The high plasma currents allowed in an RFP are expected to be sufficient to heat the plasma to ignition without the need for auxiliary neutral-beam or radio-frequency heating systems. An important quantity in fusion reactor design is the engineering beta, which is defined as the ratio of the plasma pressure to the pressure exerted by the magnetic field on the magnet windings. This quantity can be rather large in an RFP because the toroidal field at the windings is small, and the poloidal field strength is much smaller at the magnet windings than at the plasma surface. The engineering beta in present RFP experiments is typically 10 percent. With this value of engineering beta, the magnet windings in a reactor could be made of copper rather than superconductors. These features have led to the design of compact RFP reactors that offer several potential advantages over the larger conventional reactor designs. Present RFP experiments (see Table 4.4) operate with a plasma current only 1-2 percent of that needed in a reactor. The major research goals of the RFP program therefore are to raise the plasma current and (i) maintain the high beta currently achieved, (ii) demonstrate adequate

192 PLASMAS AND FLUIDS confinement and plasma heating, and (iii) develop the necessary technology for exploiting the high-power density potential of the RFP reactor. RFP research in the United States is centered at the Los Alamos National Laboratory. Both Europe and Japan are also active in RFP research. Major Advances · We now understand that the RFP is a minimum-energy state. This helps to explain its stability and persistence and may permit steady-state operation of an RFP reactor. The last decade has seen considerable progress in RFP research both in the United States and abroad. The most important advance has been the understanding that the RFP is one of a class of minimum-energy states. All such minimum-energy states lie on the curve shown in Figure 4.13, which shows the ratio of the toroidal magnetic field at the wall to the average toroidal magnetic field (F) versus the ratio of the poloidal field at the wall to the average toroidal field (called 01. As ~ is increased (by increasing the plasma current, for instance) F must decrease, and when ~ reaches 1.2, the toroidal field at the wall must vanish. (This configuration, called a spheromak, is discussed in the section on Compact Toroids.) When ~ exceeds 1.2, the toroidal magnetic field at the wall must become negative, and we have an RFP. 0.50 0.25 o -0.25 -0.50< \ \ EXPERIMENT THEORY \ \ b=0 \ ~ - \ ~L RFP \ ~ REGIME 0.5 1.0 1.5 2.0 FIGURE 4.13 The F-D diagram. F is the ratio of the toroidal magnetic field at the wall to the average toroidal magnetic field, and ~ is the ratio of the poloidal magnetic field at the wall to the average toroidal magnetic field. The plot shows how F depends on ~ for the minimum-energy state.

FUSION PLASMA CONFINEMENT AND HEATING 193 The fact that the RFP is a minimum energy state explains much about the stability and persistence of this configuration and leads to the possibility of steady-state, or continuous, operation of an RFP reactor. Early RFP experiments were plagued by very-high-energy losses caused by impurities in the plasma. These losses were so serious that temperatures did not exceed 50 eV. Improvements in vacuum systems and vacuum wall materials now reduce impurities to the point where the energy losses attributable to impurities are only 5-20 percent of the total energy losses. Present experiments typically reach temperatures of 200 eV, with electron densities of (1-4) x 10~3 particles per cubic centimeter, using a magnetic field at the coils of about 1 kG; one smaller experiment has produced 600-eV plasmas. Another major step forward has been the confirmation that RFP configurations can be formed over comparatively long times. Until the induced plasma current becomes large enough to cause the pitch of the helical magnetic field lines near the wall to reverse, the plasma is potentially unstable. For this reason, early experiments formed RFP plasmas so quickly that instabilities did not have time to develop. Recent experiments have shown that such fast formation schemes are not required. The slower formation schemes allow lower-voltage operation and simplify engineering problems. Current Frontiers of Research · The key issue in RFP research is whether its confinement will be adequate when operated at high plasma current. Five RFP devices, of which two are in the United States, are currently operating (see Table 4.4~. Confinement properties of the RFP at higher plasma currents are the subject of continuing investigation. The energy confinement time must be increased to 1000 times its present value of 0.25 ms to meet reactor requirements. The temperature and density must also be increased by large factors, while beta must be maintained at its present value. It is important to ascertain as soon as possible whether the RFP concept will scale to the desired levels of confinement, by understanding the internal processes that determine the rate of energy leakage from the plasma across the magnetic field lines as well as the processes that sustain the RFP configuration. Theorists are beginning to use sophis- ticated three-dimensional magnetohydrodynamic (MHD) computer codes to study the internal operation of the RFP, and experimentalists

194 PLASMAS AND FLUIDS have detected MHD modes similar to those predicted by the theoretical codes. Four other areas of current research are described below: (i) The principal barrier to raising the plasma current is the resulting damage to the very thin metal vacuum walls used in present equipment. This wall damage should be reduced by use of equilibrium control and limiters. Electronics circuits are used to control the equilibrium position of the plasma, and prelimi- nary results include longer plasma lifetimes and reduced plasma interactions with the wall. Several limiter designs, which protect the thin wall by limiting plasma size, are being tested. (ii) The sensitivity of RFPs to errors in the magnetic fields is being investigated. Reductions of the field errors in existing devices (caused by perturbations such as pump ports, nearby iron, and insulating gaps in the conducting shell) have dramatically in- creased the plasma lifetime, and designs of future machines call for much lower field errors than those in the present generation machines. (iii) Improved formation schemes are being investigated including the ramped formation, which begins with a low-current RFP and then gradually increases the plasma current and density to the desired levels. This procedure avoids having to produce full plasma current before the stable RFP configuration is estab- lished. (iv) The transformer technique now used in RFPs can only sustain a plasma current for a limited time. Several techniques for steady- state current drive being tested for use in tokamaks might be applicable to an RFP, but another technique, which is unique to the RFP concept, is currently being studied most intensively. This technique is to oscillate the currents in the magnet windings at audio (~2 kHz) frequencies. Theory predicts that the plasma will rectify the oscillations and maintain a net toroidal plasma current. Recent experiments have confirmed some of the as- sumptions made in the theory, and more elaborate experiments are being planned. Prospects for Future Advances · Larger reversed-field pinches have been proposed in several countries, aimed at reactorlike plasma densities and temperatures.

FUSION PLASMA CONFINEMENT AND HEATING 195 Results from the present REP experiments appear sufficiently prom- ising that larger REP devices are being proposed in the United States, Europe, and Japan. These machines would be at least twice as large as present experiments and carry over four times more plasma current. With these machines, temperatures in the kiloelectron-volt range should be attained, with an electron density of approximately 10~4 particles per cubic centimeter and an energy confinement time in the 10-ms range. COMPACT TOROIDS Introduction · Compact toroids are a class of toroidal plasma configurations that might lead to a smaller, less expensive reactor core. Substantial progress in understanding the confinement properties of the vari- ous classes of compact toroids is needed to evaluate their potential reactor advantages. Compact toroids (CTs) are a class of toroidal confinement configu- rations that do not require any magnet coils or vacuum chamber to link the plasma through the hole in the doughnut-shaped configuration. A magnetic surface called the separatrix divides the open field lines on the outside from the closed field-line or flux-surface structure of the CT on the inside. All the fields inside the separatrix are supported by currents inside the plasma; the only fields that are supported by magnet coils are the solenoidlike fields outside the separatrix. Although a broad class of confinement schemes is possible within the CT area, the spheromak and the field-reversed configuration (FRC) are being studied most intensively at present. In their fundamental form, both are axisymmetric, like the tokamak and reversed-field-pinch. However, nonaxisymmetric variations can be added to CTs and, in fact, have been successfully used to help stabilize the FRC. The fundamental difference between these two types of CTs is that, inside the separatrix, the spheromak has both poloidal and toroidal field components (see Figure 4.14) like the tokamak and the reversed- field-pinch, but the FRC contains no toroidal field, only closed poloidal field lines. This deceptively simple change yields completely different equilibrium, stability, and confinement properties. Although CTs are at a comparatively early stage of development, gross stability and high betas have been confirmed at temperatures of about 100 eV. If the energy confinement improves favorably at higher

196 PLASMAS AND FFUlDS POLOIDAL MAGNETIC FIELD ~-\ :,~D - (~ PLASMA FRC ,>~/ AIDS/' SPHEROMAK TOROIDAL MAGNETIC FIELD CLOSED POLOIDAL MAGNETIC 4/ ~< FIELD LINES - ~ ~- - OPEN MAGNETIC FIELD LINES FIGURE 4.14 Schematic representations of a spheromak and a field-reversed config- uration (FRC). Note the closed magnetic-field region where the plasma is confined. The FRC has an elongated prolate shape, whereas stable spheromaks are ablate. values of temperature and magnetic field, while preserving the high beta and stability, CTs will offer important advantages for the fusion power core of a reactor. The large beta would allow a high power- density plasma to be supported by modest fields at the magnet coils. If the technology of the first wall (nearest the plasma) can be developed to accept the high power, then much smaller and less expensive reactor cores could be built. The simple geometry of the magnet coils and vacuum chamber allowed by the CT configuration adds to these advantages. Although the terms compact toroid, spheromak, and field-reversed configuration have all been coined during the past decade, the concepts are all more than 20 years old. Both spheromaks and FRCs had been produced in the laboratory by 1961. Some characteristic parameters of present spheromak and FRC experiments are given in Table 4.5. The particle ring was another type of CT also conceived in the 1950s. The particle ring differs from other CTs in that the fields inside the separatrix are supported by currents carried by high-energy particles (electrons or ions) whose gyration radii are comparable with the major

FUSION PLASMA CONFINEMENTAND HEATING 197 radius of the torus, hence the name particle ring. Complete field reversal (CT formation) was achieved with electron rings in 1972, but reactor studies have indicated that neither electron nor ion particle rings are likely to produce econorr,ically attractive reactors. However, some work on particle rings continues, because a merger of such rings with spheromaks or FRCs has the potential of aiding stability, heating, and sustainment of CTs. Compact toroid research in the United States is conducted at Los Alamos, Princeton, the University of Maryland, Spectra Technology (formerly Mathematical Sciences Northwest), and several smaller institutions. Japan and the Soviet Union are also particularly active in this area. TABLE 4.5 Representative Compact Toroids Toroidal Major Minor Plasma Radius Radius Current Program Location (m) (cm) (MA) Contributions Spheromaks CTX LANL 0.25 15 0.4 C,F,S,ST COP U. of Wash. 0.04 4 0.01 F,M PS-2 Maryland 0.09 9 0.10 C,F Proto S-1C PPPL 0.12 8 0.06 C,F,S S-1 PPPL 0.50 27 0.2 (0.4) C,F,S CTCC-1 Japan 0.26 14 0.2 C,F,M Field-Reversed Configurations FRX-C LANL 0.07 3 1.5 C,S,T CTTX-1 Penn State 0.02 1 0.14 H,T TRX-1 Spectra 0.045 2 0.75 C,F,S TRX-2 Spectra (0.045) (2) (0.75) (C,F) BN-1 USSR 0.05 2.5 0.5 F,T TOR USSR 0.07 3 1.1 F,T TL USSR 0.04 2 0.3 F,T,CH NUCTE-2 Japan 0.028 12 1.6 C,F OCT Japan 0.035 2 0.5 F,T PIACE Japan 0.026 1 0.6 C,S,T STP-L Japan 0.01 1 1.2 C,S a Program contribution codes are as follows: confinement (C), compressional heating (CH), formation (F), merging (M), stability (S), sustainment (ST), translation (T).

198 PLASMAS AND FLUIDS Major Advances · Substantial experimental and theoretical progress in the last decade has reawakened interest in compact toroids. Substantial progress has been made during the past decade in both forming and understanding spheromaks and FRCs. Although important theoretical and experimental work was accomplished earlier, the results were not sufficiently convincing to capture the attention of a major segment of the fusion community. Important advances in plasma theory and computation, and some pioneering experimental work, motivated a closer examination of CTs. Improvements in diagnostics, impurity control, and other experimental techniques developed in the fusion community have also contributed strongly to the recent suc- cesses. One measure of the rapid progress that has been made is shown by the improvement in plasma lifetime plotted in Figure 4.15. 3.00 1.00 U) LL ~ 0.30 - U] 11 0.03 A / ~ ' ' A GARCHING, GERMANY B KURCHATOV, USSR C LANL D LLNL E PPPL / / F OSAKA UNIV, JAPAN ,J / G LANL / /, / H CORNELL UNIVH /, / l /' / / / / / G/ I I / l l / F/ / E I / / / D ~ / I l l 0 0 1 · 74 75 76 77 78 79 80 81 82 83 CALENDAR YEAR FIGURE 4.15 The maximum compact-toroid lifetimes produced by a variety of experiments during the past 10 years. The solid lines are FRCs, and the dashed lines are spheromaks.

FUSION PLASMA CONFINEMENT AND HEATING 199 SPHEROMAKS · Spheromaks are compact toroids with both poloidal and toroidal magnetic-field components; significant progress has been made in impurity control, in formation and sustainment techniques, and in extending the lifetime of the plasma. The long lifetimes recently achieved (see Figure 4.15) are evidence that spheromaks can be maintained in stable configurations for many (hundreds of) dynamic time scales. These positive results are depen- dent on maintaining the proper plasma shape and boundary conditions, as prescribed by stability calculations. In addition, spheromaks have been produced with temperatures over 100 eV, indicating that they are no longer dominated by light-ion impurity radiation. This was first achieved in 1983 on the CTX device at Los Alamos, using a source with electrodes. Typical spheromak plasma parameters are shown in Table 4.6, along with parameters for FRCs. Major breakthroughs have also been made in the techniques of forming and sustaining spheromaks. The older techniques formed the plasma on the dynamic time scale, i.e., the time scale determined by the "springiness" of the magnetic field and the mass or inertia of the plasma. This rapid formation required high-voltage electrical technol- ogy that would be unattractive for projected reactors. The Proto S-1A device at Princeton, guided by sophisticated computations, was the first to demonstrate a slower technique that would operate close to the resistive time scale. Reactors based on this slower technique could use standard rotating machinery to power the spheromak source. The breakthrough in sustainment was achieved on the CTX device when magnetic fields and plasma density were held constant for 1 ms, a time long compared with the natural decay time of the configuration, by applying continuous electrical currents from the electrodes of the plasma source. The technique is based on a minimum-energy principle, which the spheromak shares with its cousin the reversed-field pinch, namely, that the plasma and magnetic fields within a conducting boundary relax to a state of minimum energy under the constraint of conserved magnetic helicity (linked fluxes). On a longer time scale, the configuration would decay as the currents are decreased by the plasma resistivity. In the sustainment process, the source supplies a continu- ous flow of a helicity into the separatrix region of the spheromak to replace that dissipated internally by the resistive losses, and the spheromak redistributes the fields as it continues to relax toward its minimum energy state. The sustainment experiments in CTX indicate

200 sit ~ .C ~ E sin 3 O ._ ·~= ~ Ct C,0 Ce _% ._ I_ ·- V) _ 5~ o 'V ~ I_ ~_ ILL 0 U. ._ 5~ o o V 5~ ~0 Cal So Cal Cal - C~ .o EM O O _ O . . rid ID O O O O _ _ _% . ~ C) I: ~ O ~ _ ; Cry ~ 0.s EN O O oo O O O O ._ ~ ~ -o .0 O ~ ~ ~ ~ O CC ~ Ct ~ CL ._ O O ~ E

FUSION PLASMA CONFINEMENT AND HEATING 201 that it may be possible to create and then sustain spheromaks contin- uously using do power, obviating any need for current drive and perhaps also for additional heating. FIELD-REVERSED CONFIGURATIONS · Field-reversed configurations are compact toroids having poloidal magnetic field only; major advances have been made in under- standing confinement scaling and equilibrium physics, in achieving increased confinement parameters, and in stabilizing the rotational instability using quadrupole magnetic fields. The increased effort in FRC studies in the United States initiated 7 years ago was largely motivated by experimental results from the Soviet Union and Germany during the early 1970s. Figure 4.15 shows that significant progress has been made since that time in extending the lifetime of FRCs. In part, the increased lifetimes have been achieved by using theoretical models of transport and equilibrium to guide the experiments. The confinement scaling predicted by these models has been confirmed by experiments. The best FRC confinement parame- ters have been produced on FRX-C, which has achieved values of the confinement parameter of about 4 x 10~i particles per cubic centimeter seconds. Plasma parameters consistent with this value are given in Table 4.6. The latest jump in the FRC lifetime (see Figure 4.15) was achieved on FRX-C by stabilizing the rotational mode by a technique first developed on the PIACE experiment in Japan in 1982. The stabilization technique uses special (quadrupole) fields to produce small nonaxisym- metric bumps on the FRC. Current Frontiers of Research · The physics of particle and energy transport in spheromaks is largely unknown and is a central issue for assessing the promise of this configuration; other areas of research include stability, heat- ing, and sustainment. Particle and energy transport are better understood for FRCs than for spheromaks, but unresolved ques- tions remain. Although existing FRCs are stable, it is unknown whether this will remain the case for reactor-sized plasmas; translation experiments may lead to improved FRCs, but forma- tion of the configuration on a slow time scale remains an important problem.

202 PLASMAS AND FLUIDS The most important issue for spheromaks is to understand the particle and energy transport processes. In the higher-temperature plasmas (A 100 eV), the energy loss appears to be dominated by particle transport. Since the beta value is higher than stability theory would predict, the plasma pressure may be driving turbulence that results in particle loss. In addition, edge conditions near the separatrix appear to affect strongly the plasma behavior, particularly at higher tempera- tures. These complex physics issues can be translated into a practical concern. If the boundaries are made properly, will the energy confine- ment time increase sufficiently with size and field to meet-the require- ments of a practical reactor? Much of the near-term research will be focused on this question. Other important areas of research include the sustainment and heating of spheromaks. The do current technique for sustainment will be examined to determine the efficiency of helicity injection, as well as its effects on energy confinement. Studies of radio-frequency heating are planned, as well as other auxiliary heating techniques such as compression and particle beams. Transport physics is also a major issue in FRC research but is somewhat more developed than for spheromaks. Particle transport models are consistent with experiments, but two related issues remain unresolved, namely, additional energy-loss processes and stability. In the largest experiment (FRX-C), the particle transport accounts for slightly less than half of the energy loss. Oxygen and carbon radiation are not significant, but radiation from heavier impurities and thermal conduction may be important energy-loss mechanisms. Understanding and reducing the energy loss by radiation and conduction will become even more important as scaling experiments continue to reduce the particle loss. The instability issue may arise when FRCs are scaled to larger size to improve confinement. In spite of substantial theoretical progress, existing theories cannot predict whether FRCs large enough to provide reactor-level confinement will be stable or unstable. Continued theo- retical and experimental efforts are being directed to help resolve this issue. Translation of the FRC out of the source into a steady-state solenoidal field region is an integral part of some FRC reactor con- cepts. Translation has been successfully demonstrated in Soviet, Japanese, and U.S. experiments. It is currently being studied in the United States as a means to facilitate longer plasma lifetimes, diagnos- tic access, impurity control, and alteration of the FRC's radial profile, which affects the particle loss rate.

FUSIONPLASMACONFINEMENTANDHEATING 203 Formation of FRCs on a slow time scale is important for the same reasons as for spheromaks. Several proposed concepts are being studied theoretically and await experimental verification. Prospects for Future Advances · At the current rate of progress, in the next 10 years or so the unique features of compact toroids should be well enough under- stood to assess their potential in comparison with other advanced concepts. During the next 10 years, substantial progress is expected in under- standing the transport processes for both FRCs and spheromaks. For spheromaks, the PS-2 device at the University of Maryland and its successor (e.g., the proposed MS experiment) will study mixed forma- tion (i.e., a combination of inductive and electrode drive) and the transport of higher-density (about 10~5 particles per cubic centimeter) plasmas. The S-1 experiment at Princeton and its upgrades will address inductive formation, transport, gross stability, and auxiliary heating. The CTX experiment at Los Alamos and its upgrades will investigate the transport, and also the sustainment by currents from external electrodes, of spheromaks with densities in the range 10~3-10~4 particles per cubic centimeter. If these are successful, the confinement param- eter for spheromaks should exceed 10~ particles per cubic centimeter seconds. Similarly, the FRX-C and TRX-2 experiments at Los Alamos and at Spectra Technology (formerly Mathematical Sciences Northwest), respectively, will be extended for further confinement scaling studies on FRCs. The next generation experiments, however, will probably require the development of slower formation techniques. The Soviet FRC experiments are expected to continue to investigate formation issues and compressional heating, probably using imploding liners. The Japanese FRC experiments will probably continue to address transla- tion, transport, and energy-balance questions. In addition, plasma engineering tests are needed to verify the feasibility of the CT configuration to meet requirements imposed by reactor considerations. These tests should include slow formation techniques for both spheromaks and FRCs and, where appropriate, auxiliary heating, sustainment, and feedback control. In addition, small experiments on merging particle rings with CTs should have been completed, to see if particle rings offer substantial advantages for CTs for stability, heating, or sustainment. One possible experiment would

204 PLASMAS AND FLUIDS be ion-beam injection into the S-1 spheromak, to test for plasma heating and stabilizing effects against the gross tilt/shift mode. PLASMA HEATING Introduction · To heat a fusion plasma to ignition, about 30-50 MW of power will be needed-either in the form of beams of very energetic neutral particles or, preferably, in the form of radio-frequency power. In order to generate a significant level of power output from the D-T fusion reaction, it is necessary to attain thermonuclear plasma temper- atures (see Figure 4.21. In a typical reactor-grade plasma, it will be necessary to provide 30-50 MW of power for several seconds to heat the plasma to 10-20 keV before alpha-particle heating would maintain a self-sustaining burn cycle. Such power could be provided either in the form of radio-frequency waves (rf heating) or in the form of injected high-energy neutral beams, which would quickly become ionized and hence trapped in the plasma interior (neutral-beam heating). Furthermore, in the steady-state mode of operation of both tokamaks and tandem mirrors, it will be necessary to provide a steady-state form of radio-frequency (rf) power for special purposes. In tokamaks, steady-state rf power of about 50 MW could be used to produce toroidal currents (current drive) by direct momentum transfer from the waves to the particles or by preferential heating of electrons (see earlier section on Tokamak and Stellarator Magnetic Confinement Systems). In tandem mirrors, steady-state high-frequency microwaves at the multimegawatt level will be used to create potential wells or thermal barriers (see section on Magnetic Mirror Systems). In other devices (i.e., bumpy tori), it is necessary to inject high-frequency microwave power at the multimegawatt level to produce energetic electron rings (see section on the Elmo Bumpy Torus). Radio-Frequency Heating · Radio-frequency heating utilizes resonant interactions between ions and electrons and externally launched electromagnetic waves of various frequencies to heat the plasma. The technology for generating and launching radio-frequency waves is especially attractive for fusion-reactor applications. . .. , , .~

FUSION PLASMA CONFINEMENT AND HEATING 205 Plasma Vacuum Chamber Limiter Antenna b Ceramic Window , , Matching Network = i_ ~ A ~ ~ rRANS~ISSlON LINE 1~, , Matching Network 1~ l Rf Source C7amic Window FIGURE 4.16 Schematic illustration of an rf heating system. Typically, the antenna is either a set of current loops or a waveguide array installed through a port in the vacuum chamber. In Figure 4.16, we show a schematic illustration of an experimental arrangement that may be used for transferring rf power into the plasma. This may be achieved by transmitting rf power from high-power sources via a transmission line to the antenna, which then couples this power to a wave (or waves) that propagates inward and dissipates its energy near the plasma center. The basic concepts of radio-frequency heating of plasma utilize the interaction between a wave packet that propagates in the plasma and particles that move with velocities that nearly match the phase velocity of the wave. Particles that move slightly slower than the wave absorb energy from the wave, and particles that move slightly faster than the wave transfer energy to the wave. In a thermal distribution of electrons and ions, there are more particles that move slightly slower than the wave than particles that move slightly faster, and therefore a net energy transfer from the wave to the nearly resonant particles takes place. On a slower time scale, the resonant particles transfer the energy gained from the wave to the rest of the particles by collisions. Since the energy confinement time in a reactor-grade plasma (a few seconds) is longer than the collisional energy equilibration time between electrons and ions, and also longer than the collisional slowing-down time of an energetic particle, heating of the whole particle distribution will result. Approximately half of the wave heating techniques rely on this type of interaction (e.g., lower-hybrid heating). In a magnetized plasma, electrons and ions gyrate in the magnetic

206 PLASMAS AND FLUIDS TABLE 4.7 Classification of Frequencies and Power Sources Used for Radio-Frequency Heating TypicalPower Available Power/ Type of Heating FrequencyCoupler (Antenna) Source Unit Electron cyclotron 30-100 GHz Waveguide or horn Gyrotron 200 kW; cw at 28 or resonance 60 GHz (1990: 1 (ECRH) MW, 120 GHz) Lower hybrid 1-8 GHz Waveguide array Klystron 0.25-0.5 MW (LHH) (grill) (1 MW; cw possible) 0.5-1.0 MW; cw Ion cyclotron resonance (ICRH) Alfv~n wave 1-10 MHz 30-200 MHz Coils (possibly Tubes ridged waveguide) Coils in vacuum Tubes vessel 1 MW; cw field with their respective gyrofrequencies. If a wave is launched with a frequency equal to the gyrofrequency, then the particles (electrons or ions) see a dc electric field in their own gyrating frame of reference, if the wave has an electric-field component that rotates in the same direction as the particles. This effective do electric field can then accelerate the particles and transfer net energy to them if they have a thermal distribution. Heating of all particles results after collisional thermalization. In a hot plasma, a similar type of interaction can take place at harmonics of the gyrofrequency, if the finiteness of the wavelength relative to the gyration radius is taken into account. Heating at the fundamental or harmonics of the electron gyrofrequency is called electron cyclotron resonance heating (ECRH) and that at the fundamental or harmonics of the ion gyrofrequency is called ion cyclotron resonance heating (ICRH). In Table 4.7, we list a range of frequencies and the associated technology to generate the rf power and to launch the waves. The technology will not be discussed here: it is sufficient to say that rf- generating technology is either available or can be developed within the required time scale, in most frequency regimes of interest, to deliver the 50 MW of rf power required in a reactor. MAJOR ADVANCES: THEORY · Some of the important physics issues on which substantial theo- retical progress has been made include (i) propagation and absorp

FUSION PLASMA CONFINEMENTAND HEATING 207 tion of the waves in the plasma, (ii) coupling of the launcher (antenna) to the waves in the edge-plasma region, and (iii) nonlinear effects on wave propagation. While the fundamental theory of wave propagation and absorption was developed in the 1950s and 1960s, many of the applications to wave propagation in the magnetic-field geometries of tokamaks, tan- dem mirrors, and bumpy tori are being developed only now. Further- more, theories of wave heating associated with toroidal geometry, absorption of the magnetosonic wave in a two-ion-species plasma, propagation and scattering of the lower-hybrid wave by density fiuc- tuations in a tokamak, propagation and absorption of electron cyclo- tron waves in a hot dense plasma, and absorption of electron cyclotron waves in a weakly relativistic plasma were developed only recently. Large numerical codes have now been developed that describe the propagation and absorption of electron cyclotron waves, lower-hybrid waves, and magnetosonic waves in a hot plasma in a toroidal or mirror geometry. Another important area of progress over the past decade has been the development of the theory of wave-antenna coupling, which can predict the wave launching efficiency. This requires a solution of the plasma wave equations in an inhomogeneous medium near the plasma surface and their matching to the fields and currents of the sometimes rather complex wave launching (antenna) structures. One more subject that deserves attention is the progress made in understanding nonlinear wave phenomena and their effects on wave propagation and antenna coupling. These phenomena include breaking up of large-amplitude launched waves into other waves (parametric instabilities), pushing of the plasma away from the antenna when the wave radiation pressure becomes comparable with the plasma pressure (ponderomotive effect), and trapping of particles by large-amplitude waves (which may be undesirable in some applications). MAJOR ADVANCES: EXPERIMENT · Experimental results have generally confirmed antenna-coupling theory and theories of wave propagation and absorption. Ion cyclotron heating, using a variety of heating modes, has raised the ion temperature in a tokamak to 3 keV. With lower-hybrid heating, a promising electron-heating regime in tokamaks has been identi- fied. Electron cyclotron heating has been applied successfully to tokamaks and, in mirrors and bumpy tori, has produced hot

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FUSION PLASMA CONFINEMENT AND HEATING 209 electron populations with energies of several hundred kiloelectron volts. During the past decade, significant progress has been made in experimental research on rf wave launching, wave propagation, and plasma heating. Wave-propagation studies on basic research devices, mirror devices, and tokamaks verified the existence, and the dispersion relationship, of most of the waves listed in Table 4.7. Substantial advances in the plasma parameters achieved in rf heating experiments have also been evident during the past decade. This has been a consequence of a better understanding of the physics of rf heating, improvements in the technology that allowed injection of rf power at the megawatt level, and experimental devices with better particle and energy confinement times. Thus, while in the mid-1970s rf powers injected in any given device were limited to the 0.1-0.2 MW level, and consequently the temperature rise was limited to less than 200 eV, in recent experiments temperature rises in excess of a kiloelectron volt have been produced on injection of about a megawatt of power, at all frequencies of interest. In Table 4.8, we display some of these heating results at the ion cyclotron frequency and its harmon- ics (ICRH), at or near the lower-hybrid frequency (LHH), and at the electron cyclotron frequency (ECRH). In achieving these results, an understanding of the physics of wave propagation, antenna-wave ~ _ O coupling, and wave absorption has been of crucial importance. It allowed optimization of the antenna design, it helped to determine the optimal location of the antenna, and it identified the best plasma operating regimes for efficient heating. In the course of these experimental studies, we have discovered the following: (i) In ECRH (which has been made possible by the development of new high-power sources called gyrotrons), launching from the high- field side of a tokamak plasma (i.e., from inside the torus) is preferred when the temperature is not too high (there is a cut-off layer between the central resonance layer and the edge of the plasma on the low-field side). In large machines, and at high temperatures, launching from the low-field side is acceptable since single-pass absorption becomes efficient. (ii) For ICRH in tokamaks, magnetosonic wave heating is preferred, and, for heating at the fundamental gyrofrequency, a two-ion species plasma is normally essential for good absorption (otherwise the ions electrostatically shield the ion cyclotron resonance layer). It is prefer- able to set the frequency to coincide with the gyrofrequency of the

2 1 0 P. rA SMA S. A ND FF UlD S lighter minority species at the center of the device, at least when a low-field-side launch is employed. In this case, an energetic minority component is produced that will transfer its energy to the bulk of the plasma particles by collisions. Launching the wave from the high-field side results in absorption by collective effects at a two-ion hybrid layer, resulting mainly in electron heating. Finally, efficient heating at the second harmonic of the bulk ion gyrofrequency has also been achieved, producing ion temperatures as high as 3 keV. (iii) In lower-hybrid heating, wave penetration to the ion-plasma- wave resonance region proved to be problematical, resulting in only sporadic and irreproducible ion heating results. However, at frequen- cies of twice the ion-plasma-wave resonant frequency (or more), good electron absorption and subsequent plasma heating by these waves has been observed. With respect to experimental techniques, we should also briefly mention the recent results on collective scattering using infrared lasers. The collective scattering of such laser beams from the density fluctu- ations associated with lower-hybrid waves allows us to track propaga- tion of these waves inside the hot tokamak plasma where probes could not be inserted. Finally, while most of the rf heating experimental results to date were obtained in tokamaks, important work on ECRH has also been carried out in mirror devices and on bumpy tori. Here, creation of hot electrons with mean energies of several hundred kiloelectron volts have been observed. At present, important ECRH and ICRH experi- ments are being carried out on the TMX-U tandem mirror at the Lawrence Livermore National Laboratory: ECRH is being used to aid in the formation of the thermal barrier, and ICRH is being tested for heating (and start-up) of the central-cell plasma. PROSPECTS FOR FUTURE ADVANCES · The If heating power on existing tokamaks is rapidly being increased to the multimegawatt level, and new-generation larger tokamaks will have tens of megawatts of rf power. Radio- frequency power will also be applied increasingly to non-tokamak devices, such as mirrors and stellarators, both for bulk heating and other specialized applications. The theory of rf heating will be advanced by the development of large computer codes currently in the inception phase incorporating detailed models of wave propagation and absorption.

FUSION PLASMA CONFINEMENTAND HEATING 211 In the coming decade, we expect significant advances both in the theoretical understanding of rf heating and in its experimental achieve- ments. While the basic theory of wave propagation and absorption is now well understood, applications to the complex magnetic-field geometries of fusion devices are only in their infancy. At present the best theoretical models employ the geometric-optics approximation and use ray tracing in numerical computations. While this is satisfac- tory in some cases, the approximations are often not strictly valid, especially near the antenna. Furthermore, in the low-frequency regime (i.e., ICRH and Alfven-wave frequencies) the wavelengths are often comparable with the density-gradient scale length, and hence an exact solution of the wave equation must be sought. At higher frequencies (ECRH), the wavelengths are short and hence ray-tracing theory is justifiable. However, as the electron temperature increases to reactorlike values, a relativistic theory is necessary. In tandem-mirror devices, further theoretical work is needed to calculate the distribution function of hot electrons in the thermal barrier. In particular, a relativistic particle kinetic code will be neces- sary to model the ultA-a-hot electron population in future devices, such as MFTF-B. These codes will have to be interconnected with realistic transport and ray-tracing codes. The next decade should also produce new and exciting results in rf heating experiments in all frequency regimes of interest. There are now several rf experiments at the 1-5 MW level throughout the world on existing machines, some of which are listed in Table 4.8. These experiments are aimed at clarifying the physics issues of wave propa- gation and absorption, and (in the case of tokamaks) at investigating energy and particle confinement times, and impurity injection, under conditions when the rf power significantly exceeds the intrinsic heating power because of the plasma current. Later in this decade, and in the early l990s, there will be a number of larger-scale rf heating experiments, now in the planning stage, some of which are listed in Table 4.9. We also expect that further experi- ments will be proposed for heating of tandem mirrors (i.e., we expect further extension of ICRH and ECRH techniques for start-up, central- cell heating, and thermal-barrier formation). We can also expect further improvement in rf technology, and this would open up new possibilities with regard to plasma heating. Under consideration is development of (i) megawatt-level klystrons in the lower-hybrid range of frequencies (2-4 GHz), (ii) megawatt-level gyrotrons at frequencies (120 GHz) that would allow ECRH at reactorlike plasma densities, (iii) ultrahigh-frequency gyrotrons

212 PLASMAS AND FLUIDS TABLE 4.9 Major Planned Radio-Frequency Heating Experiments Heating Power Device Location Type Frequency (MOO) Status DIII-D GA ICRH 60 MHz 20 Proposed TFTR PPPL ICRH 60 MHz 30 Proposed MFTF-B LLNL ICRH ? ? Proposed DIII-D GA ECRH 60 GHz 2 Approved MFTF-B LLNL ECRH 28-56 GHz 1.6 Approved JET EEC ICRH 25-50 MHz 27 Approved JT-60 Japan ICRH 45-90 MHz 3 Approved Tore-Supra France ICRH 70 MHz 6 Approved JT-60 Japan LHH 2.0 GHz 10 Approved FT-U Italy LHH 3.7 GHz 8 Approved Tore-Supra France LHH 3.7 GHz 8 Approved T-15 USSR ECRH 86 GHz 5 Approved (140-200 GHz) suitable for high-field devices, and (iv) development of multimegawatt tubes (60 MHz) that would greatly simplify high-power ICRH technology. Radio-Frequency Current Drive · The use of radio-frequency waves to drive currents in tokamaks, typically by imparting momentum to electrons, is of enormous potential benefit, since it permits the tokamak to operate steady- state. Current drive refers to a process of interest mainly in tokamaks- for maintaining a current in a plasma by means other than transformer- induced electric fields. One of the most important areas of progress in the entire field of tokamak research has been the theoretical prediction and experimental demonstration of the feasibility of driving steady- state currents by radio-frequency waves. This would allow the possi- bility of replacing the transformer-driven pulsed toroidal current by an rf-driven steady-state toroidal current. (Current drive by neutral beams is also possible but requires very energetic beams and has somewhat lower efficiency.) In its simplest form, current drive involves a direct momentum transfer from waves to electrons. However, current generation by

FUSION PLASMA CONFINEMENT AND HEATING 213 preferential heating of electrons moving in one toroidal direction may be just as efficient as that by direct momentum transfer, and therefore essentially all waves in Table 4.8, not just those that have large toroidal wave momentum, may be utilized for current generation. MAJOR ADVANCES: THEORY · Recent theoretical calculations of rf current-drive efficiency have shown that the current-drive power required for a steady-state tokamak reactor should be acceptable. Various quasi-steady-state schemes offer the prospect of even better efficiency. Although there have been many theoretical ideas regarding current drive ever since the tokamak concept was proven to be viable, it is only recently that current-drive theories have been put on a more rigorous basis. In particular, it was shown in 1978 that rf-current drive in the lower-hybrid frequency regime may be sufficiently efficient to be of practical interest in a fusion reactor. Since then, current-drive effi- ciencies (driven current divided by rf power) have also been evaluated for most of the other waves that propagate in a plasma. The efficiency varies inversely with plasma density. Although this efficiency varies from wave to wave, it is generally found that, in a reactor, 10 percent or more of the fusion power produced would be needed to generate the rf power required to maintain the toroidal current. Specifically, at least 50 MW of rf power would be required to maintain about 5 MA of steady-state toroidal current. An ingenious quasi-steady-state variation of this technique- resulting in higher overall efficiency may also be possible by ramping up the current periodically by rf, hence "recharging" the transformer; the density may be reduced during this time. Subsequently, in the high-density phase, the transformer may be used to maintain the current for several hours to ensure a quasi-steady burn cycle. MAJOR ADVANCES: EXPERIMENT · Recent experiments using lower-hybrid waves have confirmed the theory of rf-current drive, and have succeeded in sustaining tokamak currents for pulse durations of several seconds. Both current-drive efficiency and lower-hybrid-wave penetration are found to decrease at high plasma density, as predicted theoreti- cally.

214 PLASMAS AND FLUIDS 10 IMA I 105 10 Ip(A) 10 lo2 10 I T I ~ Lower Hybrid Current Drive it: 1978 1979 1980 1981 1982 1983 Act-1 PLT ·/ AlcatorC / Petula / / / / / O / Jipp-2 / o / Versator o JFT-2 /oGA W-T-2 / o/ FIGURE 4.17 Progress in lower hybrid current drive in tokamaks. In PLT at Princeton and Alcator C at MIT, the plasma current has been sustained for a second or longer without any applied voltage. The experimental verification of theoretical predictions of lower- hybrid current drive has been one of the most exciting and productive developments in recent tokamak research. While 5 years ago the maximum rf-driven currents amounted to only a few milliamperes, today rf currents up to 400 kA have been generated in tokamaks (see Figure 4.17~. The first current-drive demonstrations at the 20-kA level were in the small Versator tokamak at MIT. The most advanced among

FUSION PLASMA CONFINEMENT AND HEATING 215 today's experiments are the 800-MHz, 0.5-MW PLT experiment and the 4.6-GHz, 1-MOO Alcator C experiment. Some of the exciting results include maintenance of the toroidal current by the rf power for time durations up to 3.5 s (PLT) and driving currents at densities up to 10~4 particles per cubic centimeter (Alcator C). In several experiments (i.e., Alcator C and PLT), the high-energy x-ray spectra were measured before and after application of the rf power. It was shown that a high-energy electron population formed on application of the rf power. In agreement with theoretical predictions, it is this asymmetric suprathermal electron population that is respon- sible for the toroidal current generation. One of the questions that current-drive experiments must answer is the current-drive efficiency, namely, current generated divided by power absorbed. The parameter nIRlP, where n is the average density, I is the total toroidal current, R is the major radius, and P is the total power, is plotted in Figure 4.18 versus the plasma electron temperature for a number of devices. If this could be extrapolated to the reactor regime, we would need at most 50 MW of circulating rf power to drive 5 MA of toroidal current. However, theory predicts that, under reactorlike conditions, the present lower-hybrid waves will be less 12 3 10 A ye 8 6 o - 4 2 ALCATOR-C (JOT) · ~ PLT (60°) _` A . ~ _ ALCATOR-C (8T) PLT (90°) · JIPP-2 WEGA VFRRATOR -A OTe(Beforerf) Te(During rf) . - ~A~ Estimote ~0 ~JFT-2 _ 1 1 1 1 1 1 1 1 1 1 1 ~ 0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 Te (key) FIGURE 4.18 Measured lower-hybrid current-drive efficiency. Theory predicts that the efficiency (current I divided by rf power P) should scale inversely with plasma density n and major radius R and should improve with increasing energy of the current-carrying electrons. To show that this relationship is verified, we plot the quantity nIRlP versus electron temperature Te from a number of different experiments.

216 PLASMAS AND FLUIDS efficient in penetrating the plasma, and other waves (such as the Alfven wave or the magnetosonic wave) may have to be used for current drive. The present lower-hybrid waves should, however, be satisfactory for the quasi-steady-state mode of current-drive operation. PROSPECTS FOR FUTURE ADVANCES · Lower-hybrid current drive will be tested at reactorlike plasma parameters in large tokamaks. Radio-frequency current drive using other waves with better penetration characteristics will be explored. The next decade should produce important advances in rf current- drive experiments, in regard to the magnitude of the driven current, the duration of the current pulse, and the number of different rf techniques that are employed. There are several lower-hybrid current-drive ex- periments that are ongoing now, are being increased in power, or are being initiated in the near future on existing tokamak devices (see Table 4.81. These experiments will extend the measurements of current drive efficiency further toward the reactor regime and will determine the best compromise between transformer and rf current drive for providing efficient quasi-steady-state operation. By the end of the decade, there will be some much-larger-scale current-drive experi- ments in operation, as indicated in Table 4.9. (Note that lower-hybrid experiments can be employed both for heating and current drive.) There are also plans on present experimental devices to explore the use of other waves for current drive, in particular the magnetosonic wave and the electron cyclotron waves the latter in combination with lower-hybrid waves to impart momentum to the hot electrons. Neutral-Beam Heating · Neutral-beam heating utilizes neutralized beams of accelerated hydrogenic ions, which are injected into the plasma. Neutral-beam heating has been particularly successful in producing reactorlike ion temperatures in tokamaks and mirrors. In the past, high-power neutral-beam heating has been the leading technique for delivering large quantities of heating power to both tokamak and mirror plasmas. The physics of neutral-beam heating is relatively simple as compared with radio-frequency heating. Beams of neutral atoms are created by accelerating ions (usually hydrogen or deuterium) extracted from a discharge plasma source by means of a

FUSION PLASMA CONFINEMENT AND HEATING 217 carefully designed grid system. The ions are accelerated to energies of 20-120 keV and focused into a directed beam that then passes through a neutralizer chamber filled with gas at low pressure. Here, a large fraction of the ions recapture electrons from the gas atoms, and a high-energy (20-120 keV) beam of neutral atoms is formed. These neutral beams are then injected through several large pumped ports of a fusion device. Subsequently, the neutral beam penetrates into the plasma interior unhindered by the magnetic field, until the neutral atoms are reionized by the plasma already present. Once reionized, the high-energy ions are captured by the magnetic bottle, and collisional thermalization on the bulk ions and electrons follows. Because of the high energies of the beam ions, megawatts of power can be delivered for beam currents of a few tens of amperes. Such sources have been developed by the Oak Ridge National Laboratory and the Lawrence Berkeley National Laboratory. MAJOR ADVANCES · Neutral-beam heating has been the key to the most notable achievements of the past decade in tokamaks and mirrors- high ion temperatures, high plasma beta, and tandem-mirror confine ment. Table 4.10 summarizes the beam energies, powers, and pulse lengths that have been achieved and indicates the most significant results that neutral-beam heating has produced for the fusion program. The most spectacular results so far have been achieved on PLT and PDX, where beam heating raised the central ion temperature from 1 keV to about 7 keV, and on Doublet III, where beam heating resulted in an average beta of a record 4.6 percent. Neutral-beam heating has also been used in TMX to demonstrate the principles of tandem-mirror confinement. In most beam-heating experiments in tokamaks so far, the deposition of the injected beam, the beam-ion slowing-down process, and the confinement of the fast ions were found to be essentially classical, i.e., determined by simple physical processes of interparticle collisions. Accordingly, the physics of the neutral-beam injection process itself can be said to be well understood. However, it has been found that, as the injected beam power exceeds a few megawatts (a few times larger than the heating power due to the plasma current), the energy confinement time deteriorates by a factor of 2-5. At present, it is not known whether these results are a consequence of plasma beta or tokamak geometry, in which case rf heating may be equally susceptible

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FUSION PLASMA CONFINEMENT AND HEATING 219 to such deterioration when comparable power levels are achieved, or whether it is caused specifically by the neutral-beam heating technique. PROSPECTS FOR FUTURE ADVANCES . Next-generation neutral-beam systems for tokamak and mirror applications will have higher beam energy and greatly increased pulse length. However, neutral-beam systems for tokamak reactor application would need even higher beam energy, necessitating the successful eventual development of negative-ion beams. In Figure 4.19, we show neutral-beam powers that have been delivered into past and present machines and also the projected beam powers during the next few years. We see that rather large powers are expected to be delivered in the upcoming DIII-D, TFTR, and MFTF-B loot I_ 3 3 10 Is Al m by 1 _ C] U] Z _ 1 _, 0.1 _ 1975 A: O ,~ 1 AL 1 ._ ~ ~ IL 1 1 I ~ r 1 1~ 1 o 1 ~ 1 ~ I_-' 1 ~ =1 1" =1 1 - 1 ~- =1 'A . ~t X' ~' _ ~ ! ! 1 1 ~1 1 1 1 1 , , 1 1 1 1 1 1 1 1 1 ~ 1 1 1 1 1 1 l l __ 1980 1985 1989 YEAR FIGURE 4.19 Progress in neutral-beam heating. We show the neutral-beam power injected into various tokamak and mirror devices; actual achievements are shown with solid lines; systems under construction are shown with dashed lines. (In the case of JET, we show the total power, which will be partly neutral beam and partly rf).

220 PLASMAS AND FLUIDS devices (i.e., up to 30 MW of beam power will be injected into TFTR, and up to 60 MW will be injected into MFTF-B). The beam energies in these next-generation neutral-beam systems will be in the range of 80-160 keV. The pulse lengths will also be substantially greater than in present-day systems (specifically, 1.5 s on TFTR, 10 s on JET and JT-60, and 30 s on MFTF-B). There is widespread confidence that these systems will be successful in heating plasmas to reactorlike energy densities. While neutral-beam heating technology has achieved outstanding progress in the past, and has succeeded in providing the large powers needed to heat the present generation of machines, its future beyond 1990 is less certain. There are two basic problems that have to be overcome: (i) The pulse length of present-day injectors has until recently been limited to about a second. Running beam sources for times longer than that causes serious deterioration of the filaments inside the beam sources. This may be remedied either by using indirectly heated cathodes or by using rf plasma sources for the beam ions. For the MFTF-B neutral-beam system, it is encouraging to note that, using an indirectly heated cathode, both Oak Ridge National Laboratory and Lawrence Berkeley Laboratory have developed 80-keV, 80-A beams that have been run for a 30-s pulse duration. Nonetheless, in the next few years significant technological advances will have to be achieved to provide the beams necessary for achieving the full potential of devices such as MFTF-B. (ii) In the present generation of devices, beam energies of 100-150 keV are satisfactory, but in reactor-size devices beam energies of about 500-keV energies may be necessary. The neutralization cross section of positive-ion beams falls rapidly above energies of about 75 keV for protons and 150 keV for deuterons; hence, to provide efficient neutral beams with energies of about 500 keV, negative-ion beams will have to be developed whose ionization cross section is more favorable. Nevertheless, neutral-beam heating has certain advantages. The capability for fueling the plasma center may be unique to neutral beams, and is particularly important for mirror reactors. Table 4.11 presents projections of requirements for neutral-beam systems in fusion reactors. Because of the very high beam energies needed in reactor-size tokamaks, neutral-beam heating is currently viewed as a backup to radio-frequency heating for tokamak applica- tions. For mirror reactor applications, no alternative to neutral beams has been established for creating the necessary confining potentials.

FUSION PLASMA CONFINEMENT AND HEATING 221 TABLE 4.11 Projected Requirements for Neutral Beams in Reactors Beam Beam Pulse Reactor Energy Power Length Concept Application (keV) (MOO) (s) Pulsed tokamak Heating to ignition 400 30-50 10-50 Pulsed tokamak Pulsed current 400 '30 100 drive Steady-state Continuous 1000- 50 Continuous tokamak current drive Tandem mirrors Central cell 20050b Continuous heating and fueling Tandem mirrors End plug potential 50010 Continuous Stellarator Heating to ignition 40050 10-50 a Tandem-mirror requirements assume 50 MW of ECH power for the thermal barrier. b Central-cell power may be reduced to 10 MW during start-up in the case of an ignited central cell in a thermal-barrier tandem mirror. The neutral-beam systems employed in present and next-generation devices are all based on neutralizing hydrogen-isotope positive-ion beams. The high beam energies needed for a reactor dictate develop- ment of a new approach to beam-ion sources, namely, by using negative ions. Several promising concepts of negative-ion sources have been recently operated at about 1 A using hydrogen. This must be raised to the level of about 10 A. Acceleration of the ions to 400 keV or more is likely to require technologies other than the high-gradient, electrostatic accelerators now used in the positive-ion systems. A promising candidate is the strong-focusing, low-gradient dc accelera- tor. For best power efficiency, development of a neutralizer based on the photodetachment of the negative ion's loosely bound electron by laser beams is at least desirable, and possibly necessary. INERTIAL-CONFINEMENT FUSION SYSTEMS Introduction · The inertial-confinement approach to fusion is based on compress- ing thermonuclear fuel to extremely high density and heating it to temperatures high enough that the fuel ignites and burns before the compressed mass has time to disassemble. Inertial-confinement fusion complements the magnetic-confinement schemes and represents an independent approach based on quite

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FUSION PLASMA CONFINEMENT AND HEATING 223 deferent physical principles. Instead of magnetically confining hot plasmas with densities of 10~4 to 10~5 particles per cubic centimeter for times of up to a second, fuel is imploded to a very high density, typically 1025 to 1026 particles per cubic centimeter, and burned in tens of picoseconds (1 picosecond equals one trillionth of a second, i.e., 10-~2 s) while inertially confined. For ultimate commercial applica- tions, inertial-confinement fusion has the very desirable feature that the driver facility and reactor chamber can be well separated from one another. This separation greatly reduces the technological problems of practical reactor-chamber design. Inertial-confinement research also has many other applications re- lated to the physics of high-energy density. The irradiation of plasmas by intense laser light allows the study of many nonlinear processes with applications throughout plasma physics. The generation of pressures of tens to hundreds of megabars (1 megabar equals a million atmospheres) allows the investigation of matter under very high pressures. The generation of highly ionized matter and of intense short pulses of x rays allows the study of atomic physics of importance in the development of x-ray lasers. Inertial fusion works by focusing an intense beam of laser light or particles onto the outer layers of a spherical shell encapsulating fusion fuel, as illustrated in Figure 4.20. The fuel is then compressed by pressures of tens to hundreds of millions of atmospheres generated by the rocketlike blowoff of the surface material. At the end of the driver pulse, when the fuel reaches about 1000 times liquid density, a portion in the center ignites at a temperature of about a hundred million degrees Celsius. The thermonuclear burn spreads rapidly through the remaining compressed fuel, yielding many times the driver energy. The high fuel density increases the thermonuclear reaction rate to allow the fuel to burn while it remains together by its own inertia. Energy is released in the form of energetic neutrons, x rays, and helium nuclei, which are captured and converted to thermal energy for various applications. For power generation, pellet gains of a hundred or more are needed to compensate for reactor and driver inefficiencies, whereas other applications, such as hybrid reactors and fissile-fuel production, are feasible with lower pellet gains. In the past decade, a vigorous effort has been undertaken to investigate the physical principles of the inertial-confinement ap- proach. The physical constraints that need to be satisfied for inertial fusion to succeed can be divided into five critical elements: · Coupling Efficiency. The fraction of driver energy utilized for fuel

224 PLASMAS AND FLUIDS compression and ignition needs to be high; efficiencies of about 5 percent are needed for high-gain applications. · Cold Compressed Fuel. The fuel must remain nearly isentropic (cold) during pellet implosion, in order to achieve high final fuel densities at low driver energy cost; an energy increase of only a few times the minimum (Fermi degenerate) level is permissible. · Ablation Pressure. Sufficient ablation pressure needs to be devel- oped at the pellet surface to achieve high-density compression and to avoid hydrodynamic instability; pressures from tens to hundreds of megabars are needed. · Implosion Symmetry. The pellet must be imploded uniformly to minimize the volume of hot fuel needed to ignite the pellet and to avoid hydrodynamic destruction of the pellet; implosion uniformities of close to 1 percent may be needed. · Ignition Concept. A practical means by which a small volume within the pellet's fuel can be ignited, and the remaining fuel consumed by propagating burn, needs to be established; the central hot spot must have temperatures above about 4 keV and have a density-radius product of about 0.3 gram per square centimeter. The remaining fuel should have a density-radius product of about 3 grams per square centimeter for efficient burn. Inertial-confinement fusion research in the United States is con- ducted mainly at the Lawrence Livermore National Laboratory, Livermore, California, and at the Los Alamo s National Laboratory, Los Alamos, New Mexico. Smaller programs are under way at the Naval Research Laboratory, Washington, D.C.; at KMS Fusion Inc., Ann Arbor, Michigan; at the University of Rochester, Rochester, New York; and at Sandia National Laboratories, Albuquerque, New Mex- ico. In addition, a number of universities contribute to inertial- confinement research. Major Advances DRIVERS FOR INERTIAL-CONFINEMENT FUSION · An impressive array of experimental facilities for inertial- confinement research has been developed over the past decade. Neodymium-glass lasers have been constructed with output ener- gies of up to 30 kJ and powers up to 25 terawatts t1 terawatt (TOO) equals 10~2 wattsl; CO2-lasers have been constructed with 30 to 40 kJ of output energy and powers up to 30 to 40 TW. Light-ion

FUSION PLASMA CONFINEMENT AND HEATING 225 beams have been generated with up to hundreds of kilojoules of output energies at several.. terawatts of power. Table 4.12 lists the major driver facilities for inertial-confinement research, both existing and under construction, worldwide. In addi- tion, several heavy-ion drivers have also been proposed for construc- tion at the Lawrence Berkeley Laboratory and in West Germany. Ultimately, for power-generation purposes, the driver must be highly efficient (about 10 percent), reliable, and capable of being repetitively pulsed. TABLE 4.12 Major Inertial-Confinement Fusion Facilities . . Driver Energy Powera Facility Location Type (kJ) (TOO) NOVA LLNL Nd-glass (100) (125) NOVETTE LLNL Nd-glass 30 25 PHAROS-III NRL Nd-glass (2) (4) PHAROS-II NRL Nd-glass 1 2 OMEGA Rochester Nd-glass 4 12 GDL Rochester Nd-glass 0.1 0.5 CHROMA- 1 KMSF Nd-glass 1 2 ANTARES LANL CO2 (30-40) (30-40) HELIOS LANL COP 5-10 10-20 LAM LANL KrF (10-20) RAPIER B LLNL KrF 0.8 PBFA-II Sandia Light ion (4000) 100 PBFA-I Sandia Light ion 1000 20 GAMBLE-II NRL Light ion 100 2 PHEBUS France Nd-glass (30) (25) OCTAL France Nd-glass 4 4 GEKKO XII Japan Nd-glass (20) (40) GEKKO IV Japan Nd-glass 2 4 HELEN UK Nd-glass 1 3 VULCAN UK Nd-glass 1 2 DEL'FIN USSR Nd-glass 5 2-7 UMI-35 USSR Nd-glass 8-10 4-6 LEKKO III Japan COP 10 10 LEKKO II Japan COP 0.5 0.5 REIDEN IV Japan Light ion 50 1 KALIF FRG Light ion 75 2 a For laser, energy quoted reflects performance at long pulse. Power quoted reflects performance at short pulse. For light ions, energy and power quoted are those delivered to the ion diode. Account is not taken of ion production and transport efficiency, which reduce these numbers by up to a factor of 4. Parameters in parentheses denote facilities under construction.

226 PLASMAS AND FL UlDS The most useful driver for inertial-fusion research to date has been the laser. Powerful laser-light pulses can be focused down to the small dimensions required to generate high pressures on a pellet surface, their pulse length and shape can be varied, and their wavelength controlled. In short, they make excellent research tools to investigate inertial-confinement physics and to test pellet concepts. The dominant lasers for inertial-fusion research have been the neodymium-glass laser, which produces light pulses in the near-infrared portion of the spectrum t1.05 micrometers; 1 micrometer (~m) equals 10-6 meterl, and the CO2-gas laser, which operates in the far-infrared (10.6 ~m). Neodymium-glass lasers have achieved powers on target up to 25 TW, and CO2 lasers have achieved powers in the 30-40 TW range. The neodymium-glass laser has proven to be a particularly flexible tool, since its output can be efficiently frequency converted. If short- wavelength light proves to be preferable for inertial fusion, then a krypton-fluoride laser, an excimer system (0.25 ~m) with good effi- ciency, is an attractive candidate. In addition to lasers, intense particle beams can be used as inertial- confinement pellet drivers. There are currently two main approaches to particle-beam inertial fusion: light ions and heavy ions. Light ions, such as protons, lithium, or carbon ions, are generated in high-current pulsed power accelerators, which provide megaamperes of ion current at a few megavolts of energy. Light-ion-beam generators are highly efficient and relatively inexpensive but cannot as yet attain the power densities required for fusion. The heavy-ion approach would use very heavy ions, such as lead ions accelerated up to gigaelectron-volt energies (a gigaelectron volt equals a billion or 109 electron volts) in conventional high-energy accelerators. Accelerators needed to supply such beams for inertial fusion would be expensive but would have many properties desirable for inertial-fusion reactors; they could provide highly efficient, repeatedly pulsable, and focusable beams. Although particle beams may one day be the preferred driver for inertial fusion, their technology has not yet advanced to the stage where they can be used for extensive inertial-fusion research involving targets. Therefore, we will concentrate here on describing inertial- fusion research using a laser driver. EASER-TARGET PHYSICS · Using a neodymium-glass laser driver, targets have been imploded to about 100 times liquid density within a factor of 10 of reactor

FUSION PLASMA CONFINEMENT AND HEATING 227 requirements. The development of increasingly sophisticated plasma instrumentation and modeling codes has led to improved agreement between the experiments and the theory of laser-target interaction. With these experimental facilities, a great deal of progress in inertial-confinement research has been made. The coupling of laser light with targets has been characterized over a wide range of laser intensity and wavelength. Numerous coupling processes, ranging from collisional absorption to collective plasma processes, have been con- firmed and quantified. A regime of excellent coupling for laser light with wavelengths of less than 1 Am has been demonstrated. D-T fuel in glass microballoons has been heated to thermonuclear temperatures. Targets and shells have been ablatively accelerated to above 107 cm/s with velocity nonuniformities below 5 percent. D-T fuel has been imploded to a final fuel density of about a hundred times its liquid density, with fuel temperatures of about 400 eV. These compres- sions are within a factor of about 10 of the compression needed for a reactor target. Instrumentation to measure the properties of the beam-target inter- action has evolved at a remarkable pace in the last decade. Typically, quite extreme ranges of plasma conditions are encountered in a single inertial-confinement experiment: the density ranges downward from 1000 times solid density to near vacuum; the temperature ranges in some cases from 1 eV to beyond 1Os eV; the electromagnetic radiation emitted extends from the infrared region into the gamma-ray region; and various ion and electron populations may be present with energies extending from electron volts to millions of electron volts. Moreover, measurements often need to be made with micrometer spatial resolu- tion and picosecond temporal resolution. Diagnostics now exist that can measure many of these properties; they have, in large measure, been instrumental in the many significant advances that have been made recently in understanding the laser-target interaction. Equally important, theory and large simulation codes have advanced toward the goal of providing a predictive capability for new irradiation conditions. These theoretical tools have guided the advances made in the experiments and have, in turn, been improved through constant comparison with these experiments. New target design concepts have been developed. New designs based on the hohlraum approach rely on x rays from driver-produced plasmas to implode the target.

228 PLASMAS AND FLUIDS Current Frontiers of Research LASER-PLASMA COUPLING · The absorption of laser light occurs in a corona plasma surround- ing the target. Experiments have generally confirmed both the collisional absorption mechanism and the theoretically predicted collective plasma effects on laser-light coupling. The experiments have also demonstrated a large increase in collisional absorption concomitant with a large decrease in deleterious collective effects as the wavelength of the laser light is decreased. In laser fusion, a target is irradiated with an intense pulse of laser light. For high-gain targets, the required intensity will be in the range of 10~4 to 3 x 10~5 watts per square centimeter (W/cm2), depending on the details of the target design, and the pulse length will be of order 10 nanoseconds [1 nanosecond (ns) equals one billionth of a second, i.e., 10-9 s]. Very early in the pulse (at intensities about 10~° W/cm2), the surface of the target breaks down, forming a plasma. As is well known, light will only propagate in a plasma up to a maximum density, the critical density, given by the condition that the electron plasma frequency equals the laser light frequency. The critical densities are about 102~ and 10~9 particles per cubic centimeter, for the neodymium- glass laser and CO2 laser, respectively. Some experiments have also been carried out using crystals to double, triple, and quadruple the frequency of a neodymium-glass laser, and the critical densities are then correspondingly higher. The critical densities are much less than solid density, and so the laser light absorption takes place in a relatively low-density "corona" plasma surrounding the irradiated target. The coupling of the laser light to this plasma is clearly one of the fundamental issues in laser fusion. Obviously, the absorption efficiency of the laser light needs to be high to maximize the efficiency of the driver. However, the heated electron velocity distributions are crucial also, because- very-high-energy electrons have a relatively long range and can penetrate into, and preheat, the fuel within the interior of the target. Even modest preheat will prevent the D-T fuel from reaching the density compression required for high-gain targets. Inverse bremsstrahlung, or collisional absorption, is the preferred laser-wave absorption mechanism. Physically, inverse bremsstrahlung is due to collisions between the electrons, which are being vibrated by the electric field in the light wave, and the background plasma ions.

FUSION PLASMA CONFINEMENT AND HEATING 229 The laser absorption rate is proportional to plasma density and inversely dependent on electron temperature. Collisional absorption thus becomes more efficient as the wavelength of the laser light is decreased, since the light can propagate into denser, relatively cooler plasma. Furthermore, since the collision frequency between electrons and ions has a strong inverse dependence on the electron velocity, slower particles are preferentially heated. Hence, favorable electron distributions are generated. There are many other mechanisms for laser-plasma coupling. These mechanisms arise from the excitation of plasma waves by the intense laser light. The waves, in turn, can heat the plasma particles or scatter the incident light. Heating of the plasma by excited plasma waves is often undesirable, since suprathermal electrons can be generated. The fast electrons originate because electron plasma waves propagate with high phase velocities, and electrons in near resonance with these waves will be preferentially energized. Suprathermal electrons can provide preheat, an effect to be avoided. The simplest absorption process involving electron plasma wave heating is resonance absorption. Whenever the laser-light electric field oscillates electrons across a spatial variation in density, a high- frequency charge-density fluctuation is driven. This density fluctuation resonantly excites an electron plasma wave at the critical density. In addition, electron plasma waves and ion acoustic waves can be excited by a variety of plasma-wave instabilities driven by the intense laser light. Most of these instabilities can be simply characterized as the resonant decay of the incident light wave into two other waves. Given that the plasma supports electron plasma waves, ion acoustic waves, and light waves, the possibilities are straightforward to list. There is parametric decay, namely decay into an electron plasma wave and an ion acoustic wave, which occurs near the critical density. The two-plasmon instability, namely decay into two electron plasma waves, occurs near one fourth of the critical density. The Raman instability, namely decay into a scattered light wave and an electron plasma wave, is a process that operates for densities even below one fourth of the critical density. These instabilities all generate an electron plasma wave and are a fuel-preheat threat. In addition, the Brillouin instability, namely decay into a scattered light wave and an ion acoustic wave, occurs throughout the underdense plasma and can scatter the light before absorption. Finally, there are self-focusing instabilities. A small hot-spot enhancement of the intensity of the incident light wave creates a density depression, either by pushing the plasma aside via the enhanced field pressure or by enhanced heating

230 PLASMAS AND FLUIDS and subsequent plasma expansion. Since a light wave locally refracts into lower-density plasma, the density depression leads to a further enhancement of the hot spot, giving rise to intense filaments. In addition to instabilities driven directly by the laser light, many other important processes can occur in laser-irradiated targets. For example, ion turbulence and self-generated magnetic fields can be created in the interaction process. Magnetic fields can be as high as several megagauss, sufficiently large to impede the heat flow or to introduce new kinds of magnetically driven fluctuations. Figure 4.21 presents a simplified summary of the many different processes operative in the underdense plasma. Virtually every cou- pling mechanism indicated in Figure 4.21 has now been observed in experiments. Important features that have been observed include generation of energetic electrons associated both with resonance absorption and with the various instabilities producing electron plasma waves and scattered light associated with the Brillouin and Raman instabilities. Most important, the experiments have demonstrated a strong increase in collisional absorption concomitant with a strong decrease in deleterious collective effects (hot-electron generation and light scattering) as the wavelength of the laser light is decreased. Figure 4.22 shows the absorption efficiency as a function of laser intensity for a variety of wavelengths ranging from 1.05 to 0.26 ,um. The scaling with wavelength has had a strong impact on laser fusion research. Most large laser facilities now planned will operate at wavelengths of half a micrometer or less. LASER-PLASMA INTERACTIONS '\ LASER LIGHT BRILLOUIN SCATTER FILAMENTATION COLLISIONAL ABSORPTION HEAT HIGH-DENSITY TRANS-ACCELERATED SHELL PORT > Tn.-ABLATION SURFACE / ~ RAYLEIGH-TAYLOR INSTABILITY { |SELF-GENERATED B-FIELDS 1 1 I ION TURBULENCE / n CRITI RESONANCE ABSORPTION if C CAL SURFACE ~ PARAMETRIC INSTABILITIES ) RADIANT 4 QUARTER-CRITICAL SURFACE ITWO-PLASMON DECAY ~PELLET RADIUS FIGURE 4.21 Regions of occurrence of various laser-plasma coupling processes, heat transport, and ablation, shown on the pellet density profile.

FUSION PLASMA CONFINEMENT AND HEATING 231 100 at o - . o 60 CD m UJ =; 40 20 o 1012 lol3 loll lols LASER IRRADIANCE (Watta/cm2) FIGURE 4.22 Experimental results on laser-light absorption in percent versus laser intensity for various laser wavelengths. Results are given for laser wavelengths, which are shown in micrometers (~m). Note the better absorption with shorter wavelength. Research on laser-plasma coupling continues to contribute to the understanding of many fundamental processes in plasma heating and turbulence. It is important to extend this research to the much larger-scale plasmas that will be encountered in reactor targets. The present understanding of the various coupling processes and detailed plasma conditions in larger-scale plasmas is inadequate to make quantitative predictions with confidence. HEAT TRANSPORT AND ABLATION · After the laser-light energy has been deposited, it must be efficiently- transported inward, to an ablation surface, within which the pellet implodes. Short-wavelength laser light improves heat transport efficiency but may lead to greater nonuniformities in the implo- sion. In the direct-illumination approach to inertial-confinement fusion, the laser-heated electrons are dominant in transporting energy to an ablation surface, as shown in Figure 4.21. Outside the ablation surface the target material is stripped away from the pellet shell by the heat wave. As this ablating material is accelerated outward toward the laser, it creates a large rocketlike ablation pressure, which accelerates the remaining shell inward and compresses the fusion fuel. Transport of the intense electron energy fluxes characteristic of laser-fusion applications is itself an important topic in applied plasma physics. The usual theory of diffusive heat flow of electrons is in general inadequate, and improved theories are now emerging. In

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.

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

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

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

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.)

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.

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.

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.)

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

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

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.

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