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The Physics of Magnetic Fusion Reactors

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The Physics of Magnetic Fusion Reactors The physics of magnetic fusion reactors John Sheffield Oak Ridge National Laboratory, Qak Ridge, Tennessee 97891 During the past two decades there have been substantial advances in magnetic fusion research. On the ex- perimental front, progress has been led by the mainline tokamaks, which have achieved reactor-level values of temperature and plasma pressure. Comparable progress, when allowance is made for their smaller programs, has been made in complementary configurations such as the stellarator, reversed-field pinch and field-reversed configuration. In this paper, the status of understanding of the physics of toroidal plasmas is reviewed. It is shown how the physics performance, constrained by technological and econom- ic realities, determines the form of reference toroidal reactors. A comparative study of example reactors is not made, because the level of confidence in projections of their performance varies widely, rejecting the vastly different levels of support which each has received. Success with the tokamak has led to the ini- tiation of the International Thermonuclear Experimental Reactor project. It is designed to produce 1500 MW of fusion power from a deuterium-tritium plasma for pulses of 1000 s or longer and to demonstrate the integration of the plasma and nuclear technologies needed for a demonstration reactor. CONTENTS 12. Electron drift-wave instability 1050 13. Ion drift waves 1050 Symbols and Units 1016 14. Trapped ion modes 1050 I. Introduction 1017 15. Electromagnetic drift-Alfven modes 1050 II. Generic Reactor Characteristics 1019 16. Rippling modes and their relatives 1051 A. Representative reactor configuration 1019 17. MHD modes 1051 B. Nuclear fusion reactions and the fuel cycle 1020 D. Dimensionless plasma scaling 1051 C. Plasma power balance 1022 IV. Tokamak Reactors 1052 D. Generic reactor characteristics 1025 A. Introduction 1052 E. Beta and thermal diffusivity requirements 1028 B. Tokamak characteristics 1053 F. Alpha physics 1029 1. Coils 1053 G. Impurities, limiters, and divertors 1031 2. Startup 1054 1. Plasma-wall interactions. 1032 3. Plasma duration 1055 2. Limiters 1033 4. Bootstrap current 1055 3. Divertors 1035 C. Noninductive current drive 1056 H. Auxiliary heating 1038 D. Tokamak transport 1058 1. Neutral-beam injection 1039 1. The H mode 1060 2. Radio-frequency (RF) heating 1040 2. Dimensionless plasma scaling 1061 a. Absorption 1040 E. MHD limits 1061 b. Efficient coupling 1040 1. Resistive ballooning modes 1062 c. Electron cyclotron frequency range 1040 2. Beta limit 1062 d. Lower hybrid frequency range 1040 3. Second stable operation 1063 e. Ion cyclotron frequency range 1040 4. Resistive modes 1063 f. Adiabatic compression 1041 5. Disruptions 1063 I. Fueling 1041 F. Density limit 1064 1. Pellet injection fueling 1041 G. Alpha-particle effects 1064 2. Compact toroid plasma injection 1041 1. Destabilization of Alfven waves 1065 III. Taxonomy of Toroidal Systems 1042 2. Destabilization of ballooning modes 1066 A. Introduction 1042 3. Fishbone oscillations 1066 1. Axisymmetric systems 1042 H. Power and particle control 1066 2. Nonaxisymmetric systems 1043 I. Modeling of tokamak plasmas 1066 3. Strength and weaknesses 1043 J. Tokamak reactor options 1067 B. Magneto-hydrodynamics 1043 K. Conclusions 1069 1. Plasma equilibrium 1043 V. Stellarator Reactors 1069 2. Plasma stability 1045 A. Introduction 1069 3. Resistive modes 1045 B. Stellarator characteristics 1070 C. Transport 1045 C. Stellarator transport 1072 1. Diffusion 1046 D. MHD and density limits 1074 2. Drift 1046 E. Alpha-particle effects 1075 3. Thermal conductivity 1046 F. Power and particle control 1076 4. RFP thermal conductivity 1047 G. Computer modeling 1076 5. FRC thermal conductivity 1047 H. Stellarator reactor options 1076 6. Stellarator thermal conductivity 1047 I. Conclusions 1078 7. Ripple transport 1047 VI ~ Reversed-Field-Pinch Reactors 1078 8. Anomalous transport 1048 A. Introduction 1078 9. Weak turbulence 1048 B. RFP characteristics 1078 10. Strong turbulence 1048 1. Plasma startup 1078 11. Low-frequency microscopic modes 1050 2. Relaxed states 1080 Reviews of Modern Physics, Vol. 66, No. 3, July 1994 0034-6861 /94/66(3) /1 015(89)/31 3.90 1994 The American Physical Society 1015 1016 John Sheffield: Physics of magnetic fusion reactors 3. Equilibrium 1080 D. Startup 1087 C. Transport 1081 E. Adiabatic compression 1088 D. MHD limits 1082 F. Transport 1088 1. Infinitely conducting shell 1083 Cx. MHD limits 1089 2. Resistive shell 1083 1. Rotational instability 1090 E. Current drive 1083 2. Tilt instability 1090 F. Power and particle handling 1084 H. Alpha effects 1090 Cx. Computer modeling 1084 I. Power and particle control 1090 H. RFP reactors 1084 J. FRC reactor options 1090 I. Conclusions 1085 1. Pulsed reactor 1091 VII. Field-Reversed Configurations 1086 2. Conclusions 1091 A. Introduction 1086 Acknowledgments 1091 B. FRC characteristics 1086 References 1091 C. Equilibrium 1086 SYMBOLS AND UNITS e =electron, i =ion, 0 =neutral, z =ion of charge z, b =beam, k =kilo, e.g., T,k =electron temperature in keV, m =mega or maximum, a =plasma edge, w =wall, P=toroidal, O=poloidal, r =radial, v =vertical, z =axial, ~~=parallel to magnetic field, J.=perpendicular to magnetic field, T =temperature or tritium, 0=deuterium, a=alpha particle, NC=neoclassical, nzo=density in units of 10 m TIo=temperature in units of 10 keV Superscripts: x =average (x ) =volume average, x =peak, or central value, x =fluctuating value. a (m) minor radius in the median Ib, (A) bootstrap current plane j (Am ) current density a (m) avel age minor 1ad1us J (Am ) current density A(m) area k =1.38X 10 (J K ')Boltzmann's constant atoIDic mass IluIIlbel k (m ') wave number b (m) minor radius in z direction Lo total magnetic helicity B (T) magnetic field l, I (m) length or gradient scale b,8„(T) magnetic-field swing in a length solenoid m (kg) mass D(m s ') diffusion coefficient poloidal mode number D~ (ms ') ambipolar di6'usion coeKcient MF, (kg) mass of the fusion island ' e =1.6X 10 (C) charge on an electron n(m ) number density E (Vm ') electric field n(m ) line-average density E„;, (eV) energy at which rate of toroidal mode number transfer to ions and p (Wm ) power density electrons is equal pb, (Wm ) breInsstrahlung radiation E,E„(J) fusion energy released in D-T power density fusion in alpha particle and p,„(Wm ) charge-exchange power neutron density Eb (MeV) neutral-beam energy p,, (Wm ) ion-electron transfer power fraction of alpha power lost density by GoIlductloIl ptR (Wm ) line radiation power density ratio of field in plasma to p, (Wm ) synchrotron radiation power maximum field on a coil density fE =N~Tk normalized potential p (Wm ) alpha power density f.s fraction of neutral-beam po (Wm ) ohmic power density shine-through nn (Wm 2) neutron Aux on first field-reversal parameter wall in an RFP p „(Wm ) average neutron Aux on first troyon factor for beta wall [a(m)B&(T)(P(%)]/I(MA) ] P (W) power I (A) current P„(W) neutron power Rev. Mod. Phys. , Vol. 66, No. 3, JUly 1994 John Sheffield: Physics of magnetic fusion reactors 1017 P, (W) total thermal power v„(s ') electron-ion collision P (W) alpha power frequency P, (W) auxiliary power ratio of time to complete safety factor banana orbit to collision time at 95%%uo flux surface p (kgm ) density q& on Aux surface y p„p; (m) electron, ion gyroradius ratio of fusion power to plasma displacement power lost by plasma (harv)DT (m s ') rate coefficient for D-T fusion ratio of fusion power to total (cru), (m's ') rate coefficient for ionization recirculated power (ou)„ (m's ') rate coefficient for charge Q, (Jms ') energy Aux exchange r (m) minor radius of a torus rF. (s) energy con6nement time R (m) major radius of a torus r, (s) slowing down time for R„(m) solenoid radius energetic ions R~ (ohms) plasma resistivty p (&) potential s =rq'/q magnetic shear g(m s ') thermal diffusivity S Lundquist number magnetic-flux function S, (m s ') source rate of charge-Z ions co (rads ') angular frequency t (s) time co„, co„(rad s ') electron and ion cyclotron t~ (s) plasma current Qat-top time angular frequency T (eV) temperature coLH (rad s ) lower hybrid angular u (ms ') How velocity frequency U, (v) loop voltage ') u (ms speed I. INTRODUCTION v~ (ms ') Alfven speed vH (ms ') thermal speed During the past two decades there have been substan- V (ms ') plasma How speed tial advances across the board in magnetic fusion V (m) plasma volume research. In tokamaks, the main line of experimental 8' (J) plasma energy research in the world program, reactor-level plasma con- Z ionic charge ditions have been achieved (see Table I). Initial tests with g, Z n, deuterium-tritium fuel in the JET tokamak in 1991 led to Zeff the generation of 1.8 MW of fusion power (JET Team, ale 1992). More recently, the TFTR tokamak obtained over ratio of plasma pressure 6 MW of fusion power (TFTR Team, 1993). The charac- to magnetic pressure teristic time scale of plasma sustainment typical of the volume-average beta (generally 1970s was 1 s. Tokamak and stellarator plasma parame- given in %%uo) ters improved we11 above those attained in the 1970s have beta 8 poloidal now been sustained for tens of seconds. The development XR neoclassical resistance anomaly of noninductive current drive (Yoshikawa and ') Yamato, I (m s Aux 1966; Ohkawa, 1970; Fisch, 1980; Bevir and Gray, 1980) e=r/R inverse aspect ratio has opened the route to steady-state operation of the oth- ~h toroidal and helical 6eld ripple erwise pulsed devices. The small superconducting gQ efficiency of auxiliary plasma tokamak TRIAM-1M (S. Itoh et al. , 1991) has been power operated for one hour, at n =2X10' m, T,(0)=500 thermal-to-electrical eV.
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