Preface
1 Nature of Plasma ............................................. 1
1.1 What is a Plasma? ....................................... 1
1.2 Debye Shielding ......................................... 3
1.3 Fusion Core Plasma ...................................... 5
2 Plasma Characteristics ...................................... 11
2.1 Velocity Space Distribution Function, Electron and
Ion Temperatures ....................................... 11
2.2 Plasma Frequency, Debye Length ......................... 12
2.3 Cyclotron Frequency, Larmor Radius ..................... 14
2.4 Drift Velocity of Guiding Center ....................... 15
2.5 Magnetic Moment, Mirror Confinement, Longitudinal
Adiabatic Constant ..................................... 19
2.6 Coulomb Collision Time, Fast Neutral Beam Injection .... 22
2.7 Runaway Electron, Dreicer Field ........................ 29
2.8 Electric Resistivity, Ohmic Heating .................... 30
2.9 Variety of Time and Space Scales in Plasmas ............ 31
3 Magnetic Configuration and Particle Orbit ................... 33
3.1 Maxwell Equations ...................................... 33
3.2 Magnetic Surface ....................................... 37
3.3 Equation of Motion of a Charged Particle ............... 38
3.4 Particle Orbit in Axially Symmetric System ............. 42
3.5 Drift of Guiding Center in Toroidal Field .............. 44
a Guiding Center of Circulating Particles
b Guiding Center of Banana Particles
3.6 Orbit of Guiding Center and Magnetic Surface ........... 49
3.7 Effect of Longitudinal Electric Field on Banana
Orbit .................................................. 51
4 Velocity Space Distribution Function and Boltzmann's
Equation .................................................... 53
4.1 Phase Space and Distribution Function .................. 53
4.2 Boltzmann's Equation and Vlasov's Equation ............. 55
5 Plasma as Magnetohydrodynamic Fluid ......................... 58
5.1 Magnetohydrodynamic Equations for Two Fluids ........... 58
5.2 Magnetogydrodynamic Equations for One Fluid ............ 61
5.3 Simplified Magnetohydrodynamic Equations ............... 64
5.4 Magnetoacoustic Wave ................................... 67
6 Equilibrium ................................................. 71
6.1 Pressure Equilibrium ................................... 71
6.2 Equilibrium Equation for Axially Symmetric and
Translationally Symmetric Systems ...................... 73
6.3 Tokamak Equilibrium .................................... 76
6.4 Poloidal Field for Tokamak Equilibrium ................. 85
6.5 Upper Limit of Beta Ratio .............................. 89
6.6 Pfirsch-Schlüter Current ............................... 90
6.7 Virial Theorem ......................................... 94
7 Diffusion of Plasma, Confinement Time ....................... 98
7.1 Collisional Diffusion (Classical Diffusion) ........... 100
a Magnetohydrodynamic Treatment
b A Particle Model
7.2 Neoclassical Diffusion of Electrons in Tokamak ........ 104
7.3 Fluctuation Loss, Bцhm Diffusion, and Stationary
Convective Loss ....................................... 108
7.4 Loss by Magnetic Fluctuation .......................... 113
8 Magnetohydrodynamic Instabilities .......................... 114
8.1 Interchange, Sausage and Kink Instabilities ........... 115
a Interchange Instability
b Stability Criterion for Interchange Instability,
Magnetic Well с Sausage Instability
d Kink Instability
8.2 Formulation of Magnetohydrodynamic Instabilities ...... 127
a Linearization of Magnetohydrodynamic Equations
b Energy Principle
8.3 Instabilities of a Cylindrical Plasma ................. 135
a Instabilities of Sharp-Boundary Configuration:
Kruskal-Shafranov Condition
b Instabilities of Diffuse-Boundary Configurations
с Suydam's Criterion
d Tokamak Configuration
e Reversed Field Pinch
8.4 Hain-Lüst Magnetohydrodynamic Equation ................ 155
8.5 Ballooning Instability ................................ 157
8.6 ηi Mode due to Density and Temperature Gradient ....... 162
9 Resistive Instability ...................................... 167
9.1 Tearing Instability ................................... 168
9.2 Resistive Drift Instability ........................... 174
10 Plasma as Medium of Electromagnetic Wave Propagation ....... 181
10.1 Dispersion Equation of Waves in a Cold Plasma ......... 182
10.2 Properties of Waves ................................... 187
a Polarization and Particle Motion
b Cutoff and Resonance
10.3 Waves in a Two-Components Plasma ...................... 189
10.4 Various Waves ......................................... 194
a Alfven Wave
b Ion Cyclotron Wave
с Lower Hybrid Resonance
d Upper Hybrid Resonance
e Electron Cyclotron Wave
10.5 Conditions for Electrostatic Waves .................... 202
11 Landau Damping and Cyclotron Damping ....................... 205
11.1 Landau Damping (Amplification) ........................ 205
11.2 Transit-Time Damping .................................. 210
11.3 Cyclotron Damping ..................................... 210
11.4 Quasi-Linear Theory of Evolution in the Distribution
Function .............................................. 213
12 Wave Propagation and Wave Heating .......................... 217
12.1 Energy Flow ........................................... 218
12.2 Ray Tracing ........................................... 223
12.3 Dielectric Tensor of Hot Plasma, Wave Absorption
and Heating ........................................... 225
12.4 Wave Heating in Ion Cyclotron Range of Frequency ...... 232
12.5 Lower Hybrid Wave Heating ............................. 237
12.6 Electron Cyclotron Heating ............................ 241
13 Velocity Space Instabilities (Electrostatic Waves) ......... 246
13.1 Dispersion Equation of Electrostatic Wave ............. 246
13.2 Two Streams Instability ............................... 248
13.3 Electron Beam Instability ............................. 249
13.4 Harris Instability .................................... 250
14 Development of Fusion Researches ........................... 255
15 Tokamak .................................................... 267
15.1 Tokamak Devices ....................................... 267
15.2 Equilibrium ........................................... 273
a Case with Conducting Shell
b Case without Conducting Shell с Equilibrium Beta
Limit of Tokamaks with Elongated Plasma Cross
Section
15.3 MHD Stability and Density Limit ....................... 276
15.4 Beta Limit of Elongated Plasma ........................ 279
15.5 Impurity Control and Divertor ......................... 281
15.6 Confinement Scaling ................................... 283
15.7 H Mode and Improved Confinement Modes ................. 286
15.8 Heating of Fusion Grade Plasmas ....................... 293
15.9 Noninductive Current Drive ............................ 295
a Lower Hybrid Current Drive
b Neutral Beam Current Drive с Bootstrap Current
15.10 Parameters of Tokamak Reactor ........................ 304
16 Non-Tokamak Confinement System ............................. 314
16.1 Reversed Field Pinch .................................. 314
a Reversed Field Pinch Configuration b MHD
Relaxation
с Confinement
d Oscillating Field Current Drive
16.2 Helical System ........................................ 321
a Helical Field
b Helical Devices
с Neoclassical Diffusion in Helical Field
d Confinement of Helical System
16.3 Open End Systems ...................................... 333
a Confinement Times in Mirrors and Cusps
b Confinement Experiments with Mirrors
с Instabilities in Mirror Systems
d Tandem Mirrors
17 Inertial Confinement ....................................... 349
17.1 Pellet Gain ........................................... 349
17.2 Implosion ............................................. 353
Appendix
A Derivation of MHD Equations of Motion ...................... 359
В Energy Integral of Axisymmetric Toroidal System ............ 364
B.l Energy Integral in Illuminating Form .................. 364
B.2 Energy Integral of Axisymmetric Toroidal System ....... 367
B.3 Energy Integral of High n Ballooning Modes ............ 374
С Derivation of Dielectric Tensor in Hot Plasma .............. 378
C.l Formulation of Dispersion Relation in Hot Plasma ...... 378
C.2 Solution of Linearized Vlasov Equation ................ 380
C.3 Dielectric Tensor of Hot Plasma ....................... 382
C.4 Dielectric Tensor of bi-Maxwellian Plasma ............. 386
C.5 Dispersion Relation of Electrostatic Wave ............. 388
C.6 Dispersion Relation of Electrostatic Wave in
Inhomogenous Plasma ................................... 389
Physical Constants, Plasma Parameters and Mathematical
Formula ....................................................... 395
Index ......................................................... 398
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