Boyd T.J.M., Sanderson J.J. The Physics of Plasmas
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Index 527
Rayleigh–Taylor, 124
MHD analogue of, 124
resistive, 148
characteristics of, 156
rippling mode, 156
sausage, 115, 128
marginal stability condition for, 116
sawtooth, 160
streaming, 244
tearing mode, 146, 148, 151, 161, 194
growth rate, 154
two-stream, 240, 314
interactions
collective, 8, 408
collisional, 253
Coulomb, 309, 470
electron, 468, 470
laser–plasma, 392, 394
resonant, 262, 274, 282
three-wave, 392
instability threshold condition, 393
wave–particle, 198, 409
wave–wave, 389, 392
internal energy, 56, 67
of fluid element, 55
interstellar plasma, 11
inverse aspect ratio, 33, 99, 305
inverse bremsstrahlung, 341
inverse Faraday effect, 47
ion acoustic wave, 230, 236, 237, 394, 397
Landau damping of, 265
ion cyclotron wave, 235, 237
first, 235
second, 235
ion flux, 491
ion plasma wave, 236
ionosphere, 197, 224
plasma parameters in, 10
isentropic transitions, 408
isobaric surface, 84
Jeans theorem, 255, 283
Joule heating, 56
kinematic dynamo problem, 163
kinetic energy
average, 16
conservation of, 14
flow, 56
particle, 14
plasma, 16
kinetic equation, 253, 479
collisional, 254, 289, 296
collisionless, 253
Landau, 472, 479, 498
kinetic temperature, 481
Klimontovich distribution function, see distribution
function, Klimontovich
Kruskal–Shafranov stability criterion, 118
Landau damping, 227, 256, 274
decrement, 261, 382
electron, 265, 267, 275
experimental verification, 263
ion, 265, 267
non-linear, 383
physical origin, 262
Landau equation, see kinetic equation, Landau
Landau growth, 262, 274
Landau theory
non-linear, 377, 388
Langmuir collapse, 404
Langmuir probe characteristics, 456
Langmuir waves, 229, 263, 394
Landau damping of, 289, 295
radiation from, 450
combination line, 451
in laser-produced plasmas, 453
Larmor formula, 328, 335
Larmor frequency, 15, 18
relativistic, 38
Larmor motion, 16, 19
Larmor orbit, 18, 19, 281
Larmor period, 16
Larmor precession, 25
Larmor radius, 12, 15, 21, 302
electron, 282
instantaneous, 18
laser-produced plasmas, 394
channel formation in, see ponderomotive force,
channel formation
harmonic emission from, 451
plasma line emission, 451
resonance absorption in, see resonant absorption
stimulated Raman scattering in, see stimulated
Raman scattering, in inhomogeneous plasmas
Lawson criterion, 3–5, 88
Leibnitz theorem, 50, 79
lighthouse effect, 351
linear mode conversion, 435
mode conversion coefficient, 437, 438
reflection coefficient, 438
transmission coefficient, 438
Liouville equation, 466, 468
Liouville operator, 466, 468
Li
´
enard–Wiechert potentials, 325
longitudinal invariant, see adiabatic invariants, second
longitudinal invariant surface, 32
Lorentz equation
non-relativistic, 13
relativistic, 38
Lorentz gas model, 297
Lorentzian line shape, 369
loss cone, 28
lower hybrid wave, 215
Lundquist number, 141, 146, 193
Mach number, 413
critical, 419, 420
magnetic bottle, 4, 27, 28
528 Index
magnetic buoyancy, 106
magnetic containment fusion, 5
magnetic convection equation, 68
magnetic curvature, 128
magnetic energy, 104
magnetic field
bumpy, 44
force-free, 99
generation, 162
geomagnetic tail, see magnetotail, magnetic field in
induced, 16
interplanetary, 195
measurement by Thomson scattering, see Thomson
scattering, coherent, effect of magnetic field
reconnection, 146
reversal, 144
solar, 106
magnetic field lines
ergodic, 94
pitch of, 88
magnetic flux
poloidal, 95
toroidal, 96
magnetic helicity, 102, 103, 143, 166
magnetic islands, 142, 158
magnetic knot, 105
magnetic mirror, 25, 26, 33, 36, 305
magnetic modulation of scattered light spectrum, 360
magnetic moment, 16, 25, 68
invariance of, 25, 34, 36, 44, 68
magnetic pressure, 83
magnetic reconnection, 142, 148, 177–179
driven, 145
spontaneous, 145
magnetic relaxation, 142
magnetic shear, 22, 125, 129, 155, 158
magnetic surface, 80
magnetic tension, 83
magnetic trap, 31
magnetic well, 93, 129
magnetization, 16, 23
magneto-ionic theory, 224
magnetoacoustic wave, 233, 411
fast, 132
slow, 132
magnetohydrostatic condition, 106
magnetopause, 31, 177–179
magnetosheath, 177–179, 405
magnetosphere, 7, 146, 169, 177–179, 197
magnetotail, 7, 177
magnetic field in, 44
Manley–Rowe relations, 392
Markov system, 494
Markovian, 307
mass conservation, 52
mass density, 485
Maxwell equations, 13, 23, 182, 255, 409
reduced, 488
Maxwell stress tensor, see stress tensor, Maxwell
mean free path, 469
collisional, 302, 304, 405
electron, 10, 63, 476
electron–ion, 176
ion, 63
turbulent dissipation, 408
MHD approximation, 58, 63, 488, 489
non-relativistic, 63
MHD equations, 48, 480, 488
dissipative, 501
MHD equilibria
solar, 105
MHD instabilities, see instabilities, MHD
micro-instabilities, 262, 268
minimum B stability condition, 129
Mirnov oscillations, 158
mirror ratio, 27
mirror trap, 27–30
mobility
electron, 300
ion, 300
mode conversion, see linear mode conversion
mode rational surface, 157
moment equations, 480–487
general moment equation, 483
moment integrals of distribution function, 482
electrodynamical, 491
hydrodynamical, 491–494
non-hydrodynamical, 491–494
non-plasmadynamical, 491
plasmadynamical, 491
momentum equation
parallel, 70
perpendicular, 70
Navier–Stokes equation, 55
neoclassical theory, 491
neoclassical transport, 304, 487
Nernst effect, 495
neutral sheet, 44, 142, 146
non-linear Schr
¨
odinger equation, 403, 423
number density, 7, 480
Nyquist diagrams, 270
Ohm’s law, 59, 64, 496, 504
generalized, 64, 73, 486, 494
in MHD approximation, 65
in warm plasma wave equations, 73, 231
omega-effect, 165–167
Onsager symmetry, 492
optical depth, see radiative transport equation, optical
depth
optically thick plasma, 333
optically thin plasma, 332
ordinary mode, 214, 411
pair correlation function, 469, 470
equilibrium, 475
parameter space, 10, 218, 219
parametric amplification, 376
parametric waves, 377
Index 529
particle acceleration, 35
at shocks, 421
particle drifts, 22
particle energy, 32
particle orbits
in torus, 93
particle trapping, 382–386, 397
in beam–plasma instability, 384
passing particles, 33–34
path variables, 56
Peltier effect, 497
Penrose criterion, 272
perfect gas, 57
Petschek model, 147–148, 193
maximum reconnection rate in, 147
phase integral, 428
phase mixing, 388
phase shift, 432
phase space, 466
phase velocity, 201
photosphere, 6, 7, 106, 107
pinch parameter, 144
pitch angle, 27, 36, 45
plasma beta, 83, 86, 88, 105
poloidal, 89
toroidal, 89
plasma bremsstrahlung, 334–339
spectrum
classical, 336
quantum mechanical, 338
plasma cavities, 402
plasma characteristics, 7
plasma containment, 4, 93, 108, 161
plasma diamagnetism, 16, 23
plasma dielectric function, 258, 276, 472, 479
plasma dispersion function, 265
plasma echoes, 388, 423
plasma frequency, 8
electron, 8, 254, 258
ion, 9
plasma oscillations, 8, 23, 260
coherent, 408
electron, 197, 229
longitudinal, 209
plasma parameter, 8, 10
plasma reflectometry, 432
plasma resistivity, 140
variable, 149
plasma sheath, 453
equation, 454
plasma sheet, 31, 44, 244
plasma transport, 158, 296
plasma wave equations, 49
plasma waves
electron, 227, 397
ion, 230
Plemelj formula, 479
Poisson equation, 378
polarization
circular, 199
elliptical, 199
extraordinary mode, 217
linear, 199
polarization drift, 37
polarization dyadic, 355
ponderomotive force, 40, 398, 401, 404
channel formation, 41
power radiated by accelerated charge, 326
Poynting flux, 357
Poynting theorem, 200
Poynting vector, 200
for radiation field, 326
pressure
fluid in motion, 54
scalar, 481, 486
tensor, 481, 491
traceless, 481, 495
thermodynamic, 54
prominences, 108
proton–proton cycle, 2
pseudo-resonance, 235, 236
quasi-linear theory, 377–382, 388
quasi-neutrality condition, 57, 64, 413, 486
quiver motion
electron, 40
quiver velocity, 441
radial force balance, 85
radial pressure balance, 101
radiation
absorption coefficient, 331
broadening, 347
emission coefficient, 331
flux, 330
spectral density of, 330
frequency spectrum from accelerated charge, 328
from Langmuir waves
combination line, see Langmuir waves, radiation
from, combination line
harmonic emission, see laser-produced plasmas,
harmonic emission from
plasma line, see laser-produced plasmas, plasma
line emission
intensity, 330
pressure, 355
temperature, 334
radiation transport in plasma, 330
radiative recombination, 339
radiative transport equation, 332
optical depth, 332
source function, 332
radio waves, 197
radiofrequency heating
ion cyclotron resonance, 439
of tokamak plasma, 439
Raman decay waves, 442
Raman gain, convective, 445
530 Index
Raman resonance, 444
detuning condition, 446
width, 446
Raman scattered light wave, 442
Raman threshold
convective, 446
Rankine–Hugoniot equations, 184
ratio of specific heats, 57
ray path, 331
ray-tracing approximation, 428
Rayleigh-Jeans limit, see black body intensity,
Rayleigh-Jeans limit
recombination radiation, 339
emission coefficient, 340
reflected ions, 419
reflection coefficient, 431
reflectometry, see plasma reflectometry
resistive MHD, 59, 503
approximations, 60, 66
equations, 60, 505
resistivity, see plasma resistivity
resonance, 207
accessibility, 433
conditions, 389
induced scattering, 389
linear Landau damping, 389
particle trapping, 389
wave–wave interactions, 389
electron cyclotron, 208, 212, 226, 236
heating
electron cyclotron, 439
ion cyclotron, 208, 212, 223, 235, 236
lower hybrid, 209, 215
principal, 207, 210, 219
upper hybrid, 209, 216
wave behaviour near, 433
resonant absorption, 460
shape function, 460
tunnelling, 459
resonant angle, 207
resonant electrons, 382
resonant surface, 128, 129, 152, 156
resonant triad, 389
response function, 277
retarded potentials, 325
retarded time, 325
reversed field pinch, 99, 143
Reynolds number, 192
hydrodynamic, 61
magnetic, 61, 140, 193
Righi–Leduc effect, 495
Rosenbluth convective gain threshold, 446
Rosenbluth potentials, 311
rotating star, 194
rotational transform, 88, 94
safety factor, 34, 88, 118, 130, 160, 305
sawtooth oscillations, 159
scale length, 12
diffusion in magnetic field, 302
dispersive steepening, 407
scale length (cont.)
sunspot, 105
wave-front, 412, 415, 418
wavetrain decay, 418
screw pinch, 87, 99
self-consistent field, 12, 470, 479
Shafranov shift, 101, 134
shape function
electron cyclotron radiation, 347
Salpeter, 364
synchrotron radiation, 352
sheath thickness, 301, 463
shock waves, 285
astrophysical, 420
collisional, 181, 406
collisionless, see collisionless shocks
fast, 190
formation of, 405
jump conditions, 184, 186, 407
low β, 408
MHD, 179
planetary, 420
slow, 190
structure, 181, 190, 407
switch-off, 190
switch-on, 187, 190
thickness, 180, 192
skin current, 74
small Larmor radius approximation, 408
solar corona, 6, 169
characteristics of, 141
plasma parameters in, 10
solar flares, 28, 108, 142, 146, 177
solar wind, 7, 31, 169, 405, 421
characteristics of, 169
plasma parameters in, 10
solitons, 403, 408, 414, 418
sound waves
propagation of, 70
space charge, 300
space plasmas, 67, 141, 503, 504
space potential, 457
spectral density of radiation flux, see radiation, flux,
spectral density of
spectral energy density of electrostatic field, 380
stability
radial, 5, 98, 99
toroidal, 5, 98
state variables, 55
static equilibrium
configurations, 82
cylindrical, 85
toroidal, 89
equations, 82
stimulated Brillouin scattering, 397
stimulated Raman scattering, 397, 441
back-scatter, 445
equations
numerical solution of, 447
forward-scatter, 445
growth rate, 442
Index 531
stimulated Raman scattering (cont.)
in homogeneous plasmas, 441
maximum growth rate, 442
in inhomogeneous plasmas, 442
absolute growth rate, 445
convective growth, 445
non-local behaviour, 446
wave damping coefficients, 442
Stokes equation, 430
Stokes phenomenon, 431
stop-band, 210
stress tensor, 52
equilibrium, 67
isotropic, 53
Maxwell, 78
non-isotropic, 54
total, 82
viscous, 54
Sun
chromosphere, see chromosphere
convection zone, 6
corona, see solar corona
magnetic field of, see magnetic field, solar
photosphere, see photosphere
radiation zone, 6
sunspots, 105, 108, 134
characteristics of, 141
diffusion time, 141
supra-thermal particles, 410
surface charge, 74
surface current, 74
surface wave, 462
Suydam criterion, 130, 136
Sweet–Parker model, 146
reconnection rate, 193
synchrotron radiation
by ultra-relativistic electrons, 351
emission intensity, 353
emission spectrum, 352
emission spectrum from Crab nebula, 354
lighthouse effect, 351
spectral index, 353
spectral width, 352
from hot plasmas, 348
emission coefficient, 349
harmonic structure, 350
relativistic broadening, 351
Taylor hypothesis, 143
temperature equilibration, 62
test particle, 287, 288, 313
model, 313, 315
thermal conductivity, 299, 494
coefficient of, 66, 297
electron, 498, 500
ion, 498, 500
thermal velocity, 481
thermodynamic equilibrium
local, 334
thermodynamic fluxes, 492
thermodynamic forces, 492
thermodynamics
first law of, 55
second law of, 184, 186, 501
thermoelectric coefficients, 494, 498
thermoelectric effect, 497
thermonuclear fusion, 2, 6
controlled, 2, 3
thermonuclear power, 3
theta-pinch, 85, 93
Thomson cross-section, 328
Thomson scattering
coherent, 361
dressed test particle approach, 361
effect of Coulomb collisions, 369
effect of impurity ions, 366
effect of magnetic field, 360
experimental verification, 365
form factor, 362
plasma diagnostic, 365
scattering parameter, 364
spectral power density, 362
electron temperature diagnostic, 358
incoherent, 355
form factor, 358
scattered power, 357
relativistic non-linear, 374
time scales
convective, 140
gravitational, 155
hydrodynamic, 62, 488
resistive diffusion, 140
temperature equilibration, 317
tokamak, 4, 99, 119
banana orbit, see banana orbit
characteristics of, 141
disruptions, 142
equilibria, 100, 101
fields, 5
instabilities, 157
Mirnov oscillations, see Mirnov oscillations
particle orbits in, 33
passing particles, see passing particles
plasma parameters in, 10
sawtooth oscillations, see sawtooth oscillations
trapped particles, see trapped particles
Tonks–Dattner resonances, 462
toroidal force balance, 89, 92, 101
transit time, 29
Alfv
´
en, 140
proton, 31
transport coefficients, 55, 297, 492–500, 503
anomalous, 318
turbulent, 420
transport equations, 190, 420, 492
transport matrix, 492
transport theory, 296
classical, 487
transverse waves, 210
trapped particles, 33–35, 305
Trubnikov function, 350
532 Index
turbulent dissipation, 407
type III solar radio noise, 450
upper hybrid frequency, 280
Van Allen radiation belts, 30–31
virial theorem, 84, 103
viscosity
bulk, 54
coefficient of, 66, 300
electron, 498, 500
ion, 498, 500
kinematic, 61
shear
coefficient of, 54
stress, 54
tensor, 495
Vlasov equation, 254, 289, 296, 377, 409
electron, 256
equivalence to particle orbit theory, 254
numerical solution of, 293
warm plasma
general dispersion relation, 230
theory, 227
wave equations, 72, 73, 398
waves, 227
wave dispersion, 200, 406
normal, 201
wave normal surface, 198, 218
destructive transition, 222
intact transition, 222
re-shaping transition, 221
wave packet, 200
wave-front, 406
wavenumber mismatch, 394, 397
weak coupling approximation, 256, 471, 475, 479,
498
whistler wave, 215
winding numbers, 95
WKBJ approximation, 426
electric field swelling, 428
equations for stimulated Raman scattering, 444
solutions to Stokes equation, 430
dominant term, 431
subdominant term, 431
validity of solutions, 427
Woltjer theorem, 143
Z-pinch, 4, 86, 90, 108, 115, 133
Zakharov equations, 397–402
first, 400
second, 401