Cover......Page 1
Half-title......Page 3
Title......Page 5
Copyright......Page 6
Contents......Page 7
Preface......Page 13
Acknowledgements......Page 17
1.1 Why?......Page 19
1.2 The purpose of this book......Page 22
1.3 Readership and background literature......Page 24
1.4 Contents and structure of this book......Page 25
(1) Core programme – for serious readers......Page 33
(4) For readers from related fields......Page 34
2.1 Introduction......Page 36
2.2.1 Basic ideas......Page 38
2.2.2.1 Coherent response and particle discreteness noise......Page 42
2.2.2.2 Fluctuations driven by particle discreteness noise......Page 44
A1.7.1 Introduction for rotating coordinates......Page 0
2.2.2.4 Correlation of particles and fluctuation spectrum......Page 47
2.2.2.5 One-dimensional plasma......Page 49
2.2.2.6 Fluctuation–dissipation theorem and energy partition......Page 50
2.2.3 Relaxation near equilibrium and the Balescu–Lenard equation......Page 53
2.2.3.1 Kinetic equation for mean distribution function......Page 55
2.2.3.2 Offset on Landau–Rosenbluth theory......Page 58
2.2.3.3 Resistivity (relaxation in one-dimensional system)......Page 59
2.2.3.4 Relaxation in three-dimensional system......Page 60
2.2.3.6 Relaxation in Landau model......Page 61
2.2.3.7 Collective mode......Page 63
2.2.4 Test particle model: looking back and looking ahead......Page 66
2.3.1.1 Kolmogorov theory......Page 69
2.3.1.3 Stretching and generation of enstrophy......Page 72
2.3.1.4 Fundamental hypothesis for K41 theory......Page 73
2.3.2.1 Forward and inverse cascade......Page 75
2.3.2.2 Self-similar spectral distribution......Page 78
2.3.2.4 Long-lived vortices......Page 81
2.3.3.1 Illustration of problem......Page 83
2.3.3.2 Viscous sublayer......Page 84
2.3.3.3 Log law of the wall......Page 85
2.3.3.4 Approach to self-similarity......Page 87
2.3.4 Parallels between K41 and Prandtl's theory......Page 89
3.1 The why and what of quasi-linear theory......Page 90
3.2.1 Irreversibility......Page 95
3.2.2 Linear response......Page 97
3.2.4 Two-point and two-time correlations......Page 100
3.2.5 Note on entropy production......Page 103
3.3.1 Various energy densities......Page 104
3.3.2 Conservation laws......Page 106
3.3.3 Roles of quasi-particles and particles......Page 108
3.4.1 Bump-on-tail instability......Page 110
3.4.2 Zeldovich theorem......Page 111
3.4.4 Selection of stationary state......Page 113
3.5.1 Geometry and drift waves......Page 117
3.5.2 Quasi-linear equations for drift wave turbulence......Page 120
3.5.3 Saturation via a quasi-linear mechanism......Page 122
3.6 Application of quasi-linear theory to ion mixing mode......Page 123
3.7 Nonlinear Landau damping......Page 126
3.8 Kubo number and trapping......Page 129
4.1 Prologue and overview......Page 132
4.2.1.3 Introduction of approximation......Page 138
4.2.2.1 Scattering in action variable......Page 142
4.2.3 Influence of resonance broadening on mean evolution......Page 146
4.3.1 Issues in renormalization in Vlasov turbulence......Page 148
4.3.2 One-dimensional electron plasmas......Page 149
4.3.2.1 Renormalization procedure......Page 150
4.3.2.2 Non-Markovian property......Page 151
4.3.2.3 Background distribution renormalization......Page 152
4.4.1 Kinetic description of drift wave fluctuations......Page 153
4.4.2 Coherent nonlinear effect via resonance broadening theory......Page 154
4.4.3 Conservation revisited......Page 155
4.4.4 Conservative formulations......Page 157
4.4.5.1 Propagator renormalization and mixing......Page 160
4.4.5.2 Nonlinear heating and saturation mechanism......Page 163
4.4.5.3 Description by moments of the drift-kinetic equation......Page 164
5.1.1 Central issues and scope......Page 168
5.1.2 Hierarchical progression in discussion......Page 169
5.2.1 Free asymmetric top (FAT)......Page 172
5.2.2 Geometrical construction of three coupled modes......Page 173
5.2.3 Manley–Rowe relation......Page 176
5.2.4 Decay instability......Page 179
5.2.5 Example – drift–Rossby waves......Page 180
5.2.6 Example – unstable modes in a family of drift waves......Page 183
5.3.1 Key concepts......Page 184
5.3.2 Structure of a wave kinetic equation......Page 187
5.3.3.1 Model dynamical equation......Page 191
5.3.3.2 Extraction of response and closure......Page 193
5.3.4.1 Model......Page 198
5.3.5 Issues to be considered......Page 203
5.4.1.1 Fokker–Planck approach......Page 204
5.4.1.2 Leith model......Page 206
5.4.1.3 Leith model with dissipation......Page 207
5.4.2 Gravity waves......Page 209
5.5.1 Elements in disparate scale interaction......Page 213
5.5.2 Effects of large/meso scale modes on micro fluctuations......Page 216
5.5.3 Induced diffusion equation for internal waves......Page 217
5.5.4 Parametric interactions revisited......Page 221
6.1 Concepts in closure......Page 226
6.1.1 Issues in closure theory......Page 228
6.1.2 Illustration: the random oscillator......Page 230
6.1.3.1 Model......Page 234
6.1.3.2 Renormalized memory function......Page 235
6.1.3.3 Non-Markovian property and nonlocal interaction......Page 238
6.1.3.5 Ballistic and diffusive dynamics......Page 241
6.1.3.6 Irreversibility......Page 242
6.1.4.1 Excitation of the test mode by a nonlinear fluctuating force......Page 243
6.1.4.2 Derivation of the transfer function......Page 245
6.1.4.3 Spectral equation......Page 246
6.1.6 On realizability......Page 249
6.2.1.1 Elimination of irrelevant variables......Page 252
6.2.2 Memory function and most probable path......Page 255
6.2.2.1 Formalism and fluctuation dissipation relation......Page 256
6.2.2.2 Memory function and nonlinear force......Page 259
6.3.1 Langevin equation approximation......Page 262
6.3.2 Markovian approximation......Page 264
6.4.1 Hasegawa–Mima equation......Page 265
6.4.2.2 Response to a direct beat......Page 267
6.4.3 On triad interaction time......Page 271
6.4.4 Spectrum......Page 273
6.4.5.1 Statistical equilibrium in nonlinear dynamics......Page 274
6.5 Closure of kinetic equation......Page 278
6.6 Short note on prospects for closure theory......Page 281
7.1 Short overview......Page 284
7.2.1 Zakharov equations......Page 287
7.2.2 Subsonic and supersonic limits......Page 291
7.2.4 Illustration of self-focusing......Page 292
7.2.5 Linear theory of self-focusing......Page 294
7.3 Langmuir wave turbulence......Page 295
7.3.2 Disparate scale interaction between Langmuir turbulence and acoustic turbulence......Page 296
7.3.3 Evolution of the Langmuir wave action density......Page 299
7.3.4 Response of distribution of quasi-particles......Page 301
7.3.5 Growth rate of modulation of plasma waves......Page 304
7.3.6 Trapping of quasi-particles......Page 305
7.3.7 Saturation of modulational instability......Page 307
7.4.1 Problem definition......Page 309
7.4.3 Collapse of plasma waves with spherical symmetry......Page 311
8.1.1 Issues in phase space turbulence......Page 317
8.1.1.2 Analogy between Vlasov system and quasi-geostrophic system......Page 319
8.1.1.3 Circulation in QG system revisited......Page 320
8.1.1.4 Circulation theorem for Vlasov system and granulations......Page 321
8.1.2.2 Evolution correlation in QG turbulence......Page 325
8.1.2.3 'Phasestrophy' in Vlasov turbulence......Page 326
8.1.2.4 Generation of eddy in QG system......Page 328
8.1.2.5 Growth of granulations......Page 329
8.2.1 Structure of the theory......Page 332
8.2.1.2 Limiting behaviours and necessity of granulations......Page 333
8.2.1.3 Impact of granulations on the evolution of the mean......Page 335
8.2.2 Physics of production and relaxation......Page 336
8.2.2.1 Property of coherent terms......Page 338
8.2.2.2 A note on productions......Page 339
8.2.2.3 Introduction of modeling for the structure of granulations......Page 341
8.2.2.4 Like-particle and inter-particle interactions......Page 343
8.2.2.5 Momentum transfer channel......Page 345
8.2.3.1 Richardson's theory revisited......Page 347
8.2.3.2 Case of Vlasov turbulence......Page 348
8.2.3.3 Closure modeling for triplet correlations......Page 349
8.2.3.4 Alternative derivation......Page 351
8.2.3.5 Physics of two-particle dispersion......Page 353
8.2.3.6 Calculation of dispersion time......Page 354
8.3 Physics of relaxation and turbulent states with granulation......Page 358
8.4 Phase space structures – a look ahead......Page 365
9.1 Introduction to MHD turbulence......Page 366
9.2.1 Basic elements: waves and eddies in MHD turbulence......Page 368
9.2.2 Cross-helicity and Alfvén wave interaction......Page 369
9.2.3 Heuristic discussion of Alfvén waves and cross-helicity......Page 371
9.2.4 MHD turbulence spectrum (I)......Page 373
9.2.5 MHD turbulence spectrum (II)......Page 375
9.2.6 An overview of the MHD turbulence spectrum......Page 377
9.3.1 Effect of small but finite compressibility......Page 380
9.4.1 A short overview of issues......Page 384
9.4.2 Flux diffusion in a two-dimensional system: model and concepts......Page 385
9.4.3 Mean field electrodynamics for
in a two-dimensional system......Page 388
9.4.3.1 Closure approximations......Page 389
9.4.3.2 Mean-field approximation for correlation time and quenching of turbulent resistivity......Page 391
9.4.3.3 Issues in the quenching of turbulent resistivity......Page 392
9.4.3.4 Evaluation of correlation time and quenching of turbulent resistivity......Page 395
9.4.4 Turbulent diffusion of flux and field in a three-dimensional system......Page 398
9.4.4.2 Closure approximations......Page 399
9.4.4.3 A short note on implications......Page 401
9.4.5 Discussion and conclusion for turbulent diffusion of a magnetic field......Page 402
A1.1 Model......Page 403
A1.4 Conservation relation......Page 407
A1.6 Propagating solitary structure......Page 409
A1.7.2 Rossby wave......Page 412
Appendix 2 Nomenclature......Page 416
References......Page 425
Index
......Page 433
