书名：Modern plasma physics. Volume 1, Physical kinetics of turbulent plasmas
责任者：Patrick H. Diamond | Sanae-I. Itoh | Kimitaka Itoh. | Itoh, K.
出版时间：2014
出版社：Cambridge University Press
摘要
This three-volume series presents the ideas, models and approaches essential to understanding plasma dynamics and self-organization for researchers and graduate students in plasma physics, controlled fusion and related fields such as plasma astrophysics. Volume I develops the physical kinetics of plasma turbulence through a focus on quasi-particle models and dynamics. It discusses the essential physics concepts and theoretical methods for describing weak and strong fluid and phase space turbulence in plasma systems far from equilibrium. The book connects the traditionally 'plasma' topic of weak or wave turbulence theory to more familiar fluid turbulence theory, and extends both to the realm of collisionless phase space turbulence. This gives readers a deeper understanding of these related fields, and builds a foundation for future applications to multi-scale processes of self-organization in tokamaks and other confined plasmas. This book emphasizes the conceptual foundations and physical intuition underpinnings of plasma turbulence theory.
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目录
Preface xi
Acknowledgements xv
1 Introduction 1
1.1 Why? 1
1.2 The purpose of This book 4
1.3 Readership and background literature 6
1.4 Contents and structure of this book 7
1.5 On using this book 15
2 Conceptual foundations 18
2.1 Introduction 18
2.2 Dressed test particle model of fluctuations in a plasma near equilibrium 20
2.2.1 Basic ideas 20
2.2.2 Fluctuation spectrum 24
2.2.3 Relaxation near equilibrium and the Balescu-Lenard equation 35
2.2.4 Test particle model: looking back and looking ahead 48
2.3 Tuirbulence: dimensional analysis and beyond - revisiting the theory of hydrodynamic turbulence 51
2.3.1 Key elements in Kolmogorov theory of cascade 51
2.3.2 Two-dimensional fluid turbulence 57
2.3.3 Turbulence in pipe and channel flows 65
2.3.4 Parallels between K41 and Prandtl's the 可 71
3 Quasi-linear theory 72
3.1 The why and what of quasi-linear theory 72
3.2 Foundations, applicability and limitations of quasi-Linear Theory 77
3.2.1 Irreversibility 77
3.2.2 Linear response 79
3.2.3 Characteristic time-scales in resonance processes 80
3.2.4 Two-point and two-time correlations 82
3.2.5 Note on entropy production 85
3.3 Energy and momentum balance in quasi-linear theory 86
3.3.1 Various energy densities 86
3.3.2 Conservation laws 88
3.3.3 Roles of quasi-particles and particles 90
3.4 Applications of quasi-linear theory to bump-on-tail instability 92
3.4.1 Bump-on-tail instability 92
3.4.2 Zeldovich theorem 93
3.4.3 Stationary states 95
3.4.4 Selection of stationary state 95
3.5 Application of quasi-linear theory to drift waves 99
3.5.1 Geometry and drift waves 99
3.5.2 Quasi-linear equations for drift wave turbulence 102
3.5.3 Saturation via a quasi-linear mechanism 104
3.6 Application of quasi-linear Theory to ion mixing mode I05
3.7 Nonlinear Landau damping 108
3.8 Kubo nu mber and trapping 111
4 Nonlinear wav←particle interaction 114
4.1 Prologue and overview 114
4.2 Resonance broadening theory 117
4.2.1 Approach via resonance broadening theory 117
4.2.2 Application to various decorrelation processes 124
4.2.3 Influence of resonance broadeni ng on mean evolution 128
4.3 Renormalization in Vlasov turbulence I: Vlasov response function 130
4.3.1 Issues in renormalization in V1asov turbulence 130
4.3.2 One-dimensional electron plasmas 131
4.4 Renormalization in Vlasov turbulence II: drift wave turbulence 135
4.4.1 Kinetic description of drift wave fluctuations 135
4.4.2 Coherent nonlinear e仔ect via resonance broadeni ng theory 136
4.4.3 Conservation revisited 137
4.4.4 Conservative formulations 139
4.4.5 Physics content and predictions 142
5 Kinetics of nonJinear wav←wave interaction 150
5.1 Introduction and overview 150
5.1.1 Central issues and scope 150
5.1.2 Hierarchical progression in discussion 151
5.2 The integrable dynamics of three coupled modes 154
5.2.1 Free asymmetric top (FAT) 154
5.2.2 Geometrical construction of three coupled modes 155
5.2.3 Manley-Rowe relation 158
5.2.4 Decay instability 161
5.2.5 Example 一 drift-Rossby waves 162
5.2.6 Example 一 unstable modes in a family of drift waves 165
5.3 The physical kinetics of wave turbulence 166
5.3.1 Key concepts 166
5.3.2 Stn』cture of a wave kinetic equation 169
5.3.3 ‘Collision' integral 173
5.3.4 Applicati on to drift-Rossby wave 180
5.3.5 Issues to be considered 185
5.4 The scaling theory of local wave cascades 186
5.4.1 Basic ideas 186
5.4.2 Gravity waves 191
5.5 Non-local interaction in wave turbulence 195
5.5.1 Elements in disparate scale interaction 195
5.5.2 E仔ects of large/meso scale modes on micro fluctuations 198
5.5.3 Induced diffi』sion equation for internal waves 199
5.5.4 Parametric interactions revisited 203
6 Closure theory 208
6.1 Concepts in closure 208
6.1.1 Issues in closure theory 210
6.1.2 Illustration: the random oscillator 212
6.1.3 DJustration by use of the driven-Burgers/KPZ equation (1) 216
6.1.4 Illustration by use of the driven-Burgers/KPZ equation (2) 225
6.1.5 Short summary of elements in closure theory 230
6.1.6 On realizability 231
6.2 Mori-Zwanzig theory and adiabatic elimination 233
6.2.1 Sketch of projection and generalized Langevin equation 234
6.2.2 Memory function and most probable paTh 237
6.3 Langevi n equation formalism and Markovian approximation 244
6.3.1 Langevin equation approximation 244
6.3.2 Markovian approximation 246
6.4 Closure model for drift waves 247
6.4.1 Hasegawa-Mirna equation 247
6.4.2 Application of closure modelling 248
6.4.3 On triad interaction time 253
6.4.4 Spectrum 255
6.4.5 Example of dynamical evolution - access to statistical equilibrium and H-theorem 256
6.5 Closure of kinetic equation 260
6.6 Short note on prospects for closure theory 263
7 Disparate scale interactions 266
7.1 Short overview 266
7.2 Langmu 让 waves and self-focusing 269
7.2.1 Zakharov equations 269
7.2.2 Subsonic and supersonic limits 273
7.2.3 Subsonic limit 274
7.2.4 Illustration of self-focusing 274
7.2.5 Linear theory of self-focusing 276
7.3 Langmuir wave turbulence 277
7.3.1 Action density 278
7.3.2 Disparate scale interaction between Langmuir turbulence and acoustic turbulence 278
7.3.3 Evolution of the Langmuir wave action density 281
7.3.4 Response of distribution of quasi-particles 283
7.3.5 Growth rate of modulation of plasma waves 286
7.3.6 Trapping of quasi-particles 287
7.3.7 Saturation of modul ational instability 289
7.4 Collapse of Langmuir turbulence 291
7.4.1 Problem definition 291
7.4.2 Adiabatic Zakharov equation 293
7.4.3 Collapse of plasma waves with spherical symmetry 293
7.4.4 Note on ‘cascade versus collapse' 297
8 Cascades, structure and transport in phase space turbulence 299
8.1 Motivation: basic concepts of phase space turbulence 299
8.1.1 Issues in phase space turbulence 299
8.1.2 Granulation - what and why 305
8.2 Statistical theory of phase space turbulence 314
8.2.1 Structure of the theory 314
8.2.2 Physics of production and relaxation 318
8.2.3 Physics of relative dispersion in Vlasov turbulence 329
8.3 Physics of relaxation and turbulent states with granulation 340
8.4 Phase space structures - a look ahead 347
9 MHD turbulence 348
9.1 Introduction to MHD turbulence 348
9.2 Towards a scaling theory of incompressible MHD turbulence 350
9.2.l Basic elements: waves and eddies in MHD turbulence 350
9.2.2 Cross-helicity and Alfven wave interaction 351
9.2.3 Heuri stic discussion of Alfven waves and cross-helicity 353
9.2.4 MHD turbulence spectrum (I) 355
9.2.5 MHD turbulence spectrum (II) 357
9.2.6 An overview of the MHD turbulence spectrum 359
9.3 Nonlinear Alfven waves: compressibility, steepening and disparate-scale interaction 362
9.3.1 Effect of small but finite compressibility 362
9.3.2 A short note, for perspective 366
9.4 Turbulent diffusion of magnetic fields: a first step in mean field electrodynamics 366
9.4.1 A short overview of issues 366
9.4.2 Flux diffusion in a two-dimensional system: model and concepts 367
9.4.3 Mean field electrodynamics for (A) in a two-dimensional system 370
9.4.4 Turbulent diffusion of flux and field in a three-dimensional system 380
9.4.5 Discussion and conclusion for turbulent diffusion of a magnetic field 384
Appendix 1 Charney-Hasegawa-Mirna equation 385
Appendix 2 Nomenclature 398
References 407
Index 415
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