Kono / Skoric Nonlinear Physics of Plasmas

2010
ISBN: 978-3-642-14694-7
Verlag: Springer
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, Band 62, 534 Seiten

Reihe: Springer Series on Atomic, Optical, and Plasma Physics

A nonlinearity is one of the most important notions in modern physics. A plasma is rich in nonlinearities and provides a variety of behaviors inherent to instabilities, coherent wave structures and turbulence. The book covers the basic concepts and mathematical methods, necessary to comprehend nonlinear problems widely encountered in contemporary plasmas, but also in other fields of physics and current research on self-organized structures and magnetized plasma turbulence. The analyses make use of strongly nonlinear models solved by analytical techniques backed by extensive simulations and available experiments. The text is written for senior undergraduates, graduate students, lecturers and researchers in laboratory, space and fusion plasmas.

Autoren/Hrsg.

Kono, Mitsuo

Skoric, Milos

Inhaltsverzeichnis

1;Nonlinear Physics of Plasmas
;3
1.1;Preface;7
1.2;Contents;11
1.3;Part I:
Fundamentals of Plasma Physics;19
1.3.1;Chapter 1:
Basic Properties of High Temperature Plasmas;20
1.3.1.1;1.1 Ionization Equilibrium;21
1.3.1.2;1.2 Plasma Temperature;22
1.3.1.3;1.3 Collision Frequency;23
1.3.1.4;1.4 Conditions for High Temperature Plasmas;24
1.3.1.5;1.5 Debye Screening;26
1.3.1.6;1.6 Plasma Diamagnetism;27
1.3.1.7;1.7 Single Particle Motions;28
1.3.1.7.1;1.7.1 Guiding Center Drifts;29
1.3.1.7.2;1.7.2 Gravitational Drift;31
1.3.1.7.3;1.7.3 Magnetic Mirrors;31
1.3.1.7.3.1;1.7.3.1 Magnetic Moment;31
1.3.1.7.3.2;1.7.3.2 Trapping in Magnetic Mirror;32
1.3.1.7.3.3;1.7.3.3 Loss Cone;32
1.3.1.7.3.4;1.7.3.4 Magnetic Pumping;33
1.3.1.7.3.5;1.7.3.5 Adiabatic Invariant J;33
1.3.1.8;1.8 Collective and Individual Motions;33
1.3.1.9;1.9 Wave-Particle Resonant Interaction;38
1.3.1.9.1;1.9.1 Landau Damping;38
1.3.1.9.2;1.9.2 Kinetic Instability;39
1.3.1.10;1.10 Dispersion and Wave Spreading;39
1.3.1.11;1.11 Nonlinearity and Wave Steepening;40
1.3.1.12;1.12 Complexity in Plasmas;41
1.3.2;Chapter 2:
The Kinetic Theory of Plasmas;42
1.3.2.1;2.1 Klimontovich Equation and Vlasov Equation;43
1.3.2.2;2.2 Linear Electrostatic Wave Without External Magnetic Field;46
1.3.2.3;2.3 Landau Damping;48
1.3.2.4;2.4 Linear Electrostatic Wave with External Magnetic Field;50
1.3.2.5;2.5 Plasma Wave Echo;52
1.3.2.6;2.6 van Kampen Mode;53
1.3.2.7;2.7 Kinetic Instability and Quasi-Linear Theory;58
1.3.2.8;2.8 Drift Kinetic Theory;61
1.3.2.9;2.9 Gyrokinetic Theory;65
1.3.3;Chapter 3:
The Fluid Theory of Plasmas;73
1.3.3.1;3.1 The Fluid Equations for Plasmas;73
1.3.3.2;3.2 Collisional Transport in Plasmas;77
1.3.3.2.1;3.2.1 Collision Integral;77
1.3.3.2.2;3.2.2 The Langevin Equation;78
1.3.3.2.3;3.2.3 The Fluctuation–Dissipation Theorem;79
1.3.3.2.4;3.2.4 Diffusion and Mobility;80
1.3.3.2.5;3.2.5 The Einstein Relation;82
1.3.3.2.6;3.2.6 Ambipolar Diffusion;84
1.3.3.3;3.3 Fluid Drifts;84
1.3.3.3.1;3.3.1 Cross Magnetic Field Drifts;84
1.3.3.3.2;3.3.2 Collisional Cross Magnetic Field Drifts;85
1.3.3.4;3.4 Magnetohydrodynamics;87
1.3.3.5;3.5 Frozen-in and Diffusion of Magnetic Field Line;88
1.3.3.5.1;3.5.1 Frozen-in Field Line;88
1.3.3.5.2;3.5.2 Diffusion of Magnetic Field Lines;89
1.3.3.6;3.6 MHD Equilibrium;90
1.3.3.6.1;3.6.1 Equilibrium for Plasma Column;90
1.3.3.6.1.1;3.6.1.1 Pinch;90
1.3.3.6.1.2;3.6.1.2 z
Pinch;91
1.3.3.6.1.3;3.6.1.3 Sausage Instability;91
1.3.3.6.1.4;3.6.1.4 Kink Instability;92
1.3.3.6.1.5;3.6.1.5 Force Free Configuration;93
1.3.3.6.2;3.6.2 Simple Torus;94
1.3.3.6.3;3.6.3 Magnetic Surface;95
1.3.3.6.4;3.6.4 Grad–Shafranov Equation;95
1.3.3.6.4.1;3.6.4.1 Axisymmetric Plasma;95
1.3.3.6.4.2;3.6.4.2 Helically Symmetric Plasma;97
1.3.3.7;3.7 Reduced MHD Equations;98
1.3.3.7.1;3.7.1 Toroidal Plasma;99
1.3.3.7.2;3.7.2 Flute Instability;100
1.3.3.7.3;3.7.3 Tearing Mode Instability;100
1.3.3.7.4;3.7.4 Ballooning Mode Instability;102
1.3.4;Chapter 4:
Waves in Plasmas;104
1.3.4.1;4.1 Electrostatic Waves;104
1.3.4.1.1;4.1.1 Waves Without an External Magnetic Field;104
1.3.4.1.2;4.1.2 Waves With an External Magnetic Field B
0;106
1.3.4.2;4.2 Electromagnetic Waves;109
1.3.4.2.1;4.2.1 Waves Without an External Magnetic Field;109
1.3.4.2.2;4.2.2 Waves With an External Magnetic Field B
0;110
1.3.4.2.2.1;4.2.2.1 Ordinary Wave (E ||
B0);110
1.3.4.2.2.2;4.2.2.2 Extraordinary Wave (E
B0);110
1.3.4.2.2.3;4.2.2.3 L-wave and R-wave;110
1.3.4.3;4.3 MHD Wave;111
1.3.4.3.1;4.3.1 Alfven Wave;111
1.3.4.3.2;4.3.2 Magnetosonic Wave;112
1.3.4.4;4.4 Wave Energy;112
1.3.4.5;4.5 Negative Energy Wave;114
1.3.4.6;4.6 Instabilities in Plasmas;116
1.3.4.6.1;4.6.1 Streaming Instability;117
1.3.4.6.2;4.6.2 Gradient Instability;120
1.3.4.6.3;4.6.3 Gravitational Instability;123
1.4;Part II:
Nonlinear Theory of Plasmas;126
1.4.1;Chapter 5:
Nonlinear Interactions in Plasmas;127
1.4.1.1;5.1 Nonlinear Wave Equation;128
1.4.1.2;5.2 Resonant Three Wave Interaction;130
1.4.1.2.1;5.2.1 Parametric Instability;134
1.4.1.2.2;5.2.2 Resonant Decay Interaction;135
1.4.1.2.3;5.2.3 Resonant Explosive Interaction;137
1.4.1.2.4;5.2.4 Chaos in Resonant Three-Wave Interaction with Dissipation and Frequency Mismatch;138
1.4.1.2.5;5.2.5 Coupled Solitons in Resonant Three-Wave Interaction;141
1.4.1.2.6;5.2.6 Spatio-Temporal Evolution in Three Wave Resonant Interaction;143
1.4.1.3;5.3 Self-Interaction and Modulation Instability;144
1.4.1.4;5.4 Nonlinear Wave-Particle Interaction;147
1.4.1.4.1;5.4.1 Nonlinear Landau Damping;147
1.4.1.4.2;5.4.2 Ponderomotive Potential Force and Magnetization;149
1.4.1.4.2.1;5.4.2.1 Ponderomotive Potential Force;149
1.4.1.4.2.2;5.4.2.2 Ponderomotive Magnetization;151
1.4.1.5;5.5 Weak Turbulence Theory;154
1.4.1.6;5.6 Kinetic Theory for Waves as Quasi-Particles;159
1.4.1.7;5.7 Modulation Instability of Plasmon Gas;160
1.4.2;Chapter 6:
Solitons in Plasmas;164
1.4.2.1;6.1 Ion Acoustic Waves and K-dV Equation;165
1.4.2.1.1;6.1.1 Reductive Perturbation Theory and K-dV Equation;166
1.4.2.1.2;6.1.2 Kinetic Theory Derivation of K-dV Equation;167
1.4.2.1.3;6.1.3 Stationary Solutions of K-dV Equation;169
1.4.2.1.4;6.1.4 Sagdeev Potential;169
1.4.2.1.5;6.1.5 Fermi–Pasta–Ulam Problem;171
1.4.2.1.6;6.1.6 K-dV Equation in the Continuum Limit of FPU Problem and Solitons;172
1.4.2.2;6.2 Langmuir Waves and Envelope Solitons;174
1.4.2.2.1;6.2.1 Langmuir Waves and Nonlinear Schrödinger Equation;174
1.4.2.2.2;6.2.2 Modulation Instability of Finite Amplitude Langmuir Wave;175
1.4.2.3;6.3 Solitons and Inverse Scattering Method;176
1.4.2.3.1;6.3.1 K-dV Equation;176
1.4.2.3.1.1;6.3.1.1 One-Soliton Solution;179
1.4.2.3.1.2;6.3.1.2 Two-Soliton Solution;179
1.4.2.3.2;6.3.2 Nonlinear Shrödinger Equation;180
1.4.2.4;6.4 Solitons and Bilinear Transformation;184
1.4.2.4.1;6.4.1 K-dV Equation;184
1.4.2.4.2;6.4.2 Nonlinear Schrödinger Equation;185
1.4.2.5;6.5 Soliton-Like Excitations in Plasmas With Multiple Modes;186
1.4.2.5.1;6.5.1 Basic Equations for Nonlinear Wave Propagation in An Ion Beam-Plasma System;187
1.4.2.5.2;6.5.2 Characteristic Times for Onset of The Explosive Instability and Soliton Formation;190
1.4.2.5.3;6.5.3 Numerical Solutions;192
1.4.2.5.4;6.5.4 K-dV Approximation for SmallAmplitude Nonlinear Modes;194
1.4.2.5.5;6.5.5 Nonlinear Explosion Modes;195
1.4.2.5.6;6.5.6 Beam Reflection and Soliton Emission;197
1.4.2.5.6.1;6.5.6.1 Linearly Stable Cases;198
1.4.2.5.6.2;6.5.6.2 Linearly Unstable Cases;201
1.4.2.6;6.6 Soliton-Like Excitations in Linearly Unstable Plasmas;203
1.4.2.6.1;6.6.1 Basic Equations for Long Wave Buneman Instability;204
1.4.2.6.2;6.6.2 Pulsating Solitons;206
1.4.2.6.3;6.6.3 Ordinary Solitons;207
1.4.2.6.4;6.6.4 Temporally Localized and Spatially Periodic Solitons;208
1.4.3;Chapter 7:
Vortical Motions in Plasmas;209
1.4.3.1;7.1 Two Dimensional Vortices;211
1.4.3.2;7.2 Point Vortex;214
1.4.3.3;7.3 Vortical Motions in Plasmas;217
1.4.3.3.1;7.3.1 Drifts for Driving Vortical Motions;217
1.4.3.3.2;7.3.2 Vortices in Electron Plasmas;219
1.4.3.3.3;7.3.3 Convective Cells;221
1.4.3.3.4;7.3.4 Drift Wave Vortices;222
1.4.3.3.4.1;7.3.4.1 Dipole Vortex Solutions;224
1.4.3.3.5;7.3.5 Particle Transport Due to Drift Wave Vortices;226
1.4.3.3.6;7.3.6 Ion Heat Transport Due to Drift Wave Vortices;227
1.4.3.3.7;7.3.7 Zonal Flow;228
1.4.3.3.8;7.3.8 Self-Organization of Monopole Vorticesin Temperature Inhomogeneity;230
1.4.3.4;7.4 Collisional Drift Wave Instability and Formationof Dipole Vortices;233
1.4.3.4.1;7.4.1 Point Vortex Description for Drift Wave Vortices;241
1.4.3.4.1.1;7.4.1.1 Dipole Vortex Solutions;244
1.4.3.4.1.2;7.4.1.2 Collision Processes of Dipole Vortices;247
1.4.3.4.2;7.4.2 Kinetic Theory of Vortex Diffusion;248
1.4.3.5;7.5 Vortex Collapse Revisited;252
1.4.3.5.1;7.5.1 Vortex Collapse;252
1.4.3.5.2;7.5.2 Boomerang Interaction of Three Vortices ;255
1.4.3.6;7.6 Spiral Structures in Magnetized Rotating Plasmas;258
1.4.4;Chapter 8:
Chaos in Plasmas;265
1.4.4.1;8.1 Chaos in Conservative Systems;265
1.4.4.1.1;8.1.1 Pendulum;265
1.4.4.1.2;8.1.2 Resonance;268
1.4.4.1.3;8.1.3 Resonance in Multiple Periodic Systems;270
1.4.4.2;8.2 Poincarè Mapping;272
1.4.4.2.1;8.2.1 Integrable System;272
1.4.4.2.2;8.2.2 Non Integrable System;272
1.4.4.2.2.1;8.2.2.1 Perturbed Twist Map;272
1.4.4.2.2.2;8.2.2.2 Radial Twist Map;273
1.4.4.3;8.3 Standard Map;274
1.4.4.3.1;8.3.1 Chaos in Standard Map;275
1.4.4.3.1.1;8.3.1.1 Primary Resonance Overlap;277
1.4.4.3.1.2;8.3.1.2 Secondary Resonance Overlap;278
1.4.4.3.2;8.3.2 Global Chaos: Greene's Method;279
1.4.4.4;8.4 Chaos in Dissipative Systems;279
1.4.4.4.1;8.4.1 Attractors and Strange Attractors;279
1.4.4.4.2;8.4.2 Bifurcation Theory;280
1.4.4.4.2.1;8.4.2.1 Tangent Bifurcation;280
1.4.4.4.2.2;8.4.2.2 Exchange of Stability;281
1.4.4.4.2.3;8.4.2.3 Pitchfork Bifurcation;282
1.4.4.4.2.4;8.4.2.4 Reversed Pitchfork Bifurcation;282
1.4.4.4.2.5;8.4.2.5 Hopf Bifurcation;283
1.4.4.4.3;8.4.3 Period Doubling Route to Chaos: Logistic Map;284
1.4.4.4.3.1;8.4.3.1 Fixed Points of
f;284
1.4.4.4.3.2;8.4.3.2 Fixed Points of f2;285
1.4.4.4.3.3;8.4.3.3 Accumulation of Period Doubling and Renormalization;286
1.4.4.5;8.5 Fractal Structure;288
1.4.4.6;8.6 Lyapunov Exponents;289
1.4.4.7;8.7 Dimension of Attractor;290
1.4.4.8;8.8 Correlation Dimension;291
1.4.4.9;8.9 Construction of Attractor with Observed Signal;291
1.4.4.10;8.10 Intermittent Chaos;293
1.4.4.10.1;8.10.1 Type I Intermittency;294
1.4.4.10.2;8.10.2 Type II Intermittency;294
1.4.4.10.3;8.10.3 Type III Intermittency;295
1.4.4.11;8.11 Chaos in Plasmas;296
1.4.4.11.1;8.11.1 Stochastic Web;296
1.4.4.11.2;8.11.2 Chaos of Particle Motion in a Magnetic Mirror Field;299
1.4.4.11.3;8.11.3 Chaos in a Current-Carrying Ion Sheath;304
1.4.4.11.4;8.11.4 Chaos of Magnetic Field Lines;308
1.4.4.11.5;8.11.5 Anomalous Transport in Tokamak and Tokamap;310
1.4.4.11.5.1;8.11.5.1 Toroidal Coupling and Transport Barrier;310
1.4.4.11.5.2;8.11.5.2 Tokamap;310
1.4.4.11.6;8.11.6 Ponderomotive Force at the Onset of Chaos;311
1.4.5;Chapter 9:
Ponderomotive Potential and Magnetization;317
1.4.5.1;9.1 Hamiltonian Formulation of Ponderomotive Interactions in a Vlasov Plasma;317
1.4.5.2;9.2 The Hydrodynamics of Ponderomotive Interactions in a Collisionless Plasma;323
1.4.5.3;9.3 Spontaneous Generation of Magnetostatic Fields;328
1.4.5.3.1;9.3.1 Coupled Mode Equations;329
1.4.5.3.2;9.3.2 Parametric Instability Analysis;329
1.5;Part III:
Structures in Strong Plasma Turbulence;332
1.5.1;Chapter 10:
Strong Langmuir Turbulence;333
1.5.1.1;10.1 Introduction;333
1.5.1.2;10.2 Derivation of the Generalized Zakharov Equations;334
1.5.1.3;10.3 Adiabatic Scaling and Spherical Collapse;341
1.5.1.4;10.4 Qualitative Discussion of the Collapse;344
1.5.2;Chapter 11:
Wave Collapse in Plasmas;346
1.5.2.1;11.1 Langmuir Soliton Stability and Collapse;346
1.5.2.1.1;11.1.1 Introduction;346
1.5.2.1.2;11.1.2 Basic Equations;348
1.5.2.1.3;11.1.3 Variational Treatment of Soliton Stability;350
1.5.2.1.4;11.1.4 Numerical Treatment;352
1.5.2.1.5;11.1.5 Nonlinear Stage of Soliton Instability;356
1.5.2.1.6;11.1.6 Self-Similarity and Collapse Regimes;358
1.5.2.2;11.2 Virial Theory of Wave Collapse;363
1.5.2.3;11.3 Hierarchy of Collapse Regimes in a Magnetized Plasma;365
1.5.2.3.1;11.3.1 Introduction;366
1.5.2.3.2;11.3.2 Model Equation;366
1.5.2.3.3;11.3.3 Nonexistence of Three-Dimensional Solitons;368
1.5.2.3.4;11.3.4 Necessary Condition for Wave Collapse;370
1.5.2.3.5;11.3.5 Classification of Wave Collapse Regimes;372
1.5.2.4;11.4 Weak and Strong Langmuir Collapse;374
1.5.2.4.1;11.4.1 Preliminaries;375
1.5.2.4.2;11.4.2 Nonlinear Model Equations;375
1.5.2.4.3;11.4.3 Simulation Results and Discussions;377
1.5.3;Chapter 12:
Spatiotemporal Complexity in Plasmas;380
1.5.3.1;12.1 Spatiotemporal Effects in Three-Wave Interaction;380
1.5.3.1.1;12.1.1 Convective and Absolute Instability;381
1.5.3.1.2;12.1.2 Space-Only Problem in Three Wave Interaction;383
1.5.3.1.3;12.1.3 Spatiotemporal Evolution in Three-Wave Interaction;385
1.5.3.2;12.2 Complexity in Laser Plasma Instabilities;388
1.5.3.2.1;12.2.1 Introduction to Stimulated Raman Scattering;388
1.5.3.2.2;12.2.2 Nonlinear Saturation of SRS;390
1.5.3.2.3;12.2.3 Break-up of Manley–Rowe Invariantsand Nonstationary SRS;393
1.5.3.2.4;12.2.4 Bifurcations and Route to Low-Dimensional Chaos;393
1.5.3.2.5;12.2.5 Complexity of Spatiotemporal Wave Patterns;397
1.5.3.2.6;12.2.6 Quantitive Signatures of Spatiotemporal Regimes;400
1.5.3.2.7;12.2.7 Transition from Spatiotemporal Intermittency to Spatiotemporal Chaos;403
1.5.3.2.8;12.2.8 Summary;406
1.5.3.3;12.3 Self-Organization in a Dissipative 3WI-Saturated SRS Paradigm;407
1.5.3.3.1;12.3.1 Introduction;407
1.5.3.3.2;12.3.2 Preliminaries on Nonlinear Kinetic SRS;408
1.5.3.3.3;12.3.3 Dissipative SRS Saturation Model;409
1.5.3.3.4;12.3.4 Kinetic-Hybrid Scheme;410
1.5.3.3.5;12.3.5 Open Boundary Model;413
1.5.3.3.6;12.3.6 Self-Organization at Micro- and Macro-Scales;414
1.5.3.3.7;12.3.7 Dissipative Structures and Entropy Rate;419
1.5.3.3.8;12.3.8 Summary;422
1.5.4;Chapter 13:
Relativistic Laser Plasma Interactions;424
1.5.4.1;13.1 Electronic Parametric Instabilities;425
1.5.4.1.1;13.1.1 Stimulated Raman Scattering;426
1.5.4.1.2;13.1.2 Relativistic Dispersion Relation for Cold Plasma;426
1.5.4.1.2.1;13.1.2.1 Solutions of Relativistic Dispersion Relation;431
1.5.4.1.3;13.1.3 Summary;434
1.5.4.2;13.2 Computer Simulations of Relativistic Plasmas;435
1.5.4.2.1;13.2.1 Particle-In-Cell Simulations;436
1.5.4.3;13.3 Relativistic Electromagnetic Solitons;437
1.5.4.3.1;13.3.1 Dynamical Equations;438
1.5.4.3.2;13.3.2 Relativistic Soliton Stability;441
1.5.4.3.3;13.3.3 Soliton Dynamics;443
1.5.4.3.4;13.3.4 Strongly-Relativistic Solitons;443
1.5.4.4;13.4 Stimulated Raman Cascade into Photon Condensation;447
1.5.4.4.1;13.4.1 Introduction;447
1.5.4.4.2;13.4.2 Relativistic Fluid-Maxwell Simulation;450
1.5.4.4.3;13.4.3 Particle Simulations;454
1.5.4.4.3.1;13.4.3.1 Stimulated Raman Cascade into Photon Condensation;455
1.5.4.4.3.2;13.4.3.2 Effect of Laser Intensity on SRS Cascadeinto Photon Condensation;459
1.5.4.5;13.5 Relativistic EM Solitons in a Low Density Plasma;463
1.5.4.5.1;13.5.1 Introduction;464
1.5.4.5.2;13.5.2 Relativistic EM Solitons;464
1.5.4.5.2.1;13.5.2.1 Standing EM Solitons;466
1.5.4.5.2.2;13.5.2.2 Backward- and Forward Accelerated EM solitons;467
1.5.4.5.2.3;13.5.2.3 Merging of Two Relativistic EM Solitons;470
1.5.4.6;13.6 Stimulated Electron Acoustic Scattering;470
1.5.4.6.1;13.6.1 The Electron Acoustic Waves;471
1.5.4.6.2;13.6.2 Stimulated Raman and Acoustic Wave Scattering;471
1.5.4.6.3;13.6.3 SEAS Model ;473
1.5.4.6.4;13.6.4 Simulations of SEAS;475
1.5.4.7;13.7 Trapped SEAS, EM Soliton and Ion-Vortices in Subcritical Plasmas;477
1.5.4.7.1;13.7.1 Introduction;478
1.5.4.7.2;13.7.2 Stimulated Trapped Electron Acoustic Wave Scattering;479
1.5.4.7.3;13.7.3 Electromagnetic Soliton and Ion-Vortices;482
1.6;Part IV:
Multiscale Plasma Interactions;487
1.6.1;Chapter 14:
Multifractal Characterization of Plasma Edge Turbulence;488
1.6.1.1;14.1 Introduction;488
1.6.1.2;14.2 Edge Turbulence Datasets;489
1.6.1.3;14.3 Quantification of Long-Range Dependence;489
1.6.1.3.1;14.3.1 Wavelet Transform of Scaling Processes;492
1.6.1.3.2;14.3.2 Log-Scale Diagrams of Turbulent Datasets;493
1.6.1.3.3;14.3.3 Testing Time Constancy of Scaling Exponents;495
1.6.1.3.4;14.3.4 Randomization Method for Long Range Correlations;497
1.6.1.4;14.4 Multifractal Properties of Datasets;500
1.6.1.4.1;14.4.1 Basic Properties of Multifractal Processes;500
1.6.1.4.2;14.4.2 Multiscale Diagrams and Wavelet Coefficients;502
1.6.1.4.3;14.4.3 Multiscale Diagrams and MultifractalSpectra for L and H Modes;503
1.6.1.5;14.5 Coupled Effects of Long-Range Dependenceand Intermittency;510
1.6.1.6;14.6 Conclusion;513
1.6.2;Chapter 15:
Multi-Scale Modelling of Nonlinear Plasmas;515
1.6.2.1;15.1 Basics on Multi-Scale Modelling;515
1.6.2.2;15.2 Multi-Scale Plasma Models;516
1.6.2.3;15.3 Equation-Free Macro-Projective Integration Method;518
1.6.2.4;15.4 The Nonlinear Ion-Sound Wave;520
1.6.2.5;15.5 Electrostatic Particle-In-Cell Code;520
1.6.2.6;15.6 Primal Macro-Projective Simulation Method;521
1.7;References;525
1.8;Index;537