Nonlinear MHD Waves and Turbulence

0536titl......Page 1
Preface......Page 5
Contents......Page 6
1 Introduction......Page 10
2 Dispersive Alfvén Waves in a Uniform Plasma......Page 12
3.1 The Excitation by Electron Beams......Page 14
3.2 Parametric Excitation......Page 15
4 Nonlinear Effects Caused by Inertial Alfvén Waves......Page 19
5 Amplitude Modulation of Kinetic Alfvén Waves......Page 23
6 Modulation of MICA Waves......Page 25
7.1 Derivation of the Nonlinear Equations......Page 27
7.2 The Dispersion Relation in an Inhomogeneous Plasma......Page 29
7.3 Quasi-Stationary Dipolar Vortices......Page 30
8 Chaos in Alfvénic Turbulence......Page 33
9 Summary and Conclusions......Page 35
References......Page 37
1 Introduction......Page 40
2 Basic Equations. Sla Ducts......Page 41
3 Full Wave Solutions for the Sla Ducts......Page 46
4 Sla Whistler Solitons......Page 50
5 Self-Focusing of Whistler Wave Beams......Page 53
6 Concluding Remarks......Page 60
References......Page 61
1 Introduction......Page 63
2.1 Modulation Analysis......Page 65
2.2 Convective Filamentation......Page 68
2.3 Energy Dissipation and Application to the Solar Corona......Page 70
2.4 Coupling to Low-Frequency Magneto-Sonic Waves......Page 71
3 Filamentation of Weakly Dispersive Wave Trains......Page 73
3.1 Envelope Dynamics......Page 75
3.2 Dissipation of Weakly Dispersive Alfvé Wave......Page 80
4.1 Equations for the Long-Wavele gth Dynamics when ß is Far From Unity......Page 83
4.2 Long-Wavelength Dynamics for ß ~ 1......Page 86
4.3 Transverse Modulational Analysis of the Generalized DNLS Equations......Page 88
5 Conclusions......Page 89
References......Page 90
1 Introduction......Page 92
2 Basic Equations and Assumptions......Page 93
3 Derivation of the Governing Equations......Page 96
4 Energetics......Page 99
5 Multistability......Page 100
5.1 One-Mode Approximation......Page 101
5.2 Numerical Results......Page 106
6 Solutions with Shocks and High-Reynolds-Number Bifurcations......Page 107
7 Conclusions......Page 110
References......Page 111
1 Introduction......Page 113
2.1 Effects of Density Stratification and Hall Currents......Page 116
2.2 Alvén Waves in a Spiral External Magnetic Field......Page 124
2.3 Effects of Vertical Mean Flow in a Plane Parallel Atmosphere......Page 129
2.4 Steepening of the Energy Spectrum with Kolmogorov or Kraichnan Exponents......Page 134
3 Models Combining Radial Stratification, Mean Flow and Monopole External Magnetic Field......Page 141
2.1 One- and Three-Dimensional Alfvén Waves in a Radial Uniform Mean Flow......Page 142
2.2 Exacts Solution for Mean Flow Velocity Proportional to the Radius......Page 147
2.3 Effects of the Transition Layer on the Properties of Alfvén Waves......Page 152
2.4 Wave Transmission at the Critical Layer and Modification of the Wave Fields......Page 158
References......Page 165
1 Introduction......Page 169
2.1 Inertial Effect in a Cosmic Ray Plasma......Page 170
2.2 Relativistic MHD......Page 172
2.4 Relativistic Hada’s System......Page 174
3.1 Electrostatic Potential in the Wavefront......Page 175
3.2 Nonlinear Landau Damping of Waves......Page 176
4 Electron-Positron Plasma......Page 177
5.1 The Acceleration Scheme......Page 178
5.2 The Non-relativistic Second and First Order Processes......Page 181
6 Astrophysics Consequences and Head on Collision of Solitons......Page 183
7.1 Pitch Angle Scattering by Delocalized Waves......Page 185
8 Conclusion......Page 188
References......Page 189
1 Introduction......Page 191
2 The Four-Field Model......Page 194
3 The NI-MH Model......Page 197
4 Four-Field Simulations: Implications for Pressure Fluctuations......Page 199
5 Anisotropic Spectra in Weak Turbulence Theory......Page 201
References......Page 205
1 Alfvén Waves Observed in the Solar Wind......Page 207
2.1 Propagation throught a Static Atmosphere......Page 208
2.2 Propagation in the Solar Wind......Page 210
3 Observations of Alfvén Wave Generation......Page 213
4 Non-linear Propagation in the Lower Atmosphere: Parametric Decay and Filamentation......Page 217
5 Alfvén Solitons in the Solar Wind......Page 224
6 Conclusions......Page 229
References......Page 230
1 Introduction......Page 231
2 A Model for Alfvén Wave Interaction with Heliospheric Current Sheet......Page 234
2.1 Numerical Model......Page 235
2.2 Numerical Technique......Page 236
2.3 Initial Condition......Page 237
3.1 Time Evolution of the Alfvénic Correlation......Page 239
3.2 Time Evolution of the Spectra......Page 241
3.3 Density Magnetic Field Intensity Correlation......Page 244
4 The Effects of an Inhomogeneous Entropy Distribution......Page 247
4.1 A Physical Mechanism to Gener te Negative n-Tp Correlation......Page 249
4.2 A Numerical Model with Inhomogeneous Entropy Distribution......Page 251
4.3 Density–Temperature Correlations......Page 252
5 Discussion and Conclusions......Page 254
Acknowledgements......Page 256
References......Page 257
1 Introduction......Page 260
2 Coherent Ion Acoustic Waves in the Solar Wind......Page 261
3.1 S3-3, VIKING, POLAR, and FAST Observations in the Earth’s Auroral Regions......Page 267
3.2 GEOTAIL and WIND Recent Observations in Other Parts of the Magnetosphere......Page 270
3.3 Comparative Analysis of the Wave Properties......Page 271
4 Theoretical Interpretat ons......Page 272
References......Page 274
1 Observational Background......Page 278
2.1 Hyperresistivity and Hyperviscosity......Page 285
2.2 Generalized Dissipation Operators......Page 287
2.3 Hall MHD and Finite Larmor Radius Corrections......Page 289
2.4 Kinetic Effects: Quasi-Invariants and Coarse-Graining......Page 293
3 Summary and Conclusions......Page 295
References......Page 296
1 Introduction and General Discussion......Page 300
1.1 Alfvén Weak Turbulence: the Kinematics, the Asymptotic Closure, and Some Results......Page 301
2 The Derivation of the Kinetic Equations......Page 307
2.1 The Basic Equations......Page 308
2.2 Toroidal and Poloidal Fields......Page 309
2.3 Moments and Cumulants......Page 310
2.4 The Kinetic Equations......Page 312
3.1 Dynamical Decoupling in the Direction Parallel to B0......Page 313
3.3 Properties of Rs and Is......Page 314
3.4 Purely 2D Modes and Two-Dimensionalisation of 3D Spectra......Page 315
5 Two-Dimensional Problem......Page 317
5.1 Kolmogorov Spectra......Page 318
5.2 Temporal Evolution of the Kinetic Equations......Page 324
6 Front Propagation......Page 327
7 Nonlocal Isotropic 3D MHD Turbulence......Page 332
8 Conclusion......Page 333
Appendix......Page 335
References......Page 337
1 Introduction......Page 340
2 Models with Nearest Neighbour Interactions......Page 341
3 Models with Nearest and Next-Nearest Interactions......Page 342
4 Dynamo Action in MHD Shell Models......Page 344
5 Spectral Properties in Stationary Forced State......Page 347
6 Fluxes, Inertial Range, and Intermittency......Page 348
7 Conclusions......Page 352
References......Page 353
1 Introduction......Page 355
2 General Remarks......Page 358
3 Vortex Line Representation......Page 362
4 Variational Principle......Page 365
5 Integrable Hydrodynamics......Page 366
6 Lagrangian Description of MHD......Page 368
7 Frozen-In MHD Fields......Page 370
8 Relabeling Symmetry in MHD......Page 373
9 Variational Principle for Incompressible MHD......Page 375
References......Page 376
1 Introduction......Page 378
2 Quasi-Two-Dimensional Hydrodynamics......Page 379
3 Dynamics of the Isolated Vortex Tube......Page 382
4 Vortex Tube in a External Flow......Page 387
5 Interaction of Vortex Tubes......Page 389
6 Instability and Collapse of Traveling Vortex Pair......Page 390
7 Solitons on the Co-rotating Vortex Pair......Page 392
References......Page 394