1 Introduction .................................................. 1
1.1 General Overview ......................................... 1
1.2 Complexity of the Inner Magnetosphere .................... 5
References .................................................... 8
2 Kinetic Equations and Particle Collisions .................... 11
2.1 Kinetic and Maxwell Equations ........................... 11
2.2 Elastic Collisions ...................................... 13
2.3 Inelastic Collisions .................................... 17
2.4 Plasma Source ........................................... 20
2.5 Superthermal Electron Kinetic Equation Simplification ... 24
References ................................................... 26
3 General Description of Wave-Particle Interaction Phenomena ... 27
3.1 Plasma Electrodynamics .................................. 27
3.2 Energy of the Electromagnetic Field ..................... 31
3.3 Electromagnetic Waves ................................... 34
3.4 Dielectric Tensor of Collisionless Plasma ............... 36
3.5 Maxwellian Plasma ....................................... 41
3.6 Cold Plasma Approximation ............................... 43
3.7 Wave Damping and Growth ................................. 46
3.8 The Quasilinear Approximation ........................... 53
3.9 Nonlinear Drift-Kinetic Equation ........................ 56
References ................................................... 62
4 Hydrodynamic Description of Space Plasma ..................... 65
4.1 Moments of the Kinetic Equation ......................... 65
4.2 General Transport Equations ............................. 72
4.3 The 16-Moment Approximation ............................. 79
4.4 Coulomb Collision Terms ................................. 82
4.4.1 General Expressions .............................. 82
4.4.2 Collisions with Superthermal Electrons ........... 86
4.5 Collisions with Neutral Particles ....................... 90
4.5.1 Electrons ........................................ 90
4.5.2 Ions ............................................. 98
4.6 Wave-Particle Interaction Terms ........................ 102
4.6.1 Quasilinear Interaction in Hydrodynamics:
General Relationships ........................... 103
4.6.2 Moments in a Bi-Maxwellian plasma ............... 108
4.6.3 Moments in the Absence of a Transverse Drift .... 110
4.7 Heat Balance Equation in the Presence of Temperature
Anisotropy ............................................. 113
4.8 Equations of Anisotropic Hydrodynamics for Modeling
the Ionosphere-Magnetosphere Plasma .................... 119
References .................................................. 121
5 Transport of Superthermal Electrons: General Analysis ....... 125
5.1 Exact Solution of the Collisionless Drift Kinetic
Equation ............................................... 125
5.1.1 Introduction .................................... 125
5.1.2 Moments of the Velocity Distribution Function ... 128
5.1.3 The Generalized Approach ........................ 130
5.1.4 Implementation .................................. 133
5.2 Legendre Polynomial Expansion .......................... 140
5.3 Description of Electron-Electron Collisions in the
Lower Ionosphere ....................................... 146
5.3.1 Lower Energies .................................. 146
5.3.2 Fine Structure of Photoelectron Fluxes .......... 149
5.4 Pitch-Angle Distribution in the Upper Ionosphere ....... 154
5.5 Transport in the Plasmasphere .......................... 159
5.5.1 Infinite Trapped Zone Approximation ............. 162
5.5.2 The Distribution Function of Superthermal
Electrons in the Plasmasphere ................... 165
5.5.3 Plasmaspheric Transparency and Heating Rate ..... 170
5.6 Thermal Electron Heating Rate .......................... 174
5.7 The Loss Cone Distribution ............................. 184
References .................................................. 188
6 Analysis of Cold Plasma Transport ........................... 193
6.1 Convective Plasma Motion in the Magnetosphere .......... 193
6.2 Density Distribution ................................... 194
6.2.1 Model of the Electric Field ..................... 194
6.2.2 Effects of Perpendicular Transport on
Equatorial Density .............................. 196
6.2.3 Plasma Distribution Along a Field Line .......... 201
6.3 Effects of Magnetospheric Convection on Temperature .... 205
6.3.1 Adiabatic Variations ............................ 206
6.3.2 Heat Conduction ................................. 209
6.4 Plasma Electron Temperature Anisotropy ................. 211
6.4.1 The Effect of Anisotropy on Electron
Temperature in the Plasmasphere ................. 212
6.4.2 Electron Temperature Anisotropy Estimations ..... 215
6.4.3 Discussion ...................................... 229
6.5 Heating and Cooling of the Plasmasphere ................ 232
6.5.1 Electron Energy Equation and Sources of
Heating ......................................... 233
6.5.2 Electron Temperatures in the Upper Ionosphere ... 234
6.5.3 Plasmaspheric Solution .......................... 235
6.5.4 Analysis ........................................ 237
6.6 Polar Wind ............................................. 241
6.6.1 Historical Remarks .............................. 241
6.6.2 General Relations ............................... 244
6.6.3 The Solution of the Kinetic Equation ............ 245
6.6.4 Moments of the Velocity Distribution Function ... 247
6.6.5 Thermal Electron Fluid Equations ................ 249
6.6.6 The Necessity of a Generalized Model ............ 251
6.6.7 Applications of the General Formulation ......... 256
References .................................................. 263
7 Kinetic Theory of Superthermal Electron Transport ........... 271
7.1 Superthermal Electron Studies .......................... 271
7.2 Ionosphere-Plasmasphere Superthermal Electrons
Coupling ............................................... 272
7.2.1 Mathematical Formulation ........................ 272
7.2.2 Steady-State Solution ........................... 276
7.2.3 Nonsteady-State Solution ........................ 279
7.2.4 Plasmaspheric Transparency ...................... 284
7.2.5 Plasmaspheric Energy Interplay .................. 289
7.2.6 Comparison with Observations .................... 292
7.3 Global Superthermal Electron Transport ................. 294
7.3.1 The Field-Aligned and Bounce-Averaged Models .... 295
7.3.2 Combined Global Model ........................... 297
7.3.3 Numerical Implementation ........................ 298
7.3.4 The Low-Energy Limit ............................ 300
7.3.5 Photoelectron Distribution Function Formation ... 304
7.3.6 Injection of Plasma Sheet Electrons ............. 309
7.3.7 The Combined Electron Distribution Function ..... 312
7.4 Artificial Relativistic Electrons Injection ............ 317
7.4.1 Interhemispheric Transport ...................... 318
7.4.2 Global Transport ................................ 325
7.5 Magnetospheric Convection Electric Field Dynamics and
Storm-Time Particle Energization ....................... 351
7.5.1 Electric Fields Models .......................... 351
7.5.2 Model Description ............................... 353
7.5.3 The 1-7 May 1998 Storm .......................... 355
7.5.4 Results ......................................... 356
References .................................................. 368
8 Kinetic Superthermal Electron Instabilities in the
Ionosphere .................................................. 377
8.1 The Generation of Plasma Oscillations by
Photoelectrons ......................................... 377
8.1.1 Dielectric Permittivity of Plasma ............... 377
8.1.2 Cherenkov Resonance ............................. 379
8.1.3 Cyclotron Resonance ............................. 385
8.1.4 Double Resonance ................................ 388
8.2 High-Frequency Fluctuations in the Ionospheric
Plasma ................................................. 390
8.2.1 Fluctuations of a Non-equilibrium Stable
Plasma .......................................... 390
8.2.2 Coulomb Scattering in a Weakly Non-equilibrium
Plasma .......................................... 393
8.2.3 Unstable Plasma Fluctuations .................... 396
8.3 Relaxation of Electron Fluxes in the Auroral
Ionosphere ............................................. 399
8.3.1 The Origin of Electron Beams .................... 399
8.3.2 Peculiarities of the Plasma Noise Distribution
in the Auroral Ionosphere ....................... 406
8.3.3 Instabilities of the Secondary Electrons in
the Region of Their Production .................. 409
8.4 Some Radio Physical Effects of Superthermal
Electrons .............................................. 413
8.4.1 The RIS Spectrum in the Presence of
Photoelectrons: Diagnostic of Aeronomical
Parameters ...................................... 414
8.4.2 Ground-Based Diagnostic of Photoelectron
Fluxes .......................................... 421
8.4.3 Generation of VLF Emission ...................... 423
References .................................................. 425
9 Kinetic Theory of Ring Current and Electromagnetic Ion
Cyclotron Waves: Fundamentals ............................... 429
9.1 General Overview ....................................... 429
9.1.1 Terrestrial Ring Current ........................ 429
9.1.2 Electromagnetic Ion Cyclotron Waves ............. 431
9.2 EMIC Wave Generation and Propagation in
Magnetosphere .......................................... 434
9.2.1 EMIC Wave Modes in Multicomponent Plasma ........ 434
9.2.2 Propagation in the Magnetosphere ................ 438
9.2.3 Tunneling Effects ............................... 441
9.3 Bouncing EMIC Waves Versus Unidirectional
Propagation ............................................ 445
9.3.1 Poynting Flux Analysis: No Reflection ........... 446
9.3.2 Poynting Flux Analysis: With Reflection ......... 448
9.3.3 EMIC Wave Ellipticity Argument .................. 454
9.3.4 Convective Instability Argument ................. 456
9.4 Governing Equations .................................... 458
9.4.1 Wave Kinetic Equation ........................... 458
9.4.2 Ring Current Particle Transport ................. 462
9.4.3 Coupling with the Magnetospheric Electric
Field ........................................... 463
9.4.4 Simulation Scenarios ............................ 465
9.5 The EMIC Wave Normal Angle Distribution ................ 471
9.5.1 Prediction from Theory .......................... 471
9.5.2 Comparison with Observations .................... 476
9.6 The Effect of Ring Current H+ Density .................. 479
References .................................................. 482
10 Kinetic Theory of Ring Current and Electromagnetic Ion
Cyclotron Waves: Applications ............................... 491
10.1 Wave-Induced Precipitated RC Fluxes .................... 491
10.2 Heating of Thermal Plasmaspheric Electrons and
Subauroral Ionospheric Temperature Enhancement ......... 494
10.2.1 EMIC Wave and Coulomb Heating of Thermal
Plasmaspheric Electrons ......................... 494
10.2.2 Electron Heating Events in Subauroral Topside
Ionosphere: Qualitative Comparison with
Observations .................................... 498
10.2.3 Relationship of Wave Heating to SAR Arcs ........ 501
10.3 Associated Global Inner Magnetosphere Environment ...... 502
10.3.1 Magnetospheric Electric Field ................... 502
10.3.2 Plasmasphere .................................... 505
10.4 Relativistic Electrons Scattering by EMIC Waves ........ 507
10.4.1 Introduction .................................... 507
10.4.2 Pitch-Angle Diffusion Coefficients: Model
Calculations .................................... 509
10.4.3 Bounce-Averaged Diffusion Coefficient: Self-
Consistent Calculations ......................... 513
10.4.4 CRRES-Based Calculations ........................ 515
10.5 The Nonlinear Coupling of Electromagnetic Ion
Cyclotron and Lower Hybrid Waves in the Ring Current
Region ................................................. 521
10.5.1 Lower Hybrid Waves .............................. 521
10.5.2 Generation of Lower Hybrid Waves ................ 523
10.5.3 Results and Discussion .......................... 531
References .................................................. 535
Concluding Remarks ............................................. 541
Appendix A ..................................................... 545
Appendix В ..................................................... 549
Appendix С ..................................................... 553
Appendix D ..................................................... 557
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