Nonlinear Cosmic Ray Diffusion Theories (eBook)

Preface 6
Contents 8
Acronyms 13
Chapter 1 The General Scenario 14
1.1 Cosmic Rays 14
1.2 The Unperturbed System 18
1.3 Particle Diffusion and the TGK Formulation 21
1.4 The Physics of Parallel Scattering 24
1.5 The Physics of Perpendicular Scattering 29
1.6 The Diffusion Tensor and Momentum Diffusion 33
1.7 Cosmic Ray Mean Free Paths Deduced from Observations 36
Chapter 2 On Astrophysical Turbulence 42
2.1 General Forms of the Magnetic Correlation Tensor 42
2.2 The Magnetostatic Slab Model 49
2.3 The Magnetostatic 2D Model 53
2.4 Linear and Nonlinear Theories for Stochastic Field Line Wandering 57
2.5 Dynamical Turbulence and PlasmaWave Propagation Effects 65
Chapter 3 The Quasilinear Theory 70
3.1 The Quasilinear Approximation 70
3.2 General Forms of Quasilinear Fokker–Planck Coefficients 72
3.3 Standard QLT (Magnetostatic Slab Turbulence) 76
3.4 Quasilinear Theory for Magnetostatic 2D Turbulence 79
3.5 Quasilinear Transport in the Slab/2D Composite Model 84
3.6 Test-particle Simulations 86
3.7 The Three Problems of QLT 88
Chapter 4 The Nonlinear Guiding Center Theory 95
4.1 The Nonlinear Closure Approximation 95
4.2 The Bieber and Matthaeus Model 99
4.3 The Nonlinear Guiding Center Theory 103
4.4 Analytical Solutions of the NLGC Theory for Magnetostatic Slab Turbulence 105
4.5 NLGC Theory for Slab/2D Composite Geometry 107
Chapter 5 TheWeakly Nonlinear Theory 110
5.1 The Basic Idea of a Nonlinear Transport Theory 110
5.2 The Weakly Nonlinear Resonance Function 112
5.3 The Nonlinear Fokker–Planck Coefficients for Two-component Turbulence 115
5.4 Results of WNLT for the Parallel and the Perpendicular Mean Free Path 119
5.5 Is the Weakly Nonlinear Theory Reasonable? 125
Chapter 6 The Second-order QLT 126
6.1 Nonlinear Pitch-angle Diffusion in Pure Slab Turbulence 126
6.2 The Resonance Function of SOQLT 132
6.3 Comparison with Previous Theories 133
6.4 Analytical Results of SOQLT 136
6.5 Numerical Results for Fokker–Planck Coefficients and Mean Free Paths 139
6.6 Aspects of SOQLT 143
Chapter 7 The Extended Nonlinear Guiding Center Theory 146
7.1 The Slab Problem of Perpendicular Transport 146
7.2 Integration of the Equations of Motion 147
7.3 Application of Quasilinear Theory 148
7.4 The Nonlinear Guiding Center Model 152
7.5 The Extended Nonlinear Guiding Center Theory 156
7.6 Comparison with Test-particle Simulations 158
7.7 Compound Subdiffusion for Pure Slab Turbulence 161
7.8 Aspects of ENLGC Theory 163
Chapter 8 Applications 165
8.1 Particle Transport in the Heliosphere 165
8.2 Particle Acceleration at Perpendicular Shock Waves 178
8.3 Primary-to-Secondary Abundance Ratio of Galactic Cosmic Rays 185
Chapter 9 Summary and Outlook 189
9.1 Summary 189
9.2 Outlook 193
References 197
Index 205