Nonlinear Cosmic Ray Diffusion Theories

Nonlinear Cosmic Ray Diffusion Theories

by Andreas Shalchi

Paperback(Softcover reprint of hardcover 1st ed. 2009)

$169.99
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Overview

This book deals with the physics of cosmic ray diffusion theory, focusing at the physics of nonlinear transport of cosmic rays through turbulent interplanetary or interstellar plasma.

The author discusses fundamental processes such as cosmic ray propagation and acceleration in the solar system or in interstellar space, the properties of such plasmas, the standard quasilinear approach to describing plasma particle interactions as well as several more accurate nonlinear theories, Within a nonlinear treatment he revisits the mechanism of diffusive shock acceleration, Which is responsible for the high cosmic ray energies. Based on new results presented in this book the author proposes future numerical, theoretical and observational research that could advance the field of cosmic ray diffusion theory.

Product Details

ISBN-13: 9783642101397
Publisher: Springer Berlin Heidelberg
Publication date: 12/22/2010
Series: Astrophysics and Space Science Library , #362
Edition description: Softcover reprint of hardcover 1st ed. 2009
Pages: 199
Product dimensions: 6.10(w) x 9.25(h) x 0.02(d)

Table of Contents

1 The General Scenario 1

1.1 Cosmic Rays 1

1.1.1 General Properties of Cosmic Rays 2

1.1.2 Cosmic Rays in the Solar System 4

1.2 The Unperturbed System 5

1.3 Particle Diffusion and the TGK Formulation 8

1.3.1 Mean Square Displacements and Diffusion Coefficients 8

1.3.2 The TGK Formulation 9

1.4 The Physics of Parallel Scattering 11

1.4.1 The Two-Dimensional Fokker-Planck Equation 11

1.4.2 The Diffusion Equation 12

1.4.3 Solution of the Diffusion Equation 15

1.5 The Physics of Perpendicular Scattering 16

1.6 The Diffusion Tensor and Momentum Diffusion 20

1.6.1 Fokker-Planck vs. Diffusion Coefficients 22

1.6.2 Cosmic Ray Momentum Diffusion Due to Electric Fields 23

1.7 Cosmic Ray Mean Free Paths Deduced from Observations 23

1.7.1 Observed Mean Free Paths in the Heliosphere 24

1.7.2 Transport in the Interstellar Medium 26

2 On Astrophysical Turbulence 29

2.1 General Forms of the Magnetic Correlation Tensor 29

2.1.1 The Isotropic Correlation Tensor 30

2.1.2 Axisymmetric Turbulence and Vanishing Magnetic Helicity 32

2.1.3 The Correlation Length 36

2.2 The Magnetostatic Slab Model 36

2.2.1 The Slab Correlation Function 37

2.2.2 The Slab Correlation Length 38

2.3 The Magnetostatic 2D Model 40

2.3.1 The 2D Correlation Function 40

2.3.2 The Correlation Length for Pure 2D Turbulence 43

2.3.3 The Vector Potential of Pure 2D Turbulence 43

2.4 Linear and Nonlinear Theories for Stochastic Field Line Wandering 44

2.4.1 The Initial Free-Streaming Regime 45

2.4.2 Field Line Random Walk for Slab Turbulence 46

2.4.3 Quasilinear Theory of Field Line Random Walk 47

2.4.4 The Nonlinear Approach for Field Line Random Walk 47

2.4.5 TheDiffusion Limit of Matthaeus et al 50

2.5 Dynamical Turbulence and Plasma Wave Propagation Effects 52

2.5.1 Damping and Random Sweeping Models 52

2.5.2 Plasma Wave Turbulence 53

2.5.3 The Nonlinear Anisotropic Dynamical Turbulence Model 54

3 The Quasilinear Theory 57

3.1 The Quasilinear Approximation 57

3.2 General Forms of Quasilinear Fokker-Planck Coefficients 59

3.2.1 General Form of the Pitch-angle Fokker-Planck Coefficient 59

3.2.2 General Form of the Fokker-Planck Coefficient of Perpendicular Diffusion 62

3.3 Standard QLT (Magnetostatic Slab Turbulence) 63

3.3.1 The Pitch-angle Fokker-Planck Coefficient 63

3.3.2 The Parallel Mean Free Path 64

3.3.3 The Perpendicular Mean Free Path 65

3.4 Quasilinear Theory for Magnetostatic 2D Turbulence 66

3.4.1 Pitch-angle Diffusion in Pure 2D Turbulence by Using the Traditional Approach 66

3.4.2 Pitch-angle Diffusion in Pure 2D Turbulence by Using a Vector-potential Approach 67

3.4.3 Perpendicular Diffusion in Pure 2D Turbulence 69

3.5 Quasilinear Transport in the Slab/2D Composite Model 71

3.6 Test-particle Simulations 73

3.6.1 The Simulations of Giacalone and Jokipii 74

3.6.2 The Simulations of Qin 74

3.6.3 Confirmation of QLT for Parallel Diffusion in the Slab Model 74

3.7 The Three Problems of QLT 75

3.7.1 The 90°-Scattering Problem 75

3.7.2 The Problem of Perpendicular Diffusion 78

3.7.3 The Geometry Problem 79

4 The Nonlinear Guiding Center Theory 83

4.1 The Nonlinear Closure Approximation 83

4.1.1 The Results of the NCA 84

4.1.2 Test of the NCA by Comparing it with Simulations 87

4.2 The Bieber and Matthaeus Model 87

4.2.1 The Basic Formulas of the BAM Theory 88

4.2.2 Results of the BAM Theory for Slab Geometry 90

4.2.3 The BAM Theory for Slab/2D Composite Geometry 91

4.3 The Nonlinear Guiding Center Theory 91

4.4 Analytical Solutions of the NLGC Theory for Magnetostatic Slab Turbulence 93

4.5 NLGC Theory for Slab/2D Composite Geometry 95

5 The Weakly Nonlinear Theory 99

5.1 The Basic Idea of a Nonlinear Transport Theory 99

5.2 The Weakly Nonlinear Resonance Function 101

5.3 The Nonlinear Fokker-Planck Coefficients for Two-component Turbulence 104

5.3.1 The Fokker-Planck Coefficient Dslabμμ 104

5.3.2 The Fokker-Planck CoefficientD2Dμμ 105

5.3.3 The Fokker-Planck Coefficient Dslab 106

5.3.4 The Fokker-Planck Coefficient D2D 106

5.4 Results of WNLT for the Parallel and the Perpendicular Mean Free Path 108

5.4.1 The Nonlinear Fokker-Planck Coefficients DμμandD 108

5.4.2 λ,λ,andλ/λ or Two-component Turbulence 109

5.4.3 The Parallel Mean Free Path as a Function of8B2slab/8B2 112

5.4.4 Equal Bend over Scales in the Composite Model 112

5.5 Is the Weakly Nonlinear Theory Reasonable? 114

6 The Second-order QLT 115

6.1 Nonlinear Pitch-angle Diffusion in Pure Slab Turbulence 115

6.1.1 The Quasilinear Velocity Correlation Function 116

6.1.2 The Time-dependent Pitch-angle Fokker-Planck Coefficient 117

6.1.3 The Ensemble Averaged Parallel Position 119

6.1.4 The Quasilinear Mean Square Displacement 119

6.2 The Resonance Function of SOQLT 121

6.2.1 The 90°-Approximation 121

6.2.2 The 90°-Late-time Approximation 122

6.3 Comparison with Previous Theories 122

6.3.1 The Nonlinear Perturbation Theory 123

6.3.2 The Partially Averaged Field Theory 123

6.3.3 The Heuristic Ansatz by Völk 124

6.3.4 The Strong Turbulence, Weak Coupling Theory 125

6.4 Analytical Results of SOQLT 125

6.4.1 Different Forms of the Wave Spectrum 126

6.4.2 Analytical Results for 90°-Scattering 127

6.5 Numerical Results for Fokker-Planck Coefficients and Mean Free Paths 128

6.5.1 Numerical Results for D(2)μμ 129

6.5.2 Numerical Results for λλ(2) 129

6.5.3 Steep Wave Spectra 132

6.6 Aspects of SOQLT 132

7 The Extended Nonlinear Guiding Center Theory 335

7.1 The Slab Problem of Perpendicular Transport 135

7.2 Integration of the Equations of Motion 136

7.3 Application of Quasilinear Theory 137

7.3.1 Time-dependent Perpendicular Transport 138

7.3.2 Finite Box-size Effects 139

7.4 The Nonlinear Guiding Center Model 141

7.4.1 Analytical and Numerical Results of the Nonlinear Model 142

7.4.2 Running Diffusion Coefficient and Velocity Correlation Function 144

7.5 The Extended Nonlinear Guiding Center Theory 145

7.5.1 Analytic Forms of the Perpendicular Mean Free Path 147

7.6 Comparison with Test-particle Simulations 147

7.6.1 Run 1 Pure Slab Geometry 148

7.6.2 Run 2 Strong Slab Geometry 148

7.6.3 Run 3 Strong 2D Geometry 149

7.7 Compound Subdiffusion for Pure Slab Turbulence 150

7.8 Aspects of ENLGC Theory 152

8 Applications 155

8.1 Particle Transport in the Heliosphere 155

8.1.1 The Quasilinear Parallel Mean Free Path 156

8.1.2 The Nonlinear Perpendicular Mean Free Path 160

8.1.3 Numerical Results Obtained by Using the NADT Model 162

8.1.4 Can We Indeed Reproduce Heliospheric Observations? 167

8.2 Particle Acceleration at Perpendicular Shock Waves 168

8.2.1 Interplanetary Shock Waves 169

8.2.2 The Perpendicular Diffusion Coefficient 171

8.2.3 The Shock Acceleration Time Scale 172

8.2.4 Influence of Nonlinear Diffusion on Shock Acceleration 174

8.3 Primary-to-Secondary Abundance Ratio of Galactic Cosmic Rays 175

8.3.1 Rigidity Dependence of the Weakly Nonlinear Parallel Mean Free Path 176

8.3.2 Importance of Nonlinear Effects 177

8.3.3 Validity of the WNLT Results 177

9 Summary and Outlook 179

9.1 Summary 179

9.1.1 Turbulence and Cosmic Rays 179

9.1.2 Specific Conclusions 180

9.2 Outlook 183

9.2.1 Future Test-particle Simulations 184

9.2.2 Future Theoretical Work 184

9.2.3 Future Observational Work 185

References 187

Index 195

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