Nonlinear cosmic ray diffusion theories /

Nonlinear cosmic ray diffusion theories /

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Bibliographic Details
Author / Creator:Shalchi, Andreas.
Imprint:Berlin : Springer-Verlag, c2009.
Description:xiii, 199 p. : ill. ; 24 cm.
Language:English
Series:Astrophysics and space science library ; 362
Subject:
Cosmic rays.
Astrophysics.
Plasma (Ionized gases)
Particle acceleration.
Astrophysics.
Cosmic rays.
Particle acceleration.
Plasma (Ionized gases)
Format: Print Book
URL for this record:http://pi.lib.uchicago.edu/1001/cat/bib/7805395
Hidden Bibliographic Details
ISBN:9783642003080
3642003087
Notes:Includes bibliographical references (p. 187-194) and index.
Table of Contents:
  • 1. The General Scenario
  • 1.1. Cosmic Rays
  • 1.1.1. General Properties of Cosmic Rays
  • 1.1.2. Cosmic Rays in the Solar System
  • 1.2. The Unperturbed System
  • 1.3. Particle Diffusion and the TGK Formulation
  • 1.3.1. Mean Square Displacements and Diffusion Coefficients
  • 1.3.2. The TGK Formulation
  • 1.4. The Physics of Parallel Scattering
  • 1.4.1. The Two-Dimensional Fokker-Planck Equation
  • 1.4.2. The Diffusion Equation
  • 1.4.3. Solution of the Diffusion Equation
  • 1.5. The Physics of Perpendicular Scattering
  • 1.6. The Diffusion Tensor and Momentum Diffusion
  • 1.6.1. Fokker-Planck vs. Diffusion Coefficients
  • 1.6.2. Cosmic Ray Momentum Diffusion Due to Electric Fields
  • 1.7. Cosmic Ray Mean Free Paths Deduced from Observations
  • 1.7.1. Observed Mean Free Paths in the Heliosphere
  • 1.7.2. Transport in the Interstellar Medium
  • 2. On Astrophysical Turbulence
  • 2.1. General Forms of the Magnetic Correlation Tensor
  • 2.1.1. The Isotropic Correlation Tensor
  • 2.1.2. Axisymmetric Turbulence and Vanishing Magnetic Helicity
  • 2.1.3. The Correlation Length
  • 2.2. The Magnetostatic Slab Model
  • 2.2.1. The Slab Correlation Function
  • 2.2.2. The Slab Correlation Length
  • 2.3. The Magnetostatic 2D Model
  • 2.3.1. The 2D Correlation Function
  • 2.3.2. The Correlation Length for Pure 2D Turbulence
  • 2.3.3. The Vector Potential of Pure 2D Turbulence
  • 2.4. Linear and Nonlinear Theories for Stochastic Field Line Wandering
  • 2.4.1. The Initial Free-Streaming Regime
  • 2.4.2. Field Line Random Walk for Slab Turbulence
  • 2.4.3. Quasilinear Theory of Field Line Random Walk
  • 2.4.4. The Nonlinear Approach for Field Line Random Walk
  • 2.4.5. The Diffusion Limit of Matthaeus et al
  • 2.5. Dynamical Turbulence and Plasma Wave Propagation Effects
  • 2.5.1. Damping and Random Sweeping Models
  • 2.5.2. Plasma Wave Turbulence
  • 2.5.3. The Nonlinear Anisotropic Dynamical Turbulence Model
  • 3. The Quasilinear Theory
  • 3.1. The Quasilinear Approximation
  • 3.2. General Forms of Quasilinear Fokker-Planck Coefficients
  • 3.2.1. General Form of the Pitch-angle Fokker-Planck Coefficient
  • 3.2.2. General Form of the Fokker-Planck Coefficient of Perpendicular Diffusion
  • 3.3. Standard QLT (Magnetostatic Slab Turbulence)
  • 3.3.1. The Pitch-angle Fokker-Planck Coefficient
  • 3.3.2. The Parallel Mean Free Path
  • 3.3.3. The Perpendicular Mean Free Path
  • 3.4. Quasilinear Theory for Magnetostatic 2D Turbulence
  • 3.4.1. Pitch-angle Diffusion in Pure 2D Turbulence by Using the Traditional Approach
  • 3.4.2. Pitch-angle Diffusion in Pure 2D Turbulence by Using a Vector-potential Approach
  • 3.4.3. Perpendicular Diffusion in Pure 2D Turbulence
  • 3.5. Quasilinear Transport in the Slab/2D Composite Model
  • 3.6. Test-particle Simulations
  • 3.6.1. The Simulations of Giacalone and Jokipii
  • 3.6.2. The Simulations of Qin
  • 3.6.3. Confirmation of QLT for Parallel Diffusion in the Slab Model
  • 3.7. The Three Problems of QLT
  • 3.7.1. The 90°-Scattering Problem
  • 3.7.2. The Problem of Perpendicular Diffusion
  • 3.7.3. The Geometry Problem
  • 4. The Nonlinear Guiding Center Theory
  • 4.1. The Nonlinear Closure Approximation
  • 4.1.1. The Results of the NCA
  • 4.1.2. Test of the NCA by Comparing it with Simulations
  • 4.2. The Bieber and Matthaeus Model
  • 4.2.1. The Basic Formulas of the BAM Theory
  • 4.2.2. Results of the BAM Theory for Slab Geometry
  • 4.2.3. The BAM Theory for Slab/2D Composite Geometry
  • 4.3. The Nonlinear Guiding Center Theory
  • 4.4. Analytical Solutions of the NLGC Theory for Magnetostatic Slab Turbulence
  • 4.5. NLGC Theory for Slab/2D Composite Geometry
  • 5. The Weakly Nonlinear Theory
  • 5.1. The Basic Idea of a Nonlinear Transport Theory
  • 5.2. The Weakly Nonlinear Resonance Function
  • 5.3. The Nonlinear Fokker-Planck Coefficients for Two-component Turbulence
  • 5.3.1. The Fokker-Planck Coefficient Dslab¿¿
  • 5.3.2. The Fokker-Planck CoefficientD2D¿¿
  • 5.3.3. The Fokker-Planck Coefficient Dslab
  • 5.3.4. The Fokker-Planck Coefficient D2D
  • 5.4. Results of WNLT for the Parallel and the Perpendicular Mean Free Path
  • 5.4.1. The Nonlinear Fokker-Planck Coefficients D¿¿andD
  • 5.4.2. ¿,¿,and¿/¿
  • 5.4.3. The Parallel Mean Free Path as a Function of8B2slab/8B2
  • 5.4.4. Equal Bend over Scales in the Composite Model
  • 5.5. Is the Weakly Nonlinear Theory Reasonable?
  • 6. The Second-order QLT
  • 6.1. Nonlinear Pitch-angle Diffusion in Pure Slab Turbulence
  • 6.1.1. The Quasilinear Velocity Correlation Function
  • 6.1.2. The Time-dependent Pitch-angle Fokker-Planck Coefficient
  • 6.1.3. The Ensemble Averaged Parallel Position
  • 6.1.4. The Quasilinear Mean Square Displacement
  • 6.2. The Resonance Function of SOQLT
  • 6.2.1. The 90°-Approximation
  • 6.2.2. The 90°-Late-time Approximation
  • 6.3. Comparison with Previous Theories
  • 6.3.1. The Nonlinear Perturbation Theory
  • 6.3.2. The Partially Averaged Field Theory
  • 6.3.3. The Heuristic Ansatz by Völk
  • 6.3.4. The Strong Turbulence, Weak Coupling Theory
  • 6.4. Analytical Results of SOQLT
  • 6.4.1. Different Forms of the Wave Spectrum
  • 6.4.2. Analytical Results for 90°-Scattering
  • 6.5. Numerical Results for Fokker-Planck Coefficients and Mean Free Paths
  • 6.5.1. Numerical Results for D(2)¿¿
  • 6.5.2. Numerical Results for ¿¿(2)
  • 6.5.3. Steep Wave Spectra
  • 6.6. Aspects of SOQLT
  • 7. The Extended Nonlinear Guiding Center Theory
  • 7.1. The Slab Problem of Perpendicular Transport
  • 7.2. Integration of the Equations of Motion
  • 7.3. Application of Quasilinear Theory
  • 7.3.1. Time-dependent Perpendicular Transport
  • 7.3.2. Finite Box-size Effects
  • 7.4. The Nonlinear Guiding Center Model
  • 7.4.1. Analytical and Numerical Results of the Nonlinear Model
  • 7.4.2. Running Diffusion Coefficient and Velocity Correlation Function
  • 7.5. The Extended Nonlinear Guiding Center Theory
  • 7.5.1. Analytic Forms of the Perpendicular Mean Free Path
  • 7.6. Comparison with Test-particle Simulations
  • 7.6.1 Run 1. Pure Slab Geometry
  • 7.6.2 Run 2. Strong Slab Geometry
  • 7.6.3 Run 3. Strong 2D Geometry
  • 7.7. Compound Subdiffusion for Pure Slab Turbulence
  • 7.8. Aspects of ENLGC Theory
  • 8. Applications
  • 8.1. Particle Transport in the Heliosphere
  • 8.1.1. The Quasilinear Parallel Mean Free Path
  • 8.1.2. The Nonlinear Perpendicular Mean Free Path
  • 8.1.3. Numerical Results Obtained by Using the NADT Model
  • 8.1.4. Can We Indeed Reproduce Heliospheric Observations?
  • 8.2. Particle Acceleration at Perpendicular Shock Waves
  • 8.2.1. Interplanetary Shock Waves
  • 8.2.2. The Perpendicular Diffusion Coefficient
  • 8.2.3. The Shock Acceleration Time Scale
  • 8.2.4. Influence of Nonlinear Diffusion on Shock Acceleration
  • 8.3. Primary-to-Secondary Abundance Ratio of Galactic Cosmic Rays
  • 8.3.1. Rigidity Dependence of the Weakly Nonlinear Parallel Mean Free Path
  • 8.3.2. Importance of Nonlinear Effects
  • 8.3.3. Validity of the WNLT Results
  • 9. Summary and Outlook
  • 9.1. Summary
  • 9.1.1. Turbulence and Cosmic Rays
  • 9.1.2. Specific Conclusions
  • 9.2. Outlook
  • 9.2.1. Future Test-particle Simulations
  • 9.2.2. Future Theoretical Work
  • 9.2.3. Future Observational Work
  • References
  • Index
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