NUMERICAL ANALYSIS OF THE FOKKER-PLANCK EQUATION WITH ADIABATIC FOCUSING: ISOTROPIC PITCH-ANGLE SCATTERING

Journal Article · Sat Jul 20 04:00:00 EDT 2013 · Astrophysical Journal

DOI:https://doi.org/10.1088/0004-637X/772/1/35· OSTI ID:22121892

Danos, Rebecca J.; Fiege, Jason D.; Shalchi, Andreas ^[1]

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1. Department of Physics, University of Manitoba, Winnipeg, MB R3T 2N2 (Canada)

We present numerical solutions to both the standard and modified two-dimensional Fokker-Planck equations with adiabatic focusing and isotropic pitch-angle scattering. With the numerical solution of the particle distribution function, we then discuss the related numerical issues, calculate the parallel diffusion coefficient using several different methods, and compare our numerical solutions for the parallel diffusion coefficient to the analytical forms derived earlier. We find the numerical solution to the diffusion coefficient for both the standard and modified Fokker-Planck equations agrees with that of Shalchi for the mean squared displacement method of computing the diffusion coefficient. However, we also show the numerical solution agrees with that of Litvinenko and Shalchi and Danos when calculating the diffusion coefficient via the velocity correlation function.

• OSTI ID: 22121892
• Journal Information: Astrophysical Journal, Journal Name: Astrophysical Journal Journal Issue: 1 Vol. 772; ISSN ASJOAB; ISSN 0004-637X
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
79 ASTRONOMY AND ASTROPHYSICS
ADIABATIC PROCESSES
CORRELATION FUNCTIONS
DIFFUSION
DISTRIBUTION FUNCTIONS
FOCUSING
FOKKER-PLANCK EQUATION
INCLINATION
NUMERICAL ANALYSIS
NUMERICAL SOLUTION
PARTICLES
SCATTERING
TWO-DIMENSIONAL CALCULATIONS
VELOCITY