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

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.
Authors:
; ;  [1]
  1. Department of Physics, University of Manitoba, Winnipeg, MB R3T 2N2 (Canada)
Publication Date:
OSTI Identifier:
22121892
Resource Type:
Journal Article
Resource Relation:
Journal Name: Astrophysical Journal; Journal Volume: 772; Journal Issue: 1; Other Information: Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; 79 ASTROPHYSICS, COSMOLOGY AND ASTRONOMY; ADIABATIC PROCESSES; CORRELATION FUNCTIONS; DIFFUSION; DISTRIBUTION FUNCTIONS; FOCUSING; FOKKER-PLANCK EQUATION; INCLINATION; NUMERICAL ANALYSIS; NUMERICAL SOLUTION; PARTICLES; SCATTERING; TWO-DIMENSIONAL CALCULATIONS; VELOCITY