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Title: Comparison of the telegraph and hyperdiffusion approximations in cosmic-ray transport

Abstract

The telegraph equation and its generalizations have been repeatedly considered in the models of diffusive cosmic-ray transport. Yet the telegraph model has well-known limitations, and analytical arguments suggest that a hyperdiffusion model should serve as a more accurate alternative to the telegraph model, especially on the timescale of a few scattering times. We present a detailed side-by-side comparison of an evolving particle density profile, predicted by the telegraph and hyperdiffusion models in the context of a simple but physically meaningful initial-value problem, compare the predictions with the solution based on the Fokker–Planck equation, and discuss the applicability of the telegraph and hyperdiffusion approximations to the description of strongly anisotropic particle distributions.

Authors:
;  [1]
  1. Department of Mathematics, University of Waikato, P. B. 3105, Hamilton (New Zealand)
Publication Date:
OSTI Identifier:
22600126
Resource Type:
Journal Article
Resource Relation:
Journal Name: Physics of Plasmas; Journal Volume: 23; Journal Issue: 6; Other Information: (c) 2016 Author(s); Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
70 PLASMA PHYSICS AND FUSION TECHNOLOGY; 79 ASTROPHYSICS, COSMOLOGY AND ASTRONOMY; ANISOTROPY; APPROXIMATIONS; COMPARATIVE EVALUATIONS; COSMIC RADIATION; DENSITY; DISTRIBUTION; FOKKER-PLANCK EQUATION; PARTICLES; SCATTERING; TRANSPORT THEORY

Citation Formats

Litvinenko, Yuri E., and Noble, P. L. Comparison of the telegraph and hyperdiffusion approximations in cosmic-ray transport. United States: N. p., 2016. Web. doi:10.1063/1.4953564.
Litvinenko, Yuri E., & Noble, P. L. Comparison of the telegraph and hyperdiffusion approximations in cosmic-ray transport. United States. doi:10.1063/1.4953564.
Litvinenko, Yuri E., and Noble, P. L. Wed . "Comparison of the telegraph and hyperdiffusion approximations in cosmic-ray transport". United States. doi:10.1063/1.4953564.
@article{osti_22600126,
title = {Comparison of the telegraph and hyperdiffusion approximations in cosmic-ray transport},
author = {Litvinenko, Yuri E. and Noble, P. L.},
abstractNote = {The telegraph equation and its generalizations have been repeatedly considered in the models of diffusive cosmic-ray transport. Yet the telegraph model has well-known limitations, and analytical arguments suggest that a hyperdiffusion model should serve as a more accurate alternative to the telegraph model, especially on the timescale of a few scattering times. We present a detailed side-by-side comparison of an evolving particle density profile, predicted by the telegraph and hyperdiffusion models in the context of a simple but physically meaningful initial-value problem, compare the predictions with the solution based on the Fokker–Planck equation, and discuss the applicability of the telegraph and hyperdiffusion approximations to the description of strongly anisotropic particle distributions.},
doi = {10.1063/1.4953564},
journal = {Physics of Plasmas},
number = 6,
volume = 23,
place = {United States},
year = {Wed Jun 15 00:00:00 EDT 2016},
month = {Wed Jun 15 00:00:00 EDT 2016}
}