Comparison of the telegraph and hyperdiffusion approximations in cosmicray transport
Abstract
The telegraph equation and its generalizations have been repeatedly considered in the models of diffusive cosmicray transport. Yet the telegraph model has wellknown 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 sidebyside comparison of an evolving particle density profile, predicted by the telegraph and hyperdiffusion models in the context of a simple but physically meaningful initialvalue 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:
 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; FOKKERPLANCK EQUATION; PARTICLES; SCATTERING; TRANSPORT THEORY
Citation Formats
Litvinenko, Yuri E., and Noble, P. L.. Comparison of the telegraph and hyperdiffusion approximations in cosmicray 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 cosmicray transport. United States. doi:10.1063/1.4953564.
Litvinenko, Yuri E., and Noble, P. L.. 2016.
"Comparison of the telegraph and hyperdiffusion approximations in cosmicray transport". United States.
doi:10.1063/1.4953564.
@article{osti_22600126,
title = {Comparison of the telegraph and hyperdiffusion approximations in cosmicray 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 cosmicray transport. Yet the telegraph model has wellknown 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 sidebyside comparison of an evolving particle density profile, predicted by the telegraph and hyperdiffusion models in the context of a simple but physically meaningful initialvalue 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 = 2016,
month = 6
}

Diffusive cosmicray transport in nonuniform largescale magnetic fields in the presence of boundaries is considered. Reflecting and absorbing boundary conditions are derived for a modified telegraph equation with a convective term. Analytical and numerical solutions of illustrative boundary problems are presented. The applicability and accuracy of the telegraph approximation for focused cosmicray transport in the presence of boundaries are discussed, and potential applications to modeling cosmicray transport are noted.

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