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dc.contributor.authorLitvinenko, Yuri E.
dc.contributor.authorSchlickeiser, Reinhard
dc.identifier.citationLitvinenko, Y. E. & Schlickeiser, R. (2013). The telegraph equation for cosmic-ray transport with weak adiabatic focusing. Astronomy & Astrophysics, 554, A59.en_NZ
dc.description.abstractTime-dependent solutions of a spatial diffusion equation are often used to describe the transport of solar energetic particles, accelerated in large solar flares. Approximate analytical solutions of the diffusion approximation can complement and guide detailed numerical solutions of the Fokker-Planck equation for the particle distribution function. The accuracy of the diffusion approximation is limited, however, because the signal propagation speed is infinite in the diffusion limit. An improved description of cosmic-ray transport is provided by the telegraph equation, characterised by a finite signal propagation speed. We derive the telegraph equation for the particle density, taking into account adiabatic focusing in a large-scale interplanetary magnetic field in a weak focusing limit. As an illustration, we calculate a propagating pulse solution of the telegraph equation, determine the rise time when the maximum particle intensity is reached at a given distance from the Sun, and compare the results with those obtained in the diffusion approximation. In comparison with the diffusion equation, the telegraph equation predicts an asymmetrical shape of the pulse and a shorter rise time. These potentially significant differences suggest that the more accurate telegraph equation should be used in analysis of the solar energetic particle data, at least to quantify the accuracy of the focused diffusion model.en_NZ
dc.publisherEDP SCIENCES S Aen_NZ
dc.subjectparticle emissionen_NZ
dc.subjectmagnetic fieldsen_NZ
dc.subjectcosmic raysen_NZ
dc.titleThe telegraph equation for cosmic-ray transport with weak adiabatic focusingen_NZ
dc.typeJournal Articleen_NZ
dc.relation.isPartOfAstronomy & Astrophysicsen_NZ
uow.identifier.article-noARTN A59en_NZ

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