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Similarity solutions of the steady state cosmic-ray equation of transport

Published online by Cambridge University Press:  17 February 2009

G. M. Webb
G. M. Webb
Affiliation:
Department of Mathematics, Monash University, Clayton, Vic. 3168, Australia
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Abstract

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Similarity solutions of the steady-state equation of transport for the distribution function F0 of cosmic rays in the interplanetary region are obtained by theuse of transformation groups. The solutions are derived in detail for a spherically-symmetric model of the interplanetary region with an effective radial diffusion coefficient κ = κ0(p)rb with r the heliocentric radial distance. p the particle momentum, κ0(p) an arbitary function of p, and the solar wind velocity is radial and of constant speed V. Solutions for which the similarity variable η is a function of r only are also derived; these are of particular impoartance when the F0 is specified on a boundary of given radius. Non spherically-symmetric solutions can also be obtained by group methods and examples of such solutions are listed, without derivation, for the equation of transport incorporating the effects of anisotropic diffusion (diffusion coefficient κ1 in the radial direction and κ2 normal to it). The solutions are the most extensive steady-state analytic solutions yet obtained, and contain previous analytic solutions as special cases.

Type
Research Article
Information
The ANZIAM Journal , Volume 19 , Issue 4 , December 1976 , pp. 432 - 451
Copyright
Copyright © Australian Mathematical Society 1976

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