Abstract
AbstractSimilarity solutions of the steady-state equation of transport for the distribution functionF0of 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)rbwithrthe heliocentric radial distance.pthe particle momentum, κ0(p) an arbitary function ofp, and the solar wind velocity is radial and of constant speed V. Solutions for which the similarity variable η is a function ofronly are also derived; these are of particular impoartance when theF0is 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 κ1in the radial direction and κ2normal to it). The solutions are the most extensive steady-state analytic solutions yet obtained, and contain previous analytic solutions as special cases.
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