Other
Scientific paper
Jun 1994
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1994apj...427.1035k&link_type=abstract
Astrophysical Journal, Part 1 (ISSN 0004-637X), vol. 427, no. 2, p. 1035-1041
Other
14
Astronomical Models, Charged Particles, Coherent Scattering, Cosmic Rays, Diffusion Theory, Particle Acceleration, Transport Theory, Dispersion, Fokker-Planck Equation, Pitch (Inclination), Relaxation Time
Scientific paper
We present exact solutions to the diffusive transport of charged particles following impulsive injection for a simple model of scattering. A modified, two-parameter relaxation-time model is considered that simulates the low rate of scattering through perpendicular pitch-angle. Scattering is taken to be isotropic within each of the foward- and backward-pointing hemispheres, respectively, but, at the same time, a reduced rate of scattering is assumed from one hemisphere to the other one. By applying a technique of Fourier- and Laplace-transform, the inverse transformation can be performed and exact solutions can be reached. By contrast with the first, and so far only exact solutions of Federov and Shakov, this wider class of solutions gives rise to coherent pulses to appear. The present work addresses omnidirectional densities for isotropic injection from an instantaneous and localized source. The dispersion relations are briefly discussed. We find, for this particular model, two diffusive models to exist up to a certain limiting wavenumber. The corresponding eigenvalues are real at the lowest wavenumbers. Complex eigenvalues, which are responsible for coherent pulses, appear at higher wavenumbers.
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