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arXiv · 1610.01584

An Exact Solution of the Fokker-Planck Equation for Isotropic Scattering

M. A. Malkov
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Abstract

An analytic solution for a Fokker-Planck equation that describes propagation of energetic particles through a scattering medium is obtained. The solution is found in terms of an infinite series of mixed moments of particle distribution. The spatial dispersion of a particle cloud released at t=0 evolves through three phases, ballistic (t >Tc), where Tc is the collision time.The ballistic phase is characterized by a decelerating expansion of the initial point source in form of a "box" distribution with thickening walls. The next, transdiffusive phase is marked by the box walls thickened to its size and a noticeable slow down of expansion. Finally, the evolution enters the conventional diffusion phase.

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M. A. Malkov. 2016-10-05. An Exact Solution of the Fokker-Planck Equation for Isotropic Scattering. https://doi.org/10.1103/physrevd.95.023007

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