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Title: Analytical solutions of a fractional diffusion-advection equation for solar cosmic-ray transport

Motivated by recent applications of superdiffusive transport models to shock-accelerated particle distributions in the heliosphere, we analytically solve a one-dimensional fractional diffusion-advection equation for the particle density. We derive an exact Fourier transform solution, simplify it in a weak diffusion approximation, and compare the new solution with previously available analytical results and with a semi-numerical solution based on a Fourier series expansion. We apply the results to the problem of describing the transport of energetic particles, accelerated at a traveling heliospheric shock. Our analysis shows that significant errors may result from assuming an infinite initial distance between the shock and the observer. We argue that the shock travel time should be a parameter of a realistic superdiffusive transport model.
Authors:
;  [1]
  1. Department of Mathematics, University of Waikato, P.B. 3105 Hamilton (New Zealand)
Publication Date:
OSTI Identifier:
22370140
Resource Type:
Journal Article
Resource Relation:
Journal Name: Astrophysical Journal; Journal Volume: 796; Journal Issue: 2; Other Information: Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
79 ASTROPHYSICS, COSMOLOGY AND ASTRONOMY; ADVECTION; ANALYTICAL SOLUTION; APPROXIMATIONS; COSMIC RADIATION; DENSITY; DIFFUSION; DISTRIBUTION; EQUATIONS; FOURIER TRANSFORMATION; HELIOSPHERE; NUMERICAL SOLUTION; ONE-DIMENSIONAL CALCULATIONS; SERIES EXPANSION; SUN; TRANSPORT THEORY