Solution of the electron continuity equation in an inhomogeneous medium via the method of characteristics

Statistics – Computation

Scientific paper

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Anisotropic Media, Continuity Equation, Electron Distribution, Method Of Characteristics, Solar Flares, Solar X-Rays, Bursts, Computational Astrophysics, Coulomb Collisions, Electron Scattering, Inhomogeneity, Relativistic Electron Beams, Spatial Distribution, Temporal Distribution

Scientific paper

Many astrophysical problems require a knowledge of the spatial and temporal evolution of fast electron distributions as they interact with an ambient medium; an example is provided by hard X-ray burst modelling in solar flares. In the mean scattering-rate approximation this evolution is governed by the continuity equation in phase space. Here the authors present a rigorous solution of the continuity equation, derived via the method of characteristics, which confirms and generalises the results of previous authors, and gives greater physical and mathematical insight into these solutions. The authors illustrate the calculation of this solution for mildly relativistic electrons undergoing Coulomb collisions, and briefly indicate the extension of the method to other physical situations.

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