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Analytical Study of Diffusive Relativistic Shock Acceleration

Uri Keshet
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Abstract

Particle acceleration in relativistic shocks is studied analytically in the test-particle, small-angle scattering limit, for an arbitrary velocity-angle diffusion function D. Accurate analytic expressions for the spectral index s are derived using few (2-6) low-order moments of the shock-frame angular distribution. For isotropic diffusion, previous results are reproduced and justified. For anisotropic diffusion, s is shown to be sensitive to D, particularly downstream and at certain angles, and a wide range of s values is attainable. The analysis, confirmed numerically, can be used to test collisionless shock models and to observationally constrain D. For example, strongly forward- or backward-enhanced diffusion downstream is ruled out by GRB afterglow observations.

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BibTeXRIS

Uri Keshet. 2006-10-12. Analytical Study of Diffusive Relativistic Shock Acceleration. https://doi.org/10.1103/physrevlett.97.221104

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