Relativistic Shock Acceleration: A Hartree-Fock Approach

Paul Dempsey; John G. Kirk

doi:10.1063/1.3076743

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arXiv · 0809.2657

Relativistic Shock Acceleration: A Hartree-Fock Approach

Paul Dempsey·John G. Kirk

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Abstract

We examine the problem of particle acceleration at a relativistic shocks assuming pitch-angle scattering and using a Hartree-Fock method to approximate the associated eigenfunctions. This leads to a simple transcendental equation determining the power-law index, $s$, given the up and downstream velocities. We compare our results with accurate numerical solutions obtained using the eigenfunction method. In addition to the power-law index this method yields the angular and spatial distributions upstream of the shock.

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Paul Dempsey, John G. Kirk. 2008-09-16. Relativistic Shock Acceleration: A Hartree-Fock Approach. https://doi.org/10.1063/1.3076743

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