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Paper: Self-Similar Evolution of Cosmic-Ray Modified Shocks
Volume: 429, Numerical Modeling of Space Plasma Flows, Astronum-2009
Page: 85
Authors: Kang, H.; Ryu, D.
Abstract: Diffusive shock acceleration (DSA) is widely accepted as the primary mechanism through which cosmic rays (CRs) are produced in a variety of astrophysical environments. We used kinetic simulations of DSA to study the time-dependent evolution of the energy spectrum of CRs accelerated by plane, quasi-parallel shocks. We found that the precursor and subshock transition approach the time-asymptotic state, and then evolve in an approximately self-similar fashion, depending only on the similarity variable, x/(us t). During this self-similar stage, the CR spectrum at the subshock maintains a characteristic form as it evolves: the sum of two power-laws with the slopes determined by the subshock and total compression ratios with an exponential cutoff at the highest accelerated momentum. This analytic form may represent an approximate solution to the DSA problem for astrophysical shocks during the self-similar evolutionary stage.
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