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- W3104255309 abstract "The selfconsistent steady state solution for a strong shock, significantly modified by accelerated particles is obtained on the level of a kinetic description, assuming Bohm-type diffusion. The original problem that is commonly formulated in terms of the diffusion-convection equation for the distribution function of energetic particles, coupled with the thermal plasma through the momentum flux continuity equation, is reduced to a nonlinear integral equation in one variable. Its solution provides selfconsistently both the particle spectrum and the structure of the hydrodynamic flow. A critical system parameter governing the acceleration process is found to be $Lambda = M^{-3/4}Lambda_1 $, where $ Lambda_1 =eta p_1/mc $, with a suitably normalized injection rate $ eta $, the Mach number M >> 1, and the cut-off momentum $ p_1 $. We particularly focus on an efficient solution, in which almost all the energy of the flow is converted into a few energetic particles. It was found that (i) for this efficient solution (or, equivalently, for multiple solutions) to exist, the parameter $ zeta =etasqrt{p_0 p_1}/mc $ must exceed a critical value $zeta_{cr} sim 1$ ($p_0$ is the injection momentum), (ii) the total shock compression ratio r increases with M and saturates at a level that scales as $ r propto Lambda_1 (iii) the downstream power-law spectrum has the universal index q=3.5 over a broad momentum range. (iv) completely smooth shock transitions do not appear in the steady state kinetic description." @default.
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- W3104255309 date "1997-08-20" @default.
- W3104255309 modified "2023-09-27" @default.
- W3104255309 title "Analytic Solution for Nonlinear Shock Acceleration in the Bohm Limit" @default.
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- W3104255309 doi "https://doi.org/10.1086/304471" @default.
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