Structure of a collisionless shock front with relativistically accelerated particles

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Abstract
A nonlinear self-consistent analytic theory is developed to describe the front structure of a strong magnetohydrodynamic (MHD) collisionless shock wave that generates accelerated particles (including ultrarelativistic particles). The theory is used to predict the degree of compression of matter at the plane front of such a wave, which can greatly exceed compression at an ordinary gas-dynamic front, and also the velocity, density, and pressure profiles. The energy spectrum of the accelerated particles, which is produced by the complex velocity profile at the shock transition, is determined self-consistently. New nonlinear effects are predicted that have not been discussed previously in the literature: a strong dependence of the particle acceleration regimes on the rate of injection; the existence of several regimes within a certain range of injected powers with differing spectra of accelerated particles, shapes of the shock transition profile, and magnitudes of compression of the medium; and the possibility of spontaneous jumps between different states of the shock transition. The question of stability of these states is discussed. For the values of the system parameters used here, the nonlinear regimes correspond to extremely low injection rates, of order 10−2–10−10 of the plasma flux density advancing into the front, and to exponents of the power-law spectra of accelerated particles between 5 and 3.