A Kinetic Approach to Relativistic Shocks in Astrophysics
Stochastic acceleration of charged particles across highly relativistic shock is often considered as the main source for observed emission. Here is shown that the derivation of the appropriate quasilinear equation describing particle transport across such shocks depends on the assumptions made for the power spectra in the upstream region ahead of the shock. For both an ambient magnetic field perpendicular to the shock front and for an oblique magnetic field derivation is given of the quasilinear diffusion equation for particle transport appropriate to both sides of the shock. There is both pitch angle diffusion and energy diffusion; the relative strengths of the two processes depends on the assumptions made concerning the upstream wave power spectra. Transformations of the diffusion equations into the frame where the shock is stationary are given for the upstream and downstream regions including both energy diffusion and pitch angle scattering. The remaining outstanding concern is the determination of the continuity of the transport equations across the shock. This latter problem has yet to be solved fully in even the simple case of assumed pitch angle scattering only. Including energy diffusion and pitch angle scattering presumably makes the determination of the correct continuity behaviour more difficulty.
J. G. Kirk and P. Duffy, “Particle acceleration and relativistic shocks,” Journal of Physics G, vol. 25, no. 8, pp. R163–R194, 1999.View at: Google Scholar
P. D. Hudson, “Reflection of charged particles by plasma shocks,” Monthly Notices of the Royal Astronomical Society, vol. 131, pp. 23–50, 1965.View at: Google Scholar
P. D. Hudson, “Perpendicular shocks in a medium containing cosmic rays,” Monthly Notices of the Royal Astronomical Society, vol. 140, pp. 255–263, 1968.View at: Google Scholar