Time dependent cosmic-ray shock acceleration with self-consistent injection

Gieseler, U. D. J.; Jones, T. W.; Kang, Hyesung

Time dependent cosmic-ray shock acceleration with self-consistent injection

Authors

Gieseler, U. D. J.

Jones, T. W.

Kang, Hyesung

Description

One of the key questions to understanding the efficiency of diffusive shock acceleration of the cosmic rays (CRs) is the injection process from thermal particles. A self-consistent injection model based on the interactions of the suprathermal particles with self-generated magneto-hydrodynamic waves has been developed recently by Malkov (1998, Phys. Rev. E 58, 4911). By adopting this analytic solution, a numerical treatment of the plasma-physical injection model at a strong quasi-parallel shock has been devised and incorporated into the combined gas dynamics and the CR diffusion-convection code. In order to investigate self-consistently the injection and acceleration efficiencies, we have applied this code to the CR modified shocks of both high and low Mach numbers (M=30 and M=2.24) with a Bohm type diffusion model. We find the injection process is self-regulated in such a way that the injection rate reaches and stays at a nearly stable value after quick initial adjustment. For both shocks about 0.1% of the incoming thermal particles are injected into the CRs. For the weak shock, the shock has reached a steady state within our integration time and about 10% of the total available shock energy is transfered into the CR energy density. The strong shock has achieved a higher acceleration efficiency of about 20% by the end of our simulation, but has not yet reached a steady-state.
13 pages, 10 figures, LaTeX209 (epsf.sty, l-aa.sty), Astron.Astrophys. in press