We have studied the CR injection and acceleration efficiencies at cosmic shocks by performing numerical simulation of CR modified,quasi-parallel,shocks in 1D plane-parallel geometry for a wide range of shock Mach numbers and preshock conditions.The shock formation simulation includes a thermal leakage injection model that transfers a small proportion of the thermal proton flux through the shock into low energy CRs.We adopted the Bohm diffusion model for CRs,based on the hypothesis that strong Alfven waves are self-generated by streaming CRs.Our hydro/CR code is designed to follow in a very cost-effective way the evolution of CR modified shocks by adopting subzone shock-tracking and multi-level adaptive mesh refinement techniques.We found that both injection and acceleration efficiencies increase with shock Mach number,and that CRs can absorb up to 60 % of initial upstream shock kinetic energy in the strong shock limit with an associated CR particle fraction of 10~(-4)- 10~(-3).
展开▼
