  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.
