Previous
abstract 
Next
abstract
The diffusion-convection equation has been solved numerically in order to study the injection and acceleration of cosmic-ray particles at quasi-parallel shocks. Our previous numerical code has been improved to include realistic momentum-dependent diffusion coefficient. The particle distribution function is solved in the grid whose size is chosen in a momentum-dependent way, so that a fixed number of zones are contained in a diffusion length. Injection of the suprathermal particles is approximated through the diffusive scattering process itself, that is, the diffusion and acceleration of the thermal particles near the Maxwellian tail across the shock front. We show how the acceleration process is dependent on the details of the injection, the momentum-dependent diffusion, and the escaping high energy particles. The simulated particle spectrum from our calculation will be compared with that of a Monte-Carlo simulation of the particle acceleration at earth's bow shock by Ellison, M\"obius and Paschmann (1990).
Support for this work at the University of Minnesota is provided through the NSF, NASA and the University of Minnesota Supercomputer Institute. HK is supported in part by the Korea Research Foundation through the Brain Pool Program.
{\noindent References:\hfil\break Ellison, D.~C., M\"obius, E., \& Paschmann, G. 1990, Ap.~J., 352, 376. }
