NUMERICAL-STUDIES OF THE ACCELERATION OF COSMIC-RAYS IN SUPERNOVA-REMNANTS

The process of acceleration of cosmic ray particles by a shock in a su pernova explosion, taking account of the reverse action of the cosmic ray pressure on the structure and dynamics of the shock, is investigat ed using numerical solution of the diffusion transport equation for th e cosmic ray distribution function, jointly with the gas dynamic equat ions. The realization of a Bohm diffusion coefficient near the shock f ront is shown to result id high acceleration efficiency: more than 50% of the energy released in the explosion may be transmitted to cosmic rays if the acceleration process involves more than 3 X 10(-4) of the total number of particles in the medium. The shock is substantially mo dified by the reverse action of the accelerated cosmic rays; energy di lution into the pre-shock region causes the compression ratio at the s hock front to greatly exceed the classical limit. Non-linear modificat ion of the shock leads to hardening of the cosmic ray spectrum and inc rease in the maximum cosmic ray energy, At the same time, contrary to the predictions of plane-wave theory, a shock of finite size is not co mpletely modified by the cosmic ray pressure. Our calculations show th at the acceleration of cosmic rays in supernova remnants can provide s pectra with the required shape and amplitude up to energy similar to 1 0(15) eV.