Numerical investigation of cosmic ray acceleration in supernova remnants

The process of cosmic ray (CR) acceleration by supernova blast wave with CR pressure back reaction taken into account is studied numerically. The efficiency of acceleration was shown to be especially high in the Bohm limit case: even at a small injection rate (10(-4)) CR absorb about 20% of the explosion energy. At each current time moment the CR spectrum is not a pure power law, especially at late evolution times when the effect of escaping particles is pronounced. The overall spectrum of CR produced by the supernova shock during the whole evolution period is extremely close to the power law with an index gamma approximate to 2.1.