A numerical study of diffusive shock acceleration of cosmic rays in supernova shocks

The evolution of the energy spectrum of cosmic rays accelerated by the first order Fermi mechanism, by a supernova remnant shock wave, including adiabatic deceleration effects behind the front, is carried out by means of a time-dependent numerical code. The calculations apply to the adiabatic stage (or Sedov stage) of the supernova explosion, and the energetic particle spectrum is calculated in the test particle limit (i.e., the back reaction of the cosmic rays on the flow is not included). The particles are injected mono-energetically at the shock. The radial distribution, The radial distribution, and the spectrum of the accelerated and decelerated particles is shown