Acceleration of cosmic rays by shock waves

The acceleration of cosmic rays in gas flows involving shock and other compressional waves is considered. The calculation is carried out in the framework of the diffusion approximation for one-dimensional steady flows. The results of the paper suggest that for strong transitions (M12=100, where M1 is the Mach number) a small fraction of the kinetic energy of the gas flow is converted to thermal energy of the gas and the major part is converted into cosmic ray energy. It is concluded that shock wave acceleration of cosmic rays can be a very efficient process