Acceleration of relativistic charged particles by supersonic hydromagnetic turbulence

The acceleration of relativistic particles is considered during their intersection with hydromagnetic shock fronts in the presence of randomly distributed large-scale magnetic fields. In a series of astronomical objects, the Larmor radius of the relativistic particles exceeds the width of the shock front. In this case there is a change in the adiabatic invariant which results in an increase in the energy of the particle when it crosses the front in any direction. We have proved that the adiabatic part of the energy change will be partially or completely compensated by its reverse change in the weaker regions of the magnetic field. The acceleration mechanism considered is found to be more effective than the Fermi mechanism.If the mean free path of the particles is much less than the distance between the shock fronts, magnetic small-scale fluctuations cause further scattering of the particles. In this case the particles following and crossing the front will return to it. After reversed crossing, a fraction of the particles-defined by the ratio of the front speed to the particle velocity or of the distance between the fronts to the free path — will not return to the front. It is proved that for both large and small free paths the rates at which the particle gains energy are nearly the same.