DIFFUSIVE SHOCK ACCELERATION IN THE PRESENCE OF A STRONG AMBIENT MAGNETIC-FIELD

In various astrophysical situations, the acceleration achieved by the enormously successful diffusive shock acceleration mechanism is bounded upward by the profuse synchrotron losses suffered by the charged particles. The earlier treatments to determine the sharp spectral changes occurring near the upper bound of energy are idealized and are inconsistent in the sense that, although the upper bound was determined by using an energy-dependent diffusion coefficient, the spectrum was determined by neglecting the energy dependence of the diffusion coefficient, and the need for a treatment which can handle a realistic form of the diffusion coefficient was felt. The present paper is devoted to this goal. By an appeal to the microscopic approach of the process, we have developed here a framework which can take into account arbitrary energy dependence of the diffusion coefficient and an arbitrary ratio of the ambient magnetic field strengths in the upstream and downstream region within the approximation of a plane shock. There are significant departures from the results obtained by earlier authors. In particular, we have paid attention to the problem of particle acceleration by an accretion shock in the X-ray binary Cygnus X-3.