Acceleration of charged particles in quasi-perpendicular magnetohydrodynamic shocks

The energy gain of a non-relativistic charged particle in a quasi-perpendicular shock is studied. This is done by the usual procedure of transforming the shock structure to a perpendicular one. The difference with earlie'r studies is that we are able to derive a new, exact expression for this energy gain in closed form. Two successive approximations of this expression are presented and discussed. Finally, the average energy gain of an isotropie particle distribution in the original shock system is derived.