COSMIC-RAY HYDRODYNAMICS AT SHOCK FRONTS

When a magnetised, thermal plasma containing a shock wave efficiently accelerates Cosmic Rays (CR) a reaction is exerted on the fluid struct ure. The simplest description of this process involves three conservat ion equations for the background fluid, with the CR pressure gradient included as an extra force, plus a hydrodynamic equation for the CR en ergy density. Since the CR spectrum is not determined in this approach two quantities are introduced, the ratio of CR pressure to energy den sity and a mean diffusion coefficient, that must be specified to close the system of equations. Physical arguments are presented for how the se quantities should evolve and then compared with time dependent nume rical solutions of acceleration at a plane parallel, piston driven sho ck.