### abstract

- The nonlinear theory of shock acceleration developed in earlier papers, which treated the waves as being completely frozen into the fluid, is generalized to include wave dynamics. In the limit where damping keeps the wave amplitude small, it is found that a finite phase velocity of the scattering waves through the background fluid, ..nu../sub ph/, tempers the acceleration generated by high Mach number shocks. Asymptotic spectra proportional to E/sup -2/ are possible only when the ratio of wave velocity to shock velocity is less than 0.13. For a given asymptotic spectrum, the efficiency of relativistic particle production is found to be practically independent of the value of ..nu../sub ph/, so that earlier results concerning its value remain valid for finite ..nu../sub ph/. In the limit where there is no wave damping, it is shown that for modest Alfven Mach numbers, 4approximately-less-than-tildeM/sub A/approximately-less-than-tilde6, the magnetic field is amplified by the energetic particles to the point of being in rough equipartition with them, as models of synchrotron emission frequently take the field to be. In this case, the disordering and amplification of field energy may play a major role in the shock transition.