Distribution functions of ions heated in quasi-perpendicular bow shocks have a large perpendicular temperature anisotropy that provides free energy for the growth of Alfv¿n ion cyclotron (AIC) waves and mirror waves. Both types of waves have been observed in the Earth's magnetosheath downstream of quasi-perpendicular shocks. The question of whether these waves are produced at the shock and convected downstream or whether they are produced locally in the magnetosheath has not yet been answered. If the latter were true, then under most magnetosheath conditions AIC waves should dominate the wave activity, yet frequently mirror waves either dominate or are competitive with the AIC mode.

We address this question by using two-dimensional hybrid simulations to give a self-consistent description of the evolution of the wave spectra downstream of quasi-perpendicular shocks. Both mirror and AIC waves are identified in the simulated magnetosheath. They are generated at or near the shock front and convected away from it by the sheath plasma. Near the shock, the waves have a broad spectrum, but downstream of the shock, shorter-wavelength modes are heavily damped and only longer-wavelength modes persist. The characteristics of these surviving modes can be predicted with reasonable accuracy by linear kinetic theory appropriate for downstream conditions. Throughout the downstream region, the power in compressive magnetic oscillations is of the same order as the power in transverse oscillations.

We also follow the evolution of the ion distribution function. The shocked ions that provide the free energy for wave growth have a two-component distribution function: a core population of directly transmitted ions and a smaller halo of initially reflected ions that contains the bulk of the free energy. The halo is initially gyrophase-bunched and extremely anisotropic. Within a relatively short distance downstream of the shock (of the order of 10 ion inertial lengths), wave-particle interactions remove these features from the halo and reduce the anisotropy of the distribution to near-threshold levels for the mirror and AIC instabilities. A similar evolution has been observed for ions at the Earth's bow shock. ¿ American Geophysical Union 1995