Upstream whistlers generated by protons reflected from a quasi-perpendicular shock

Numerical simulations of collisionless supercritical quasi-perpendicular shocks suggest that the upstream whistlers may be generated near the shock by the reflected protons which gyrate back to the shock. We investigate in detail results of hybrid simulations and a linear theory for a gyrotropic gyrating beam in a Maxwellian plasma, and we compare their outcomes. We find good agreement between the linear theory and the simulations. We compare these theoretical issues with observations, and we discuss the results. We also discuss dimensionality effects on the simulations of upstream whistlers. The investigation of lower Mach shocks leads us to a condition for the existence of a so-called shock rippling.