Two Types of Whistler Instabilities in the Foot of Quasi-perpendicular Supercritical Shocks: a Poynting Flux Analysis

Supercritical shocks in collisionless plasmas are characterized by a substantial population of ions reflected off of the steep shock ramp. These ions carry a significant amount of energy and are fundamental to the transformation of directed kinetic energy into thermal energy. For quasi-perpendicular geometries and as seen in the normal incidence frame (NIF), the velocity of the reflected ions is mostly directed at 90o to the magnetic field Bo. Streaming instabilities can develop, which are excited by the relative drifts between incoming ions, reflected ions, and electrons across the shock's foot. Two types of waves from the whistler branch and with frequencies in the lower-hybrid range are shown to be unstable:Oblique waves with wavelengths a fraction of the ion inertia length that propagate toward upstream at angles about 50o to Bo. Quasi-perpendicular waves with wavelengths several times the electron inertia length that propagate toward downstream at angles larger than 80o to Bo. For each type of whistlers we perform electromagnetic pseudo-oblique 1D PIC simulations. These are carried out in the proper frame where the total momentum density vanishes. Field data issued from the simulations are used to construct hodograms and compute the Poynting fluxes. We apply the Lorentz transformation in order to express the results in the NIF, where they can be discussed and compared to measurements from Cluster at Earth's bow shock [Sundkvist D, et al., PRL 108, 2012].