Microinstabilities from the Ion Inertia Length to the Electron Gyroradius Due to Reflected Ions in the Front of Supercritical Perpendicular Shocks

We present a synthetic view of the plasma microinstabilities which can occur in the foot of supercritical perpendicular shocks. In these shocks a substantial fraction of ions is reflected at the steep shock ramp. Then, some streaming instabilities are excited by the relative drifts between populations of incoming ions, reflected ions, and electrons across the foot's magnetic field. The instabilities cover wavelengths from the ion inertia length to the electron gyroradius and frequencies from the lower-hybrid to the electron cyclotron, depending upon solar wind characteristics. The particle distributions are modelled as three components: a broad electron population and two ion populations, namely a core and a beam representing the reflected ions. The two ion populations drift in opposite direction with respect to the electron population so as to ensure the zero current condition along the shock normal direction. Assuming the ion beam is directed along the shock normal at 90° to B0, we investigate the possible instabilities under various wave propagation angles. The plasma considered is characterized by a double anisotropy: one defined by the direction of B0, the other by that of the reflected beam. Let Ψ be the magnetic coplanarity plane defined by these two directions. There are therefore two main angles playing a role for the instabilities: (a) the angle θbk between the wave vector and B0, (b) the angle ψvk between the wave vector and the plane Ψ containing the beam. As a result the 3 × 3 dielectric tensor Q is full with terms that are distinct. We show three types of instability at various angles: 1) one about the electron gyroradius with frequencies at the electron cyclotron frequency Ωe and harmonics; 2) one about the electron inertia length with frequencies less than Ωe ; 3) one about the ion inertia length with frequencies of the order of the lower-hybrid. The dispersion relation is computed with the dielectric tensor Q for different parameter values. The instabilities are analyzed with full electromagnetic PIC simulations and are compared with the MTSI-1 and 2 of Matsukyio and Scholer [JGR 111, 2006] or the low-frequency whistlers of Hellinger and Mangeney [JGR 102, 1997] are discussed.