Two-stream instabilities from the lower-hybrid frequency to the electron cyclotron frequency: application to the front of quasi-perpendicular shocks

Quasi-perpendicular supercritical shocks are characterized by the presence of a magnetic foot due to the accumulation of a fraction of the incoming ions that is reflected by the shock front. There, three different plasma populations coexist (incoming ion core, reflected ion beam, electrons) and can excite various two-stream instabilities (TSIs) owing to their relative drifts. These instabilities represent local sources of turbulence with a wide frequency range extending from the lower hybrid to the electron cyclotron. Their linear features are analyzed by means of both a dispersion study and numerical PIC simulations. Three main types of TSI and correspondingly excited waves are identified: i. Oblique whistlers due to the (so-called fast) relative drift between reflected ions/electrons; the waves propagate toward upstream away from the shock front at a strongly oblique angle (θ ∼ 50°) to the ambient magnetic field Bo, have frequencies a few times the lower hybrid, and have wavelengths a fraction of the ion inertia length c∕ωpi. ii. Quasi-perpendicular whistlers due to the (so-called slow) relative drift between incoming ions/electrons; the waves propagate toward the shock ramp at an angle θ a few degrees off 90°, have frequencies around the lower hybrid, and have wavelengths several times the electron inertia length c∕ωpe. iii. Extended Bernstein waves which also propagate in the quasi-perpendicular domain, yet are due to the (so-called fast) relative drift between reflected ions/electrons; the instability is an extension of the electron cyclotron drift instability (normally strictly perpendicular and electrostatic) and produces waves with a magnetic component which have frequencies close to the electron cyclotron as well as wavelengths close to the electron gyroradius and which propagate toward upstream. Present results are compared with previous works in order to stress some features not previously analyzed and to define a more synthetic view of these TSIs.