Whistler waves, core ion heating, and nonstationarity in oblique collisionless shocks

One-dimensional full particle simulations of supercritical collisionless shocks with an ion and electron beta of 0.1 (particle to magnetic field pressure) over a wide Alfvén Mach number range and range of shock normal-magnetic field angles between $ΘBn=60°$ and $ΘBn=80°$ are presented. The whistler critical Mach number $Mw$⁠, below which a linear phase-standing whistler can exist, is proportional to the square root of the ion-to-electron mass ratio and to $cosΘBn$⁠. In small mass ratio simulations of oblique shocks, $Mw$ can be artificially small and close to the first critical Mach number $Mc$⁠, above which the process of ion reflection is needed in order to achieve shock dissipation. We use in the simulations the physical ion-to-electron mass ratio so that $Mc$ and $Mw$ are well separated. This also allows excitation of the modified two-stream instability (MTSI) between incoming ions and electrons. We find that in oblique but close to perpendicular $(ΘBn⩾80°)$ shocks, upstream whistler waves do occur, but reformation is due to accumulation of reflected-gyrating ions at the upstream edge of the foot. In less oblique shocks above the whistler critical Mach number, the whistler amplitude in the foot upstream of the ramp grows, leading to vortices of the incoming ions and the reflected ions in velocity phase space, and eventually to phase mixing. The shock re-forms at the upstream edge of the whistler wave train, which is particularly evident in very high Mach number shocks where the scale of the foot is large compared with the whistler wave train. After reformation, the region with phase-mixed incoming and reflected ions constitutes a hot core downstream of the shock ramp. In this whistler induced reformation process, the MTSI results mainly in heating of the incoming ions in the foot.