Microinstabilities in the Transition Region of Weak Quasi-Perpendicular Intracluster Shocks

Microinstabilities play important roles in both entropy generation and particle acceleration in collisionless shocks. Recent studies have suggested that in the transition zone of quasi-perpendicular ($Q_{\perp}$) shocks in the high-beta ($\beta=P_{\rm gas}/P_{\rm B}$) intracluster medium (ICM), the ion temperature anisotropy due to the reflected-gyrating ions could trigger the Alfv\'en ion cyclotron (AIC) instability and the ion-mirror instability, while the electron temperature anisotropy induced by magnetic field compression could excite the whistler instability and the electron-mirror instability. Adopting the numerical estimates for ion and electron temperature anisotropies found in particle-in-cell (PIC) simulations of $Q_{\perp}$-shocks with sonic Mach numbers, $M_{\rm s}=2-3$, we carry out a linear stability analysis for these microinstabilities. The kinetic properties of the microinstabilities and the ensuing plasma waves on both ion and electron scales are described for wide ranges of parameters, including the dependence on $\beta$ and the ion-to-electron mass ratio. In addition, the nonlinear evolution of induced plasma waves are examined by performing 2D PIC simulations with periodic boundary conditions. We find that for $\beta\approx 20-100$, the AIC instability could induce ion-scale waves and generate shock surface ripples in supercritical shocks above the AIC critical Mach number, $M_{\rm AIC}^{*} \approx 2.3$. Also electron-scale waves are generated primarily by the whistler instability in these high-$\beta$ shocks. The resulting multi-scale waves from electron to ion scales are thought to be essential in electron injection to the diffusive shock acceleration mechanism in $Q_{\perp}$-shocks in the ICM.