Quasi-perpendicular shocks of galaxy clusters in hybrid kinetic simulations: The structure of the shocks

Context: Cosmic ray acceleration in galaxy clusters is still an ongoing puzzle, with relativistic electrons forming radio relics at merger shocks and emitting synchrotron radiation. In the present work we perform hybrid-kinetic simulations in a range of various quasi-perpendicular foreshock conditions, including plasma beta, magnetic obliquity, and the shock Mach number. Aims: We study the ion kinetic physics, responsible for the shock structure and wave turbulence, that in turn affects the particle acceleration processes. Methods: We apply a recently developed generalized fluid-particle hybrid numerical code that can combine fluid modeling for both kinetic ions and fluid electrons. The model utilizes the exact form of the generalized Ohm's law, allowing for arbitrary choice of mass and energy densities, as well as the charge-to-mass ratio of the kinetic species. Results: We show that the properties of ion-driven multi-scale magnetic turbulence in merger shocks are in agreement with the ion structures observed in PIC simulations. In typical shocks with the sonic Mach number $M_s=3$, the magnetic structures and shock front density ripples grow and saturate at wavelengths reaching approximately four ion Larmor radii. Finally, we note that the steady-state structure of $M_s=3$ shocks in high-beta plasmas shows evidence that there is little difference between 2D and 3D simulations. The turbulence near the shock front seems to be a 2D-like structure in 3D simulations.