  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.
