  Based on Magnetospheric Multiscale (MMS) observations from the Earth's bow
shock, we have identified two plasma heating processes that operate at
quasi-perpendicular shocks. Ions are subject to stochastic heating in a process
controlled by the heating function $\chi_j = m_j q_j^{-1}
B^{-2}\mathrm{div}(\mathbf{E}_\perp)$ for particles with mass $m_j$ and charge
$q_j$ in the electric and magnetic fields $\mathbf{E}$ and $\mathbf{B}$. Test
particle simulations are employed to identify the parameter ranges for bulk
heating and stochastic acceleration of particles in the tail of the
distribution function. The simulation results are used to show that ion heating
and acceleration in the studied bow shock crossings is accomplished by waves at
frequencies (1-10)$f_{cp}$ (proton gyrofrequency) for the bulk heating, and
$f>10f_{cp}$ for the tail acceleration. When electrons are not in the
stochastic heating regime, $|\chi_e|<1$, they undergo a quasi-adiabatic heating
process characterized by the isotropic temperature relation
$T/B=(T_0/B_0)(B_0/B)^{1/3}$. This is obtained when the energy gain from the
conservation of the magnetic moment is redistributed to the parallel energy
component through the scattering by waves. The results reported in this paper
may also be applicable to particle heating and acceleration at astrophysical
shocks.
