Heating of directly transmitted ions at low Mach number oblique collisionless shocks: A statistical physics formulation

In a previous study the authors analysed the evolution of the ion velocity distribution across a stationary exactly perpendicular one-dimensional model shock profile from a statistical physics perspective. The appropriate solution of Liouvilleʹs equation (which was shown to be different to the classical Hamiltonian solution) has the property that contours of equal phase space probability do not correspond to contours of equal energy and it is this feature that leads to the observed anisotropic ( T ⊥ > T ∥ ) heating. In the present study we extend this statistical physics analysis to oblique ( θ Bn ≠ 90 ∘ ) low Mach number shocks and quantify the weak dependence of the ion heating on the shock geometry.