  In the absence of frequent binary collisions to isotropize the plasma, the
fulfillment of the magnetohydrodynamic (MHD) Rankine-Hugoniot jump conditions
by collisionless shocks is not trivial. In particular, the presence of an
external magnetic field can allow for stable anisotropies, implying some
departures from the isotropic MHD jumps. The functional dependence of such
anisotropies in terms of the field is yet to be determined. By hypothesizing a
kinetic history of the plasma through the shock front, we recently devised a
theory of the downstream anisotropy, hence of the density jump, in terms of the
field strength for a parallel shock [J. Plasma Phys. (2018), vol. 84,
905840604]. Here, we extend the analysis to the case of a perpendicular shock.
We still find that the field reduces the density jump, but the effect is less
pronounced than in the parallel case.
