Quasi-perpendicular fast magnetosonic shock with wave precursor in collisionless plasma

A one-dimensional particle-in-cell (PIC) simulation tracks a fast magnetosonic shock over time scales comparable to an inverse ion gyrofrequency. The magnetic pressure is comparable to the thermal pressure upstream. The shock propagates across a uniform background magnetic field with a pressure that equals the thermal pressure upstream at the angle 85$^\circ$ at a speed that is 1.5 times the fast magnetosonic speed in the electromagnetic limit. Electrostatic contributions to the wave dispersion increase its phase speed at large wave numbers, which leads to a convex dispersion curve. A fast magnetosonic precursor forms ahead of the shock with a phase speed that exceeds the fast magnetosonic speed by about $\sim 30 \%$. The wave is slower than the shock and hence it is damped.