Shock ripples observed by the MMS spacecraft: ion reflection and dispersive properties

Shock ripples are ion-inertial-scale waves propagating within the front region of magnetized quasi-perpendicular collisionless shocks. The ripples are thought to influence particle dynamics and acceleration at shocks. With the four magnetospheric multiscale (MMS) spacecraft, it is for the first time possible to fully resolve the small scale ripples in space. We use observations of one slow crossing of the Earth's non-stationary bow shock by MMS. From multi-spacecraft measurements we show that the non-stationarity is due to ripples propagating along the shock surface. We find that the ripples are near linearly polarized waves propagating in the coplanarity plane with a phase speed equal to the local Alfvén speed and have a wavelength close to 5 times the upstream ion inertial length. The dispersive properties of the ripples resemble those of Alfvén ion cyclotron waves in linear theory. Taking advantage of the slow crossing by the four MMS spacecraft, we map the shock-reflected ions as a function of ripple phase and distance from the shock. We find that ions are preferentially reflected in regions of the wave with magnetic field stronger than the average overshoot field, while in the regions of lower magnetic field, ions penetrate the shock to the downstream region.