Statistical Study of Shock Rippling 

<p>MMS can resolve the fine structure of the shock ramp, which often shows holes in reduced ion-phase space distributions (integrated along the tangential plane of the shock). This is possible due to the high temporal resolutions of FPI/DIS. Such holes have been associated with ripples propagating along the shock surface but also can be related to the shock reformation. We statistically characterize the ion phase-space holes at the Earth&#8217;s bow shock using MMS observations. We establish a systematic procedure to find the shocks exhibiting the phase-space holes. We apply the procedure to ~500 shock crossings for which the burst data necessary to identify the holes is available. We identify phase-space holes for 66% of the crossings. We note that the actual occurrence is likely higher, as the holes are not resolved for fast shock crossings. We characterize the occurrence of the holes as a function of shock parameters such as Mach number and geometry. We find that the holes are widespread at the bow shock and are present for a wide range of shock geometries and Mach numbers (M_A) studied. Their occurrence has no dependence on the shock geometry and increases with the Mach number, M_A. The highest occurrence (70% probability) is for M_A&#160;above 5. These results are essential to understanding the non-stationary behavior of collisionless shocks.</p>