Influence of the rippling on the collisionless ion and electron motion in the shock front: A model study

Recent two‐dimensional hybrid simulations show that the shock is inhomogeneous along the shock front (rippled). Observations also provide some evidence of spatial inhomogeneity, not necessarily related to nonstationary features (waves). Recent analysis of an observed high Mach number shock has shown that its observed features are inconsistent with the assumption that it is one‐dimensional and stationary, although direct comparison of the two spacecraft measurements indicates good stationarity of its profile. We study the effects of the shock rippling alone on the collisionless motion of ions and electrons in a shock front on a simple model shock profile. We show that rippling may substantially affect ion motion, especially when the shock is rippled in the direction perpendicular to the main magnetic field. As a result, the downstream ion distribution becomes much more smooth and diffuse, which reduces the variations of the downstream ion pressure and may improve the shock stability. The smoothing is prompt and occurs at spatial scales substantially smaller than those required for the wave‐particle interaction to be significant. The required rippling scale is between the ion inertial length and upstream ion convective gyroradius, thus being significantly larger than the ramp width or spatial scale of the small‐scale structure. Electrons are much more sensitive to the rippling in the direction of the main magnetic field, which may help to partially fill the gap in the electron distribution which forms collisionlessly in the ramp.