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 inhomogene ous along the shock front (rippled). Observations also provide some evidenc e of spatial inhomogeneity, not necessarily related to nonstationary featur es (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 spac ecraft measurements indicates good stationarity of its profile. We study th e effects of the shock rippling alone on the collisionless motion of ions a nd 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 re sult, the downstream ion distribution becomes much more smooth and diffuse, which reduces the variations of the downstream ion pressure and may improv e the shock stability. The smoothing is prompt and occurs at spatial scales substantially smaller than those required for the wave-particle interactio n to be significant. The required rippling scale is between the ion inertia l length and upstream ion convective gyroradius, thus being significantly l arger than the ramp width or spatial scale of the small-scale structure. El ectrons are much more sensitive to the rippling in the direction of the mai n magnetic field, which may help to partially fill the gap in the electron distribution which forms collisionlessly in the ramp.