Wave and ion evolution downstream of quasi‐perpendicular bow shocks

Abstract

Distribution functions of ions heated in quasi‐perpendicular bow shocks have a large perpendicular temperature anisotropy that provides free energy for the growth of Alfvén ion cyclotron (AIC) waves and mirror waves. Both types of waves have been observed in the Earth's magnetosheath downstream of quasi‐perpendicular shocks. The question of whether these waves are produced at the shock and convected downstream or whether they are produced locally in the magnetosheath has not yet been answered. If the latter were true, then under most magnetosheath conditions AIC waves should dominate the wave activity, yet frequently mirror waves either dominate or are competitive with the AIC mode. We address this question by using two‐dimensional hybrid simulations to give a self‐consistent description of the evolution of the wave spectra downstream of quasi‐perpendicular shocks. Both mirror and AIC waves are identified in the simulated magnetosheath. They are generated at or near the shock front and convected away from it by the sheath plasma. Near the shock, the waves have a broad spectrum, but downstream of the shock, shorter‐wavelength modes are heavily damped and only longer‐wavelength modes persist. The characteristics of these surviving modes can be predicted with reasonable accuracy by linear kinetic theory appropriate for downstream conditions. Throughout the downstream region, the power in compressive magnetic oscillations is of the same order as the power in transverse oscillations. We also follow the evolution of the ion distribution function. The shocked ions that provide the free energy for wave growth have a two‐component distribution function: a core population of directly transmitted ions and a smaller halo of initially reflected ions that contains the bulk of the free energy. The halo is initially gyrophase‐bunched and extremely anisotropic. Within a relatively short distance downstream of the shock (of the order of 10 ion inertial lengths), wave‐particle interactions remove these features from the halo and reduce the anisotropy of the distribution to near‐threshhold levels for the mirror and AIC instabilities. A similar evolution has been observed for ions at the Earth's bow shock.

The properties and causes of rippling in quasi-perpendicular collisionless shock fronts

“…The fast mode transition is also of interest, since MHD waves are unable to propagate upstream of this point. McKean et al (1995) report an ion temperature increase at the overshoot by a factor Fig. 9.…”

“…However, it was noted that the amplitude of the structures within the ramp was reduced in the three-dimensional simulations, relative to that seen in the two-dimensional simulations. A more detailed study of the downstream plasma evolution seen in twodimensional hybrid simulations was carried out by McKean et al (1995). In these simulations waves driven by the AIC and mirror instabilities were seen, both depending on the perpendicular ion temperature anisotropy.…”

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

“…Thus it is possible that this rippling is not a result of any instability and wave growth but is an inevitable part of the shock structure (see below) and a manifestation of the intrinsic shock dynamics (probably, in the spirit of Krasnosel'skikh [1985], if it is nonstationary). It is worth mentioning that such rippling was found to occur in the direction of the magnetic field [McKean et al, 1995] as well as in the perpendicular direction [Savoini and Lembege, 1994] (the last one was observed in two-dimensional full particle simulations). There is also limited observational evidence in favor of the shock rippling based on the fact that the locally found shock normal direction varies substantially across the shock front and often differs for two spacecraft-measured profiles.…”

“…role of these waves, yet there is no explanation for how these waves could have already grown to such high amplitudes (comparable to the overall magnetic field jump) at the upstream side of the ramp (which is necessary to cause noticeable rippling) or how these waves (wavelengths of the order of several ion inertial lengths at least [McKean et al, 1995]) cannot exist inside a ramp whose width typically does not exceedi one ion inertial length ]. Thus it is possible that this rippling is not a result of any instability and wave growth but is an inevitable part of the shock structure (see below) and a manifestation of the intrinsic shock dynamics (probably, in the spirit of Krasnosel'skikh [1985], if it is nonstationary).…”

“…It is possible that the magnetic field fluctuations are directly related to the currents produced by the bunching of gyrating ions and not by instabilities. Moreover, the presented ion distributions are averaged in the direction of rippling [McKean et al, 1995] It therefore makes sense to study the effects of stationary but rippled fields on the ion and electron motion, leaving aside wave-particle interactions, to achieve better understanding of the shock physics, in particular, of whether macroscopic quasistationary fields may be responsible for the prompt ion distribution smoothing. Our approach is quite straightforward.…”