Ion kinetic processes and thermalization at quasi‐perpendicular low Mach number shocks

Abstract

Observations of some low Mach number collisionless shocks in space have revealed that their associated ion heating is greater than adiabatic, is very rapid, is primarily in the direction perpendicular to the magnetic field, and takes place in the bulk of the distribution. These features are very different from those encountered at crossings of supercritical shocks and not yet fully understood. In this paper we use a one-dimensional hybrid kinetic simulation to study the details of the evolution of the incoming ions across a set of low Mach shocks. We find that the bulk of the ion velocity distribution becomes elongated along the direction perpendicular to the shock front as the ions traverse the shock ramp. The subsequent gyration of the ions in the steady field downstream gives rise to a temperature signature with features that correspond closely to those enumerated above. This suggests that these features may originate primarily from the kinetic behavior of the ions at the shock rather than from the operation of some instability. We also investigate the dependence of our results on a number of physical and numerical parameters in the simulation. Hugoniot conservation relations across the shock [Sckopke et al., 105a]. This equality has been used in analytical studies of the dependence of the fraction of ions reflected at the shock upon various upstream parameters [e.g., Paschmann and Sckopke, 105a; Wilkinson and Schwartz, 1990]. The ion velocity distribution immediately downstream of the ramp is therefore highly non-Maxwellian, with true thermalization occurring only gradually with time [Sckopke et al., 1983] through the action of waves driven by a number of instabilities, the most important of which is thought to be the Alfv6n ion cyclotron instability [ Tanaka et al., 1983; Thomas arid Brecht, 1986; Winskeand Quest, 1988]. It should be noted that the contribution of the directly transmitted (as opposed to reflected) ions to the overall downstream heating is small but nonnegligible and results from the mutual gyration of directly transmitted and reflected ion populations about their common center of mass (their gyration about the magnetic field in the frame of reference determined by the bulk ion velocity) [Burgess et al., 1989]. The various characteristic structural elements in the magnetic field profile of supercritical quasi-perpendicular shocks are also linked to the kinetic behavior of ions at these shocks. Thus, the extended "foot" preceding the main shock ramp is caused by the reflected ions [e.g., Paul et al., 1965; .Wong, 1968; Woods, 1969; Phillips and Robson, 1972], and the overshoot that follows the ramp results from the gyrational motion of the directly transmitted ion population about the total ion center of mass [Goodrich, 1985; Burgess et al., 1989]. Many references on the subject of ion reflection and dissipation at supercritical quasi-perpendicular shocks can be found, for example, in the review article by Gosling and Robson [1985]. We now turn our attention to low Mach number quasiperpendicul...

Analytic distribution functions for an ion plasma crossing an MHD shock

“…Most unclear in all the simulation runs remains the role of shockheated electrons. Hybrid simulation codes show that reasonable results can only be achieved by them for unreasonably high electron resistivities (Scudder 1995), which perhaps could be ascribed to ion-acoustic instabilities or to Coulomb collision mediation, but as could be shown in particle-particle simulations, neither ion-acoustic instabilities nor Coulomb collision effects are likely to become of the required importance (see Wilkinson 1991;Thomsen et al 1985).…”

Kinetic study of the ion passage over the solar wind MHD termination shock

“…Most unclear in all the simulation runs remains the role of shockheated electrons. Hybrid simulation codes show that they can only achieve reasonable results for unresasonably high electron resistivities (Scudder 1995), which perhaps could be ascribed to ion-acoustic instabilities or to Coulomb collision mediation, but, as could be shown in particle-particle simulations, neither ion-acoustic instabilities nor Coulomb collision effects are likely to become of the required importance (see Wilkinson 1991;Thomsen et al 1985). Thus it may be concluded here that neither hybrid codes nor full particle in cell codes are able at present to adequately represent the full physics of collisionless shocks.…”

A quasilinear theory of ion “thermalization” and wave excitation downstream of Earth's bow shock

“…It has been shown by simulations [Burgess et al, 1989;Wilkinson, 1991;Gedalin, 1996b] that these downstream core protons are initially spread out in the direction perpendicular to the magnetic field and have a large temperature anisotropy just downstream of the shock. Similar to the reflected protons, this distribution is unstable and redistribution of these protons generates ion cyclotron waves.…”

“…[63] By analyzing the simulated behavior of the distribution of core protons, Wilkinson [1991] concludes that their distribution is elongated in the v x direction in the shock ramp; these protons gyrate and evolve into a highly anisotropic distribution once they reach the stable magnetic field downstream of the shock. His conclusion is consistent with our simple analysis.…”