Philippe Savoini

Nonstationarity of a two‐dimensional perpendicular shock: Competing mechanisms

Two-dimensional particle-in-cell (PIC) simulations are used for analyzing in detail different nonstationary behaviors of a perpendicular supercritical shock. A recent study by Hellinger et al. (2007) has shown that the front of a supercritical shock can be dominated by the emission of large-amplitude whistler waves. These waves inhibit the self-reformation driven by the reflected ions; then, the shock front appears almost “quasi-stationary.” The present study stresses new complementary results. First, for a fixed βi value, the whistler waves emission (WWE) persists for high MA above a critical Mach number (i.e., MA ≥ MAWWE). The quasi-stationarity is only apparent and disappears when considering the full 3-D field profiles. Second, for lower MA, the self-reformation is retrieved and becomes dominant as the amplitude of the whistler waves becomes negligible. Third, there exists a transition regime in MA within which both processes compete each other. Fourth, these results are observed for a strictly perpendicular shock only as B0 is within the simulation plane. When B0 is out of the simulation plane, no whistler waves emission is evidenced and only self-reformation is recovered. Fifth, the occurrence and disappearance of the nonlinear whistler waves are well recovered in both 2-D PIC and 2-D hybrid simulations. The impacts on the results of the mass ratio (2-D PIC simulations), of the resistivity and spatial resolution (2-D hybrid simulations), and of the size of the simulation box along the shock front are analyzed in detail.

Emission of nonlinear whistler waves at the front of perpendicular supercritical shocks: Hybrid versus full particle simulations

New behavior of strictly perpendicular shocks in supercritical regime is analyzed with the help of both two-dimensional (2-D) hybrid and full particle electromagnetic simulations. Surprisingly, in both simulation cases, the shock front region appears to be dominated by emission of coherent large amplitude whistler waves for some plasma conditions and shock regimes. These whistler waves are oblique with respect to the shock normal as well as to the upstream magnetic field and are phase-standing in the shock rest frame. A parametric study shows that these whistler waves are emitted in 2-D perpendicular shocks and, simultaneously, the self-reformation of the shock front associated with reflected ions disappears; the 2-D shock front is almost quasi-stationary. In contrast, both corresponding one-dimensional (1-D) hybrid and full particle simulations performed in similar plasma and Mach regime conditions show that the self-reformation takes place for 1-D perpendicular shock. These results indicate that the emission of these 2-D whistler waves can inhibit the self-reformation in 2-D shocks. Possible generating mechanisms of these waves emissions and comparison with previous works are discussed.

Electron dynamics in two‐ and one‐dimensional oblique supercritical collisionless magnetosonic shocks

Two- and one-dimensional fully electromagnetic, bounded, particle (for both electrons and ions) codes are used in order to study electron dynamics in collisionless magnetosonic shocks propagating in supercritical regime and quasi-perpendicular direction (90° > θ0 > 45°); θ0 is the angle between the shock normal and the upstream magnetic field. The purpose of the study consists in comparing electrons behavior in one-dimensional (“pseudo-oblique”) nonresistive shocks and in two-dimensional resistive oblique shocks. Resistive effects related to plasma microinstabilities can be self-consistently included in two-dimensional particle codes in contrast with one-dimensional particle codes. Present two-dimensional results reproduce local electron distribution functions (in particular, downstream “flat tops”) in a self-consistent way and in good agreement with observational results. On the other hand, one-dimensional results exhibit either local enlarged Maxwellian distributions with a partial tail, or a flat top distribution according to the particle density n. These results emphasize that (1) the differences observed between one- and two-dimensional codes may be explained in terms of a critical particle density nc used in the one-dimensional code; (2) the evidence of flat tops in both two- and one-dimensional results (provided that n > nc) proves that the macroscopic potential jump at the shock front is mainly responsible for their formation; (3) microscopic effects (herein related to the self-consistent cross-field/field-aligned currents instabilities) may represent a complementary mechanism for filling the flat top distribution; (4) some relaxation of the unstable electron flat top distribution (T∥/T⊥ ≫ 1) is observed when penetrating further into the downstream region, which means that the main filling mechanisms are localized in the ramp of the shock. Moreover, a detailed study of two-dimensional results shows that both resistive and nonresistive configurations can be easily distinguished for θ0 ≈ 90°, but not any more for large deviations of θ0 from 90° for which the self-consistent magnetic field rotates noticeably out of the coplanarity plane at the shock front.

Two‐dimensional simulations of a curved shock: Self‐consistent formation of the electron foreshock

A collisionless curved shock is analyzed in a supercritical regime with the help of a two-dimensional electromagnetic full particle code. Curvature effects are included self-consistently and allow one to follow continuously the transition from a narrow and step-like strictly perpendicular shock to a wider and more turbulent oblique shock within the quasi-perpendicular range 65° < θBn < 90°. Present results reproduce the formation of the electron foreshock without any simplifying assumptions. In agreement with experimental data, local bump-on-tail parallel distribution functions are well recovered in the foreshock region and correspond to electrons backstreaming along the magnetic field lines. Present detailed analysis shows that local back-streaming distributions have two components: (i) a high parallel energy component corresponding to back-streaming electrons characterized by a field-aligned bump-in-tail or beam signature, and (ii) a low-energy parallel component characterized by a loss cone signature (mirrored electron). Two types of bump-in-tail patterns, broad and narrow, are identified at short and large distances from the curved shock, respectively, and are due to different contributions of these two components according to the local impact of the time-of-flight effects. Present results allow one to identify more clearly the nature of the bump-in-tail pattern evidenced experimentally (narrow type). These also confirm that mirroring electrons make the dominant contribution to the bump-in-tail pattern in the total distribution in agreement with previous studies. Results suggest that low and high parallel energy populations are intimately related and may contribute together to the upstream wave turbulence.

Origin of backstreaming electrons within the quasi‐perpendicular foreshock region: Two‐dimensional self‐consistent PIC simulation

The foreshock region is populated by energetic backstreaming particles (electrons and ions) issued from the shock after having interacted with it. Several aspects concerning the origin of these high-energy particles and their corresponding acceleration mechanisms are still unresolved. The present study is focused on a quasi-perpendicular curved shock and associated electron foreshock region (i.e., for 90° ≥ θBn ≥ 45°, where θBn is the angle between the shock normal and the upstream magnetostatic field). Two-dimensional full-particle simulation is used in order to include self-consistently the electron and ion dynamics, the full dynamics of the shock, the curvature effects and the time-of-flight effects. All expected salient features of the bow shock are recovered both for particles and for electromagnetic fields. Present simulations evidence that the fast-Fermi acceleration (magnetic mirror) mechanism, which is commonly accepted, is certainly not the unique process responsible for the formation of energetic backstreaming electrons. Other mechanisms also contribute. More precisely, three different classes of backstreaming electrons are identified according to their individual penetration depth within the shock front: (i) “magnetic mirrored” electrons which only suffer a specular reflection at the front, (ii) “trapped” electrons which succeed to penetrate the overshoot region and suffer a local trapping within the parallel electrostatic potential at the overshoot, and (iii) “leaked” electrons which penetrate even much deeper into the downstream region. “Trapped” and “leaked” electrons succeed to find appropriate conditions to escape from the shock and to be reinjected back upstream. All these different types of electrons contribute together to the formation of energetic field-aligned beam. The acceleration mechanisms associated to each electron class and/or escape conditions are analyzed and discussed.