Bertrand Lembège

Nonstationarity of a two-dimensional quasiperpendicular supercritical collisionless shock by self-reformation

Two‐dimensional electromagnetic particle simulations evidence a self‐reformation of the shock front for a collisionless supercritical magnetosonic shock propagating at angle θ0 around 90°, where θ0 is the angle between the normal to the shock front and the upstream magnetostatic field. This self‐reformation is due to reflected ions which accumulate in front of the shock and is observed (i) in both electric and magnetic components, (ii) for both resistive and nonresistive two‐dimensional shocks, and (iii) over a cyclic time period equal to the mean ion gyroperiod measured downstream in the overshoot; resistive effects may be self‐consistently included or excluded for θ0≂90° according to a judicious choice of the upstream magnetostatic field orientation. The self‐reformation leads to a nonstationary behavior of the shock; however, present results show evidence that the shock becomes stationary for θ less than a critical value θr, below which the self‐reformation disappears. Present results are compared to p...

Nonstationarity of strong collisionless quasiperpendicular shocks: Theory and full particle numerical simulations

Whistler waves are an intrinsic feature of the oblique quasiperpendicular collisionless shock waves. For supercritical shock waves, the ramp region, where an abrupt increase of the magnetic field occurs, can be treated as a nonlinear whistler wave of large amplitude. In addition, oblique shock waves can possess a linear whistler precursor. There exist two critical Mach numbers related to the whistler components of the shock wave, the first is known as a whistler critical Mach number and the second can be referred to as a nonlinear whistler critical Mach number. When the whistler critical Much number is exceeded, a stationary linear wave train cannot stand ahead of the ramp. Above the nonlinear whistler critical Mach number, the stationary nonlinear wave train cannot exist anymore within the shock front. This happens when the nonlinear wave steepening cannot be balanced by the effects of the dispersion and dissipation. In this case nonlinear wave train becomes unstable with respect to overturning. In the p...

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.

Self‐Reformation of the Quasi‐Perpendicular Shock: CLUSTER Observations

Among several mechanisms issued from simulation and theoretical studies proposed to account for the nonstationarity of quasi-perpendicular supercritical shocks, one process—the so-called self-reformation—driven by the accumulation of reflected ions in the foot has been intensively analyzed with simulations. Present results based on experimental CLUSTER mission clearly evidence signatures of this self-reformation process for the terrestrial bow shock. The study based on magnetic field measurements includes two parts: (i) a detailed analysis of one typical shock crossing for almost perpendicular shock directions where the risk of pollution by other nonstationarity mechanisms is minimal. A special attention is drawn on appropriate treatment of data to avoid any wrong interpretation. One key result is that the ramp width can reach a very narrow value covering a few electron inertial lengths only; (ii) a statistical analysis allows relating the signatures of this nonstationarity with different plasma conditions and shock regimes. Present results are discussed in comparison with previous simulation works.

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.

General mechanism and dynamics of the solar wind interaction with lunar magnetic anomalies from 3‐D particle‐in‐cell simulations

We present a general model of the solar wind interaction with a dipolar lunar crustal magnetic anomaly (LMA) using three-dimensional full-kinetic and electromagnetic simulations. We confirm that LMAs may indeed be strong enough to stand off the solar wind from directly impacting the lunar surface, forming a so-called ‘mini-magnetosphere’, as suggested by spacecraft observations and theory. We show that the LMA configuration is driven by electron motion because its scale size is small with respect to the gyro-radius of the solar wind ions. We identify a population of back-streaming ions, the deflection of magnetized electrons via the E × B drift motion, and the subsequent formation of a halo region of elevated density around the dipole source. Finally, it is shown that the presence and efficiency of the processes are heavily impacted by the upstream plasma conditions and, on their turn, influence the overall structure and evolution ofthe LMA system. Understanding the detailed physics of the solar wind interaction with LMAs, including magnetic shielding, particle dynamics and surface charging is vital to evaluate its implications for lunar exploration.

Formation of downstream high-speed jets by a rippled nonstationary quasi-parallel shock: 2-D hybrid simulations

Experimental observations from space missions (including more recently CLUSTER and THEMIS data) have clearly revealed the existence of high speed jets (HSJs) in the downstream region of the quasi-parallel terrestrial bow shock. Presently, two-dimensional (2-D) hybrid simulations are performed in order to investigate the formation of such HSJs through a rippled quasi-parallel shock front. The simulation results show that (i) such shock fronts are strongly nonstationary along the shock normal, and (ii) ripples are evidenced along the shock front as the upstream ULF waves (excited by interaction between incident and reflected ions) are convected back to the front by the solar wind and contribute to the rippling formation. Then, these ripples are inherent structures of a quasi-parallel shock. As a consequence, new incident solar wind ions interact differently at different locations along the shock surface, and the ion bulk velocity strongly differs locally as ions are transmitted downstream. Preliminary results show that (i) local bursty patterns of turbulent magnetic field may form within the rippled front and play the role of local secondary shock, (ii) some incident ion flows penetrate the front, suffer some deflection (instead of being decelerated) at the locations of these secondary shocks, and are at the origin of well structured (filamentary) HSJs downstream, and (iii) the spatial scales of HSJs are in a good agreement with experimental observations. Such downstream HSJs are shown to be generated by local curvature effects (front rippling) and the nonstationarity of the shock front itself.

The spatial sizes of electric and magnetic field gradients in a simulated shock

Abstract The relative scale sizes of the magnetic field gradient and the cross-shock potential have a significant impact upon the dynamics of electrons within the shock front. In particular, strong electric field gradients affect their trajectories and heating rates. The spatial sizes of the region in which the magnetic field ramp and the associated change in the electrostatic potential observed at a quasiperpendicular, supercritical shock are compared using numerical data from a 2D full particle simulation of a planar shock. The spatial scales over which these gradients are observed are shown to be of the same order of magnitude. These results are then interpreted in terms of the dynamics of electrons observed at the shock front.