Non adiabatic electron behavior through a supercritical perpendicular collisionless shock: Impact of the shock front turbulence

International audienceAdiabatic and nonadiabatic electrons transmitted through a supercritical perpendicular shock wave are analyzed with the help of test particle simulations based on field components issued from 2 − D full-particle simulation. A previous analysis (Savoini et al., 2005) based on 1 − D shock profile, including mainly a ramp (no apparent foot) and defined at a fixed time, has identified three distinct electron populations: adiabatic, overadiabatic, and underadiabatic, respectively, identified by μds/μus ≈ 1, >1 and <1, where μus and μds are the magnetic momenta in the upstream and downstream regions. Presently, this study is extended by investigating the impact of the time evolution of 2 − D shock front dynamics on these three populations. Analysis of individual time particle trajectories is performed and completed by statistics based on the use of different upstream velocity distributions (spherical shell of radius vshell and a Maxwellian with thermal velocity vthe). In all statistics, the three electron populations are clearly recovered. Two types of shock front nonstationarity are analyzed. First, the impact of the nonstationarity along the shock normal (due to the front self-reformation only) strongly depends on the values of vshell or vthe. For low values, the percentages of adiabatic and overadiabatic electrons are almost comparable but become anticorrelated under the filtering impact of the self-reformation; the percentage of the underadiabatic population remains almost unchanged. In contrast, for large values, this impact becomes negligible and the adiabatic population alone becomes dominant. Second, when 2 − D nonstationarity effects along the shock front (moving rippling) are fully included, all three populations are strongly diffused, leading to a larger heating; the overadiabatic population becomes largely dominant (and even larger than the adiabatic one) and mainly contributes to the energy spectrum

Ion acceleration processes at reforming collisionless shocks

The identification of pre-acceleration mechanisms for cosmic ray ions in supernova remnant shocks is an important problem in astrophysics. Recent particle-in-cell (PIC) shock simulations have shown that inclusion of the full electron kinetics yields non-time-stationary solutions, in contrast to previous hybrid (kinetic ions, fluid electrons) simulations. Here, by running a PIC code at high phase space resolution, ion acceleration mechanisms associated with the time dependence of a supercritical collisionless perpendicular shock are examined. In particular the components of $\int \mathbf{F} \cdot \mathbf{v} dt$ are analysed along trajectories for ions that reach both high and low energies. Selection mechanisms for the ions that reach high energies are also examined. In contrast to quasi-stationary shock solutions, the suprathermal protons are selected from the background population on the basis of the time at which they arrive at the shock, and thus are generated in bursts.Comment: 12 Pages, 7 Figures, To be published in Phys. Plasma

Contributions to the cross shock electric field at supercritical perpendicular shocks: Impact of the pickup ions

A particle-in-cell code is used to examine contributions of the pickup ions (PIs) and the solar wind ions (SWs) to the cross shock electric field at the supercritical, perpendicular shocks. The code treats the pickup ions self-consistently as a third component. Herein, two different runs with relative pickup ion density of 25% and 55% are presented in this paper. Present preliminary results show that: (1) in the low percentage (25%) pickup ion case, the shock front is nonstationary. During the evolution of this perpendicular shock, a nonstationary foot resulting from the reflected solar wind ions is formed in front of the old ramp, and its amplitude becomes larger and larger. At last, the nonstationary foot grows up into a new ramp and exceeds the old one. Such a nonstationary process can be formed periodically. hen the new ramp begins to be formed in front of the old ramp, the Hall term mainly contributed by the solar wind ions becomes more and more important. The electric field Ex is dominated by the Hall term when the new ramp exceeds the old one. Furthermore, an extended and stationary foot in pickup ion gyro-scale is located upstream of the nonstationary/self-reforming region within the shock front, and is always dominated by the Lorentz term contributed by the pickup ions; (2) in the high percentage (55%) pickup ion case, the amplitude of the stationary foot is increased as expected. One striking point is that the nonstationary region of the shock front evidenced by the self-reformation disappears. Instead, a stationary extended foot dominated by Lorentz term contributed by the pickup ions, and a tationary ramp dominated by Hall term contributed by the solar wind ions are clearly evidenced. The significance of the cross electric field on ion dynamics is also discussed.Comment: 11 pages, 6 figs and 1 table. This paper will be published in the journal: Astrophysics and Space Scienc

Two-stream instabilities from the lower-hybrid frequency to the electron cyclotron frequency: application to the front of quasi-perpendicular shocks

Quasi-perpendicular supercritical shocks are characterized by the presence of a magnetic foot due to the accumulation of a fraction of the incoming ions that is reflected by the shock front. There, three different plasma populations coexist (incoming ion core, reflected ion beam, electrons) and can excite various two-stream instabilities (TSIs) owing to their relative drifts. These instabilities represent local sources of turbulence with a wide frequency range extending from the lower hybrid to the electron cyclotron. Their linear features are analyzed by means of both a dispersion study and numerical PIC simulations. Three main types of TSI and correspondingly excited waves are identified: i. Oblique whistlers due to the (so-called fast) relative drift between reflected ions/electrons; the waves propagate toward upstream away from the shock front at a strongly oblique angle (θ ∼ 50°) to the ambient magnetic field Bo, have frequencies a few times the lower hybrid, and have wavelengths a fraction of the ion inertia length c∕ωpi. ii. Quasi-perpendicular whistlers due to the (so-called slow) relative drift between incoming ions/electrons; the waves propagate toward the shock ramp at an angle θ a few degrees off 90°, have frequencies around the lower hybrid, and have wavelengths several times the electron inertia length c∕ωpe. iii. Extended Bernstein waves which also propagate in the quasi-perpendicular domain, yet are due to the (so-called fast) relative drift between reflected ions/electrons; the instability is an extension of the electron cyclotron drift instability (normally strictly perpendicular and electrostatic) and produces waves with a magnetic component which have frequencies close to the electron cyclotron as well as wavelengths close to the electron gyroradius and which propagate toward upstream. Present results are compared with previous works in order to stress some features not previously analyzed and to define a more synthetic view of these TSIs

Cross-bispectral analysis of the electromagnetic field in a beam-plasma interaction

International audienceThe use of bicoherence has proved its efficiency in the analysis of nonlinear wave interactions. The method has been adapted to interpret the results of a simulation of the beam-plasma interaction, in a case of broadband spectra, where many unstable modes can be suspected to couple. As the interacting waves exhibit different polarizations (electrostatic and electromagnetic), the bicoherence has been modified into a cross bicoherence in order to test the coupling of different field components. The visualization of the result has been designed in order to evidence the couplings in terms of efficiency (high bicoherence) and energy (high power). The application of this method to the simulation results shows that quadratic wave interactions are effective; new helpful information is stressed in order to interpret the observed growth of large-scale magnetic fluctuations