Q. M. Lu

Shock front nonstationarity and ion acceleration in supercritical perpendicular shocks

[1]xa0Previous particle-in-cell simulations have evidenced that quasiperpendicular shocks are nonstationary and suffer a self-reformation on gyro scale of the incoming ions due to the accumulation of reflected ions. In this paper, by separating the incoming ions into reflected and directly transmitted parts, we investigate the detailed mechanisms of ion acceleration in a nonstationary perpendicular shock. Test particle simulations are performed where the shock profiles are issued from self-consistent one-dimensional full particle-in-cell simulations. Both shell and Maxwellian incoming ion distributions are used. In both cases, most energetic particles correspond to reflected ions, and the associated acceleration mechanisms include both shock drift acceleration (SDA) and shock surfing acceleration (SSA). Two types of results are obtained. First, if we fix the shock profiles at different times within a self-reformation cycle, the mechanisms of particle acceleration are different at different profiles. SDA process appears as the dominant acceleration mechanism when the width of the ramp is broad (and overshoot amplitude is low) whereas both SDA and SSA contribute as the width of the ramp is narrow (and overshoot amplitude is high). For the different shock profiles concerned herein, SDA process is more efficient (higher resulting ion energy gain) than the SSA process. Second, in order to investigate ion acceleration in self-reforming shocks, not only the ramp but also the variations of the whole shock front need to be included. In the continuously time-evolving shock, SDA remains a dominant acceleration mechanism whereas SSA mechanism becomes more and more important with the increase of the initial particle energy. The percentage of reflected ions cyclically varies in time with a period equal to the self reformation cycle, which is in agreement with previous full particle simulations. The reflected ions not only come from the distribution wings of the incoming ions but also from the core part, in contrast with previous results based on stationary shocks.

Impact of the rippling of a perpendicular shock front on ion dynamics

[1]xa0Both hybrid/full particle simulations and recent experimental results have clearly evidenced that the front of a supercritical quasi-perpendicular shock can be rippled. Recent two-dimensional simulations have focused on two different types of shock front rippling: (1) one characterized by a small spatial scale along the front is supported by lower hybrid wave activity, (2) the other characterized by a large spatial scale along the front is supported by the emission of large amplitude nonlinear whistler waves. These two rippled shock fronts are self-consistently observed when the static magnetic field is perpendicular to (so called “B0-OUT” case) or within (so called “B0-IN” case) the simulation plane, respectively. On the other hand, several studies have been made on the reflection and energization of incoming ions with a shock but most have been restricted to a one dimensional shock profile only (no rippling effects). Herein, two-dimensional test particle simulations based on strictly perpendicular shock profiles chosen at a fixed time in two-dimensional Particle-in-cell (PIC) simulations, are performed in order to investigate the impact of the shock front ripples on incident ion (H+) dynamics. The acceleration mechanisms and energy spectra of the test-ions (described by shell distributions with different initial kinetic energy) interacting with a rippled shock front are analyzed in detail. Both “B0-OUT” and “B0-IN” cases are considered separately; in each case, y-averaged (front rippling excluded) and non-averaged (front rippling included) profiles will be analyzed. Present results show that: (1) the incident ions suffer both shock drift acceleration (SDA) and shock surfing acceleration (SSA) mechanisms. Moreover, a striking feature is that SSA ions not only are identified at the ramp but also within the foot which confirms previous 1-D simulation results; (2) the percentage of SSA ions increases with initial kinetic energy, a feature which persists well with a rippled shock front; (3) furthermore, the ripples increase the porosity of the shock front, and more directly transmitted (DT) ions are produced; these strongly affect the relative percentage of the different identified classes of ions (SSA, SDA and DT ions), their average kinetic energy and their relative contribution to the resulting downstream energy spectra; (4) one key impact of the ripples is a strong diffusion of ions (in particular through the frontiers of their injection angle domains and in phase space which are blurred out) which leads to a mixing of the different ion classes. This diffusion increases with the size of the spatial scale of the front ripples; (5) through this diffusion, an ion belonging to a given category (SSA, SDA, or DT) in y-averaged case changes class in non-averaged case without one-to-one correspondence.

Statistical results describing the bandwidth and coherence coefficient of whistler mode waves using THEMIS waveform data: Whistlers: bandwidth and coherence

The bandwidths and coherence coefficients of lower band whistler mode waves are analyzed using Time History of Events and Macroscale Interactions during Substorms (THEMIS) waveform data for rising tones, falling tones, and hiss-like emissions separately. We also evaluate their dependences on the spatial location, electron density, the ratio of plasma frequency to local electron gyrofrequency (fpe/fce), and the wave amplitude. Our results show that the bandwidth normalized by the local electron gyrofrequency (fce) of rising and falling tones is very narrow (~0.01 fce), smaller than that of the hiss-like emissions (~0.025 fce). Meanwhile, the normalized bandwidth of discrete emissions gradually decreases with increasing wave amplitude, whereas that of hiss-like emissions increases slowly. The coherence coefficient of rising and falling tones is extremely large (~1), while the coherence coefficient of hiss-like emissions is smaller but is still larger than 0.5. For all categories of whistler mode waves, the normalized bandwidth increases at larger L shells. Furthermore, the normalized bandwidth is positively correlated with local fpe/fce but is inversely correlated with the electron density. Interactions between radiation belt electrons and whistler mode waves have been widely described by quasi-linear diffusion theory. Our results suggest that although quasi-linear theory is not entirely applicable for modeling electron interactions with rising and falling tones due to their narrow bandwidth and high coherence coefficient, it is suitable to treat wave-particle interactions between electrons and low-amplitude hiss-like emissions. Moreover, the correlations between the normalized bandwidth of chorus waves (especially the discrete emissions) and other parameters may provide insights for the generation mechanism of chorus waves.

Ion velocity distribution at the termination shock: 1-D PIC simulation

The Voyager 2 (V2) plasma observations of the proton temperature downstream of the quasi-perpendicular heliospheric termination shock (TS) showed that upstream thermal solar wind ions played little role in the shock dissipation mechanism and their downstream temperature is an order of magnitude smaller than predicted by MHD Rankine-Hugoniot conditions. While pickup ions (PUI) are generally expected to play an important role in energy dissipation at the shock, the details remain unclear. Here, one-dimensional (1-D) Particle-in-cell (PIC) code is used to examine kinetic properties and downstream velocity distribution functions of pickup ions (the hot supra-thermal component) and solar wind protons (SWs, the cold component) at the perpendicular heliospheric termination shock. The code treats the pickup ions self-consistently as a third component. Present results show that: (1) both of the incident SWs and PUIs can be separated into two parts: reflected (R) ions and directly transmitted (DT) ions, the energy gain of the R ions at the shock front is much larger than that of the DT ions; (2) the fraction of reflected SWs and their downstream temperature decrease with the relative percentage PUI%; (3) no matter how large the PUI% is, the downstream ion velocity distribution function always can be separated into three parts: 1. a high energy tail (i.e. the wings) dominated by the reflected PUIs, 2. a low energy core mainly contributed by the directly transmitted SWs, and 3. a middle energy part which is a complicated superposition of reflected SWs and directly transmitted PUIs. The significance of the presence of pickup ions on shock front micro-structure and nonstationarity is also discussed.