On the reformation at quasi‐ and exactly perpendicular shocks: Full particle‐in‐cell simulations

Abstract

[1] A full particle-in-cell (PIC) simulation study is carried out on the reformation at quasi-and exactly perpendicular collisionless shocks with a relatively low Alfven Mach number (M A = 5). Previous self-consistent one-dimensional (1-D) hybrid and full PIC simulations have demonstrated that ion kinetics are essential for the nonstationarity of perpendicular collisionless shocks. These results showed that reflection of ions at the shock front is responsible for the periodic collapse and redevelopment of a new shock front on a timescale of the ion cyclotron period, which is called the shock reformation. Recent 2-D hybrid and full PIC simulations, however, suggested that the shock reformation does not take place at exactly perpendicular shocks with M A ∼ 5. By contrast, another 2-D hybrid PIC simulation showed that the shock reformation persists at quasi-perpendicular shocks with M A ∼ 5. Although these two works seem to be inconsistent with each other, the reason is not well understood because of several differences in numerical simulation conditions. Thus this paper gives a direct comparison between full PIC simulations of quasi-and exactly perpendicular shocks with almost the same condition. It is found that the time development of the shock magnetic field averaged over the shock-tangential direction shows the transition from the reformation to no-reformation phase. On the other hand, local shock magnetic field shows the evident appearance and disappearance of the shock front, and the period becomes longer in the no-reformation phase than in the reformation phase.

Nonrelativistic Perpendicular Shocks Modeling Young Supernova Remnants: Nonstationary Dynamics and Particle Acceleration at Forward and Reverse Shocks

“…Moreover, the shock-reformation process can also be influenced by the shock-front ripples. The latter was shown to modify the period of the reformation cycles in later stages in low-Mach-number perpendicular shocks (e.g., Hellinger et al 2007;Lembège et al 2009;Umeda et al 2010). However, the rippling of the shock surface is weak in our case of a high-Mach-number forward shock and we do not see any apparent change of the reformation period throughout the duration of our simulation.…”

“…For panel (b), we compensated the average velocity of all ions (see Figure 10), whereas for panel (c) on the right we compensated only the average motion of incoming ions. Umeda et al 2009Umeda et al , 2010Umeda et al , 2014. The ion temperature anisotropy arising from ion reflection at the shock can drive the Alfvén ion cyclotron (AIC) or the mirror instability in the shock ramp, and the resulting unstable modes have wavelengths of a few ion skin depths and propagate along the regular magnetic field, significantly contributing to ion isotropization and thermalization at the shock and downstream.…”

“…The process is called a cyclic self-reformation of the shock and is caused by the dynamics of the shock-reflected ions (see, e.g., Treumann 2009; Umeda et al 2010Umeda et al , 2014. Figure 18 shows the time evolution of the average density profile in the vicinity of the forward shock.…”

Microstructure in two- and three-dimensional hybrid simulations of perpendicular collisionless shocks

“…The 2-D hybrid simulations of Yuan et al (2009), on the other hand, seemed to show that reformation could occur despite the presence of whistler waves. However, it has been shown that reformation can appear to be suppressed if quantities are averaged over a direction tangential to the shock surface, even though the time evolution at a fixed point on the shock surface does show oscillations attributed to reformation (Umeda et al 2010).…”

Periodic self-reformation of rippled perpendicular collisionless shocks in two dimensions

“…In order to study the contradiction between the former (Hellinger et al, 2007;Lembege et al, 2009) and latter (Yuan et al, 2009) results, a direct comparison was made between the 2-D full PIC simulation results of quasi-perpendicular (θ B n = 80 • ) and exactly perpendicular (θ B n = 90 • ) shocks (Umeda et al, 2010). It was confirmed that the shock-normal angle does not affect the presence or the suppression of the reformation of (quasi-)perpendicular shocks.…”