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

Abstract

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 present paper it is shown that the nonlinear whistler critical Mach number corresponds to the transition between stationary and nonstationary dynamical behavior of the shock wave. The results of the computer simulations making use of the 1D full particle electromagnetic code demonstrate that the transition to the nonstationarity of the shock front structure is always accompanied by the disappearance of the whistler wave train within the shock front. Using the two-fluid MHD equations, the structure of nonlinear whistler waves in plasmas with finite beta is investigated and the nonlinear whistler critical Mach number is determined. It is suggested a new more general proof of the criteria for small amplitude linear precursor or wake wave trains to exist.

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

“…Also, the fraction of reflected ions was seen to vary strongly, and bursts of high-frequency waves were seen. The interpretation was that the reformation was driven by a fluctuating reflected fraction, and the generation of non-stationary whistler wave packets followed the reformation mechanism proposed by Krasnoselskikh et al (2002).…”

“…For example, Comişel et al (2011) performed 1-D PIC simulations and made comparisons with the same shock crossing studied by Lobzin et al (2007). Based on the simulation results, they concluded that the high-frequency fluctuations were due to the modified two-stream instability (MTSI), rather than the whistler gradient catastrophe model of Krasnoselskikh et al (2002). It could be noted that the use of a 1-D simulation introduces some strong assumptions about the microstructure of the shock, which could affect comparisons with observations.…”

“…Such recent observations, as reviewed in Krasnoselskikh et al (2013), are used to infer the importance of electron dynamics for the shock structure (e.g. Krasnoselskikh et al 1991;Sundkvist et al 2012). There is a coupling between the structure of the foot introduced by the presence of reflected-gyrating ions, whose scale is of the order of M A λ i , and the presence and behaviour of microstructure down to scales of order λ e .…”

Modified jump conditions for anisotropic temperature plasmas at parallel shocks

“…Among the theoretical approaches to MHD turbulence in astrophysical shocks, one finds e.g. Krasnoselskikh et al (2002), who performed numerical studies of MHD shocks in one dimension, describing the quasi-perpendicular shock as a superposition of Whistler waves. Lembege et al (2004) studied multiple unresolved topics of the shock transition such as the problems already mentioned earlier in this text, including shock front nonstationarity, electron heating, and particle diffusion in turbulent media, using theoretical and numerical methods.…”

The Near-Saturn Magnetic Field Environment

“…This mechanism predicts a timescale for reformation of the order of the ion cyclotron period [Chapman et al, 2005]. Nonstationarity has also been suggested to be the outcome of a gradient catastrophe of nonlinear upstream whistler, associated with Mach numbers greater than the (nonlinear) whistler critical Mach number beyond which an upstream whistler cannot phase stand in the upstream flow 98 [Krasnoselskikh et al, 2002]. An alternative mechanism found in particle-in-cell (PIC) simulations is the quasi-periodic disruption of the ion foot due to the modified two-stream instability [Scholer and Matsukiyo, 2004].…”