Nonlinear evolution of the magnetized Kelvin-Helmholtz instability: From fluid to kinetic modeling

Abstract

The nonlinear evolution of collisionless plasmas is typically a multi-scale process where the energy is injected at large, fluid scales and dissipated at small, kinetic scales. Accurately modelling the global evolution requires to take into account the main micro-scale physical processes of interest. This is why comparison of different plasma models is today an imperative task aiming at understanding cross-scale processes in plasmas. We report here the first comparative study of the evolution of a magnetized shear flow, through a variety of different plasma models by using magnetohydrodynamic, Hall-MHD, two-fluid, hybrid kinetic and full kinetic codes. Kinetic relaxation effects are discussed to emphasize the need for kinetic equilibriums to study the dynamics of collisionless plasmas in non trivial configurations. Discrepancies between models are studied both in the linear and in the nonlinear regime of the magnetized Kelvin-Helmholtz instability, to highlight the effects of small scale processes on the nonlinear evolution of collisionless plasmas. We illustrate how the evolution of a magnetized shear flow depends on the relative orientation of the fluid vorticity with respect to the magnetic field direction during the linear evolution when kinetic effects are taken into account. Even if we found that small scale processes differ between the different models, we show that the feedback from small, kinetic scales to large, fluid scales is negligable in the nonlinear regime. This study show that the kinetic modeling validates the use of a fluid approach at large scales, which encourages the development and use of fluid codes to study the nonlinear evolution of magnetized fluid flows, even in the colisionless regime.

Comparison Between Fluid Simulation With Test Particles and Hybrid Simulation for the Kelvin‐Helmholtz Instability

“…Therefore, there are several sharp jumps between t = 100 and 150 in panel c, and this process can be exaggerated by the nonlinear resistivity model. For hybrid simulation, the size of magnetic islands is smaller, and they exist not only inside of the vortex but also along the spine region, suggesting that the magnetic diffusion region becomes very patchy in the hybrid simulation, which is likely due to the kinetic physics missing in the fluid description and numeric noise (Henri et al, 2013). In contrast, the hybrid simulation gradually increases the magnetic island area and saturates at a smaller value (≈ 100) compared to the fluid result.…”

“…The symmetric treatment of the time derivative in the Boris method maintains the temporal reversibility of the Lorentz equation. The different KH growth rate between fluid simulation and kinetic simulation has been discussed by Nakamura et al (2010) and Henri et al (2013). Figure 1 shows the velocity u x component (panel a), the anomalous viscosity, ano (panel b), the area of magnetic island, A r (panel c), and the area of mixed region, A M (panel d), as functions of the time from top to bottom, respectively, which roughly represents the overall dynamic properties of the fluid with test particle simulation (blue lines) and the hybrid simulation (red crosses).…”

Self-organization of the vorticity field in two-dimensional quasi-ideal fluids: The statistical and field-theoretical formulations

“…The process consists of encounters and merging of like-sign vortices. In relaxation from strongly unstable states there is a transitory phase of opposite-sign vortex pairing [18].…”

The impact of a hot sodium ion population on the growth of the Kelvin‐Helmholtz instability in Mercury's magnetotail

“…The parameters B 0 , n 0s, and are chosen such that the boundary layer is initialized in MHD pressure balance. We note that low‐amplitude magnetoacoustic waves propagate from the boundary at t = 0 as a result of the deviation from full kinetic equilibrium [ Henri et al , ; Cerri et al , ]. Simulations are normalized such that the reference background number density n 0 =1, B 0 =1, and spatial scales are given in units of the proton inertial length d p = v A / Ω , for , and timescales are given in units of the inverse proton gyrofrequency t Ω = Ω −1 =( e B 0 / m p ) −1 , respectively.…”