Gyrokinetic Electron and Fully Kinetic Ion Particle Simulation on Current Sheet Instabilities

Abstract

Linear eigenmode stability properties of three-dimensional instabilities in a Harris current sheet with a finite guide magnetic field are systematically studied employing the gyrokinetic electron and fully kinetic ion (GeFi) particle-in-cell (PIC) particle simulation model with a realistic ion-to-electron mass ratio $m_i/m_e$, where $m_i$ and $m_e$ are the ion and electron masses, respectively. In contrast to the fully kinetic PIC simulation scheme, the fast electron cyclotron motion and plasma oscillations are systematically removed in the GeFi model, and hence one can employ the realistic mass ratio $m_i/m_e$. In order to valid the GeFi code for the small guide field limit, the GeFi simulations are benchmarked against both the fully kinetic PIC simulation and the analytical eigenmode theory, and an excellent agreement is obtained. In order to thoroughly understand the properties of both electrostatic (ES) and electromagnetic (EM) instabilities in the Harris sheet, the GeFi simulation is carried out both using a simplified code in the ES limit and using the fully EM code. Lower-hybrid drift instability (LHDI), drift-kink instability (DKI), drift-sausage instability (DSI), and Buneman instability (BI) are found to be present in the current sheet, among which the LHDI is predominantly an ES instability. Under a small guide field $B_G$, the LHDI is found to be excited, with $k\sqrt{\rho_i\rho_e} \sim 1$， where $\vec{k}$ is the wave vector perpendicular to the nonuniformity direction. For small wave numbers $k_y$ along the current direction, the most unstable eigenmodes of LHDI are peaked at the locations where $\vec{k} \cdot \vec{B}=0$, consistent with previous analytical and simulation studies. Here, $\vec{B}$ is the equilibrium magnetic field. As $k_y$ increases, however, the most unstable eigenmodes of LHDI are found to be peaked at $\vec{k} \cdot \vec{B}\not=0$. In addition, the simulation results indicate that varying $m_i/m_e$, the current sheet width, and the guide magnetic field can affect the stability of LHDI. Simulations with the varying mass ratio confirm the lower hybrid frequency and wave number scalings. Under a moderate guide field $B_G$, the DKI and DSI are excited in the long wavelength regime ($k\rho_i \sim 1$). The magnetic fluctuations of DKI are localized at the edge of current sheet, whereas the DSI has compressional perturbations localized around the center. In the $k_x$-$k_y$ space, the DKI and DSI occupy the smaller and larger $k$ regime, respectively. The most unstable DKI are away from $\mathbf{k} \cdot \mathbf{B}=0$, while the DSI is peaked at $\mathbf{k} \cdot \mathbf{B}=0$ At a larger guide field $B_G \sim B_{x0}$, an electromagnetic instability with a compressional magnetic perturbation is found to be present exactly at the center of current sheet. The growth rate of this mode is found to peak at $\mathbf{k} \times \mathbf{B} = 0$. The growth rate of this mode is consistent with that of the Buneman instability. Since the magnetic perturbations in this unstable mode are at the current sheet center and dominated by a compressional fluctuation $\delta B_{y}$ in the direction of the electron drift velocity, the mode may contribute directly to the electron anomalous resistivity in magnetic reconnection.