Linear theory of the current sheet shear instability

Abstract

The present study investigates the linear properties of the current sheet shear instability (CSSI) based on the two‐fluid equations. The mode is typically excited in the thin current layer formed around the X line during a quasi‐steady phase of collisionless reconnection and is considered to give rise to the anomalous momentum transport. The linear analyses are carried out for a realistic current sheet as evolved in collisionless reconnection, where the current density profile is produced by the nonuniform ion and electron flows and the pressure balance is maintained due to the temperature gradients. The density profile is assumed to be uniform, so that the lower hybrid drift instability is mostly suppressed. We confirm that the eigenfunctions in the numerical analysis are well consistent with the profiles in a kinetic simulation, implying that the two‐fluid approximation is valid for the CSSI. The mass ratio dependencies of the wave number and growth rate are remarkable for the electron‐scale current sheet, indicating that both the electrons and ions contribute to the wave generation. From the analytical analysis, it is found that these mass ratio dependencies originate from the fact that the ion momentum balance is coupled with the electron dynamics in the electron‐scale current layer. In particular, the electron inertia and electron flow shear play a significant role in generating the CSSI through the induction electric and magnetic fields.

Structure and Dynamics of Three‐Dimensional Magnetotail Reconnection

“…Both analyses noted that the interaction between the reconnection and the instability was very complex and that the two behaviors were hard to separate. Another closely related instability is the current sheet shear instability proposed by Fujimoto and Sydora (, ). Following an initial study by Hesse et al (), which suggested that the LHDI induces a velocity shear by modifying the diamagnetic drift and density profile leading to the Kelvin‐Helmholtz instability, Lapenta and Brackbill () and Lapenta et al () carried out 3‐D simulations in a Harris sheet and found kink‐like modes that they believe resulted from the nonlinear evolution of the LHDI that led to a Kelvin‐Helmholtz‐like instability.…”

“…The signatures in the simulations are complicated by wave‐like structures. A number of simulation studies in 2‐D and 3‐D have reported wave‐like phenomena (Divin et al, ; Fujimoto & Sydora, , ; Hesse et al, ; Karimabadi et al, ; Lapenta et al, ; Lapenta & Brackbill, ; Shinohara et al, ; Yin et al, ). For instance, in an electron positron plasma, Yin et al () found patchy reconnection and a very complex interaction between the tearing mode and kink mode.…”

“…Divin et al () used a pair of implicit PIC simulations with realistic mass ratio (1836) in 2‐D to argue for an electron Kelvin‐Helmholtz‐like mode for the jetting electron plasma similar to that suggested by Das and Kaw () for electron current channels. Recently, Fujimoto and Sydora (, ) have investigated a mode that they called the current sheet shear instability. They used both 3‐D PIC simulations in a reconnecting Harris current sheet and analytical theory and found that the current‐aligned electromagnetic mode produced turbulent electron flows.…”

Fluid simulations of three-dimensional reconnection that capture the lower-hybrid drift instability

“…The free energy source for the instability are inhomogeneities in the magnetic field and plasma pressure which drive the relative drifts of electrons and ions. Even though the LHDI does not significantly alter the reconnection rate it does lead to enhanced anomalous plasma transport which relaxes gradients, for instance the density, which in turn can give rise to secondary instabilities such as the CSSI that is driven by the electron flow shear (Fujimoto & Sydora 2017). The electromagnetic branch of the LHDI causes kinking of the current sheet.…”

Observation of Three‐Dimensional Magnetic Reconnection in the Terrestrial Magnetotail

“…Nevertheless, reconnection in Earth's magnetosphere is not necessarily a quasi‐2‐D process since observations show remarkable disagreements with the classical 2‐D reconnection model (Runov et al, ). The addition of variations in the third direction (out of plane) allows the growth of instabilities with wave vectors along the X line, such as the lower hybrid drift instability, oblique tearing instability, and current sheet shear instability (Daughton, ; Daughton et al, ; Fujimoto & Sydora, ). These waves/instabilities may play important roles in regulating the dissipation process in reconnection (Ji et al, ).…”