Plasma Compressibility and the Generation of Electrostatic Electron Kelvin-Helmholtz Instability

This study explores the generation of Electrostatic (ES) Electron Kelvin-Helmholtz instability (EKHI) in collisionless plasma with a step-function electron velocity shear akin to that developed in the electron diffusion region in magnetic reconnection. In incompressible plasma, ES EKHI doesn't arise in any velocity shear profile due to the decoupling of the electric potential from the electron momentum equation. Instead a fluid-like Kelvin-Helmholtz instability (KHI) can arise. However, in compressible plasma, the compressibility couples the electric potential with the electron dynamics, leading to the emergence of a new ES mode EKHI on Debye length $\lambda_{De}$, accompanied by the co-generation of an electron acoustic-like wave. The minimum threshold of ES EKHI is $\Delta \mathbf{U}> 2c_{se}$, i.e., the electron velocity shear larger than twice the electron acoustic speed $c_{se}$. The corresponding growth rate is $Im(\omega) = ((\Delta \mathbf{U}/c_{se})^2 - 4)^{1/2} \omega_{pe}$, where $\omega_{pe}$ is the electron plasma frequency.