The effect of external magnetic field on electron scale Kelvin-Helmholtz instability

TL;DR

This study uses particle-in-cell simulations to analyze how external magnetic fields influence the electron scale Kelvin-Helmholtz instability, revealing a hyperbolic dependence of growth rate on magnetic field strength and implications for astrophysical plasma stability.

Contribution

It provides the first empirical relationship for ESKHI growth rate dependence on external magnetic field strength, supported by simulation data and linking kinetic and MHD thresholds.

Findings

External magnetic field reduces ESKHI growth rate.

Empirical hyperbolic relation for growth rate dependence.

MHD threshold magnetic field matches kinetic saturation field.

Abstract

We use particle-in-cell, fully electromagnetic, plasma kinetic simulation to study the effect of external magnetic field on electron scale Kelvin-Helmholtz instability (ESKHI). The results are applicable to collisionless plasmas when e.g. solar wind interacts with planetary magnetospheres or magnetic field is generated in AGN jets. We find that as in the case of magnetohydrodynamic KHI, in the kinetic regime, presence of external magnetic field reduces growth rate of the instability. In MHD case there is known threshold magnetic field for KHI stabilization, while for ESKHI this is to be analytically determined. Without a kinetic analytical expression, we use several numerical simulation runs to establish an empirical dependence of ESKHI growth rate, $\Gamma(B_0)\omega_{\rm pe}$, on the strength of applied external magnetic field. We find the best fit is hyperbolic, $\Gamma(B_0)\omega_{\rm pe}=\Gamma_0\omega_{\rm pe}/(A+B\bar B_0)$, where $\Gamma_0$ is the ESKHI growth rate without external magnetic field and $\bar B_0=B_0/B_{\rm MHD}$ is the ratio of external and two-fluid MHD stability threshold magnetic field, derived here. An analytical theory to back up this growth rate dependence on external magnetic field is needed. The results suggest that in astrophysical settings where strong magnetic field pre-exists, the generation of an additional magnetic field by the ESKHI is suppressed, which implies that the Nature provides a "safety valve" -- natural protection not to "over-generate" magnetic field by ESKHI mechanism. Remarkably, we find that our two-fluid MHD threshold magnetic field is the same (up to a factor $\sqrt{\gamma_0}$) as the DC saturation magnetic field, previously predicted by fully kinetic theory.