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

Abstract

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.