  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 in 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.
