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Electron-scale Kelvin-Helmholtz instabilities (ESKHI) are found in several astrophysical eventualities. Naturally ESKHI is subject to a background magnetic discipline, however an analytical dispersion relation and an correct development price of ESKHI underneath this circumstance are lengthy absent, as former MHD derivations should not relevant in the relativistic regime. We current a generalized dispersion relation of ESKHI in relativistic magnetized shear flows, with few assumptions. ESKHI linear development rates in certain instances are numerically calculated. We conclude that the presence of an external magnetic area decreases the maximum instability progress price normally, but can slightly enhance it when the shear velocity is sufficiently high. Also, the exterior magnetic subject results in a bigger cutoff wavenumber of the unstable band and increases the wavenumber of the most unstable mode. PIC simulations are carried out to verify our conclusions, where we also observe the suppressing of kinetic DC magnetic subject generation, resulting from electron gyration induced by the exterior magnetic area. Electron-scale Kelvin-Helmholtz instability (ESKHI) is a shear instability that takes place at the shear boundary where a gradient in velocity is present.
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