Electron-scale Kelvin-Helmholtz instabilities (ESKHI) are found in several astrophysical eventualities. Naturally ESKHI is subject to a background magnetic area, but an analytical dispersion relation and an correct growth rate of ESKHI below this circumstance are long absent, as former MHD derivations should not applicable in the relativistic regime. We present a generalized dispersion relation of ESKHI in relativistic magnetized shear flows, with few assumptions. ESKHI linear progress charges in certain instances are numerically calculated. We conclude that the presence of an external magnetic discipline decreases the utmost instability development rate in most cases, but can barely enhance it when the shear velocity is sufficiently excessive. Also, the external magnetic field results in a bigger cutoff wavenumber of the unstable band and Wood Ranger brand shears increases the wavenumber of the most unstable mode. PIC simulations are carried out to confirm our conclusions, where we additionally observe the suppressing of kinetic DC magnetic discipline era, resulting from electron gyration induced by the exterior magnetic field. Electron-scale Kelvin-Helmholtz instability (ESKHI) is a shear instability that takes place on the shear boundary the place a gradient in velocity is current.
Despite the importance of shear instabilities, ESKHI was solely acknowledged lately (Gruzinov, 2008) and stays to be largely unknown in physics. KHI is stable underneath a such condition (Mandelker et al., 2016). These make ESKHI a promising candidate to generate magnetic fields in the relativistic jets. ESKHI was first proposed by Gruzinov (2008) in the restrict of a cold and collisionless plasma, the place he additionally derived the analytical dispersion relation of ESKHI growth rate for symmetrical shear flows. PIC simulations later confirmed the existence of ESKHI (Alves et al., 2012), discovering the generation of typical electron vortexes and magnetic discipline. It's noteworthy that PIC simulations additionally discovered the generation of a DC magnetic area (whose common along the streaming course is just not zero) in company with the AC magnetic field induced by ESKHI, whereas the previous is just not predicted by Gruzinov. The technology of DC magnetic fields is because of electron thermal diffusion or mixing induced by ESKHI throughout the shear interface (Grismayer et al., 2013), which is a kinetic phenomenon inevitable within the settings of ESKHI.
A transverse instability labelled mushroom instability (MI) was additionally found in PIC simulations concerning the dynamics in the aircraft transverse to the velocity shear (Liang et al., 2013a; Alves et al., 2015; Yao et al., 2020). Shear flows consisting of electrons and positrons are additionally investigated (Liang et al., 2013a, b, 2017). Alves et al. ESKHI and numerically derived the dispersion relation within the presence of density contrasts or clean velocity Wood Ranger brand shears (Alves et al., 2014), which are each found to stabilize ESKHI. Miller & Rogers (2016) extended the speculation of ESKHI to finite-temperature regimes by contemplating the strain of electrons and derived a dispersion relation encompassing both ESKHI and MI. In pure eventualities, ESKHI is often subject to an external magnetic subject (Niu et al., 2025; Jiang et al., 2025). However, works mentioned above have been all carried out in the absence of an exterior magnetic area. While the speculation of fluid KHI has been prolonged to magnetized flows a very long time in the past (Chandrasekhar, 1961; D’Angelo, 1965), the behavior of ESKHI in magnetized shear flows has been somewhat unclear.
So far, the one theoretical considerations concerning this downside are offered by Che & Zank (2023) and Tsiklauri (2024). Both works are restricted to incompressible plasmas and a few sort of MHD assumptions, which are solely valid for small shear velocities. Therefore, their conclusions cannot be immediately applied within the relativistic regime, where ESKHI is anticipated to play a major position (Alves et al., 2014). Simulations had reported clear discrepancies from their theory (Tsiklauri, 2024). As Tsiklauri highlighted, a derivation of the dispersion relation with out extreme assumptions is necessary. This types part of the motivation behind our work. On this paper, we are going to consider ESKHI underneath an external magnetic discipline by instantly extending the works of Gruzinov (2008) and Alves et al. 2014). Because of this our work is carried out in the restrict of cold and collisionless plasma. We adopt the relativistic two-fluid equations and keep away from any type of MHD assumptions. The paper is organized as follows. In Sec. 1, we current a quick introduction to the background and subject of ESKHI.