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Electron-scale Kelvin-Helmholtz instabilities (ESKHI) are present in several astrophysical eventualities. Naturally ESKHI is subject to a background magnetic field, however an analytical dispersion relation and an accurate growth price of ESKHI underneath this circumstance are long absent, as former MHD derivations usually are not relevant within the relativistic regime. We present a generalized dispersion relation of ESKHI in relativistic magnetized shear flows, with few assumptions. ESKHI linear progress rates in certain circumstances are numerically calculated. We conclude that the presence of an exterior magnetic discipline decreases the utmost instability progress charge usually, however can slightly increase it when the shear velocity is sufficiently high. Also, the exterior magnetic area results in a bigger cutoff wavenumber of the unstable band and increases the wavenumber of probably the most unstable mode. PIC simulations are carried out to verify our conclusions, the place we additionally observe the suppressing of kinetic DC magnetic field era, ensuing from electron gyration induced by the external 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 present.

Despite the significance of shear instabilities, ESKHI was solely acknowledged lately (Gruzinov, 2008) and remains to be largely unknown in physics. KHI is stable below a such situation (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) within the restrict of a cold and collisionless plasma, where he also derived the analytical dispersion relation of ESKHI development price for Wood Ranger Tools symmetrical shear flows. PIC simulations later confirmed the existence of ESKHI (Alves et al., 2012), Wood Ranger Tools finding the technology of typical electron vortexes and magnetic subject. It's noteworthy that PIC simulations also found the generation of a DC magnetic field (whose common along the streaming path isn't zero) in firm with the AC magnetic field induced by ESKHI, while the previous is just not predicted by Gruzinov. The era of DC magnetic fields is due to electron thermal diffusion or mixing induced by ESKHI throughout the shear interface (Grismayer et al., 2013), which is a kinetic phenomenon inevitable in the settings of ESKHI.

A transverse instability labelled mushroom instability (MI) was additionally found in PIC simulations concerning the dynamics in the plane 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, Wood Ranger Tools 2017). Alves et al. ESKHI and numerically derived the dispersion relation in the presence of density contrasts or clean velocity shears (Alves et al., 2014), which are each found to stabilize ESKHI. Miller & Rogers (2016) prolonged the idea of ESKHI to finite-temperature regimes by contemplating the strain of electrons and derived a dispersion relation encompassing each ESKHI and MI. In natural scenarios, ESKHI is usually topic to an exterior magnetic subject (Niu et al., 2025; Jiang et al., 2025). However, works talked about above had been all carried out within the absence of an exterior magnetic subject. While the speculation of fluid KHI has been extended to magnetized flows a very long time ago (Chandrasekhar, 1961; D’Angelo, Wood Ranger Tools 1965), the conduct of ESKHI in magnetized shear flows has been fairly unclear.

Up to now, the one theoretical considerations regarding this problem are offered by Che & Zank (2023) and Tsiklauri (2024). Both works are limited to incompressible plasmas and some type of MHD assumptions, which are only valid for cordless power shears small shear velocities. Therefore, their conclusions can't be straight utilized in the relativistic regime, where ESKHI is expected to play a major Wood Ranger Power Shears order now Ranger Power Shears role (Alves et al., 2014). Simulations had reported clear discrepancies from their principle (Tsiklauri, 2024). As Tsiklauri highlighted, a derivation of the dispersion relation without excessive assumptions is critical. This varieties a part of the motivation behind our work. In this paper, we are going to consider ESKHI beneath an exterior magnetic discipline by directly extending the works of Gruzinov (2008) and Alves et al. 2014). Which means our work is carried out within the restrict of chilly and collisionless plasma. We undertake the relativistic two-fluid equations and Wood Ranger Tools keep away from any type of MHD assumptions. The paper is organized as follows. In Sec. 1, Wood Ranger Tools we present a short introduction to the background and topic of ESKHI.