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Electron-scale Kelvin-Helmholtz instabilities (ESKHI) are present in a number of astrophysical scenarios. Naturally ESKHI is subject to a background magnetic area, but an analytical dispersion relation and an accurate growth price of ESKHI below this circumstance are long absent, as former MHD derivations are usually not applicable within the relativistic regime. We current a generalized dispersion relation of ESKHI in relativistic magnetized shear flows, with few assumptions. ESKHI linear development rates in sure instances are numerically calculated. We conclude that the presence of an external magnetic discipline decreases the maximum instability development charge in most cases, but can slightly improve it when the shear velocity is sufficiently high. Also, the external magnetic discipline results in a bigger cutoff wavenumber of the unstable band and increases the wavenumber of essentially the most unstable mode. PIC simulations are carried out to verify our conclusions, the place we also observe the suppressing of kinetic DC magnetic area generation, resulting from electron gyration induced by the external magnetic area. Electron-scale Kelvin-Helmholtz instability (ESKHI) is a shear instability that takes place on the shear boundary where a gradient in velocity is present.

Despite the significance of shear instabilities, ESKHI was only acknowledged not too long ago (Gruzinov, 2008) and stays to be largely unknown in physics. KHI is stable under 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 chilly and collisionless plasma, where he also derived the analytical dispersion relation of ESKHI growth charge for symmetrical shear flows. PIC simulations later confirmed the existence of ESKHI (Alves et al., 2012), finding the era of typical electron vortexes and magnetic subject. It is noteworthy that PIC simulations additionally found the era of a DC magnetic area (whose average along the streaming route is not zero) in company with the AC magnetic field induced by ESKHI, while the previous isn't predicted by Gruzinov. The era of DC magnetic fields is because of electron thermal diffusion or mixing induced by ESKHI across 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 within the plane transverse to the velocity shear (Liang et al., 2013a; Alves et al., 2015; Yao et al., Wood Ranger Power Shears reviews 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 smooth velocity Wood Ranger Power Shears reviews (Alves et al., 2014), that are both discovered to stabilize ESKHI. Miller & Rogers (2016) extended the theory of ESKHI to finite-temperature regimes by contemplating the stress of electrons and derived a dispersion relation encompassing both ESKHI and MI. In natural scenarios, ESKHI is often topic to an exterior magnetic discipline (Niu et al., 2025; Jiang et al., 2025). However, works mentioned above were all carried out in the absence of an exterior magnetic field. While the speculation of fluid KHI has been extended to magnetized flows a long time in the past (Chandrasekhar, 1961; D’Angelo, 1965), the habits of ESKHI in magnetized shear flows has been reasonably unclear.

To date, the one theoretical considerations concerning this downside are offered by Che & Zank (2023) and Tsiklauri (2024). Both works are limited to incompressible plasmas and a few sort of MHD assumptions, which are only legitimate for small shear velocities. Therefore, their conclusions cannot be straight applied within the relativistic regime, where ESKHI is anticipated to play a significant position (Alves et al., 2014). Simulations had reported clear discrepancies from their principle (Tsiklauri, 2024). As Tsiklauri highlighted, a derivation of the dispersion relation without extreme assumptions is important. This types a part of the motivation behind our work. On this paper, we will consider ESKHI below an external magnetic area by immediately extending the works of Gruzinov (2008) and Alves et al. 2014). Which means that our work is carried out within the restrict of chilly and collisionless plasma. We adopt the relativistic two-fluid equations and keep away from any form of MHD assumptions. The paper is organized as follows. In Sec. 1, Wood Ranger Tools we present a quick introduction to the background and subject of ESKHI.

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