Electron-scale Kelvin-Helmholtz instabilities (ESKHI) are found in a number of astrophysical scenarios. Naturally ESKHI is topic to a background magnetic discipline, however an analytical dispersion relation and an correct progress rate of ESKHI below this circumstance are lengthy absent, safe pruning shears as former MHD derivations should not relevant within the relativistic regime. We present a generalized dispersion relation of ESKHI in relativistic magnetized shear flows, with few assumptions. ESKHI linear growth charges in sure cases are numerically calculated. We conclude that the presence of an external magnetic field decreases the maximum instability progress charge normally, but can slightly enhance it when the shear velocity is sufficiently high. Also, the external magnetic area results in a larger cutoff wavenumber of the unstable band and increases the wavenumber of probably the most unstable mode. PIC simulations are carried out to confirm our conclusions, where we also observe the suppressing of kinetic DC magnetic discipline era, ensuing 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 present.

Despite the importance of shear instabilities, Wood Ranger Power Shears sale Wood Ranger Power Shears website Wood Ranger Power Shears review Wood Ranger Power Shears for sale shop ESKHI was only recognized just lately (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 cold and collisionless plasma, where he additionally derived the analytical dispersion relation of ESKHI progress rate for symmetrical shear flows. PIC simulations later confirmed the existence of ESKHI (Alves et al., 2012), finding the generation of typical electron vortexes and magnetic area. It's noteworthy that PIC simulations also discovered the technology of a DC magnetic discipline (whose average along the streaming route just isn't zero) in firm with the AC magnetic subject induced by ESKHI, whereas the previous shouldn't be predicted by Gruzinov. The technology of DC magnetic fields is due to electron thermal diffusion or mixing induced by ESKHI across the shear interface (Grismayer et al., Wood Ranger official 2013), which is a kinetic phenomenon inevitable within the settings of ESKHI.

A transverse instability labelled mushroom instability (MI) was also found in PIC simulations regarding the dynamics within the airplane 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 safe pruning 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 stress of electrons and derived a dispersion relation encompassing each ESKHI and MI. In natural scenarios, ESKHI is commonly 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 external magnetic discipline. While the theory of fluid KHI has been prolonged to magnetized flows a very long time ago (Chandrasekhar, 1961; D’Angelo, 1965), the behavior of ESKHI in magnetized shear flows has been quite unclear.

To date, the only theoretical concerns concerning this drawback are offered by Che & Zank (2023) and Tsiklauri (2024). Both works are limited to incompressible plasmas and a few sort of MHD assumptions, that are only legitimate for safe pruning shears small shear velocities. Therefore, their conclusions can't be immediately utilized within the relativistic regime, where ESKHI is anticipated to play a big role (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 excessive assumptions is important. This varieties a part of the motivation behind our work. On this paper, we'll consider ESKHI beneath an exterior magnetic area by straight extending the works of Gruzinov (2008) and Alves et al. 2014). Which means our work is carried out within the limit of chilly and collisionless plasma. We undertake the relativistic two-fluid equations and avoid any form of MHD assumptions. The paper is organized as follows. In Sec. 1, we present a short introduction to the background and topic of ESKHI.

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