Electron-scale Kelvin-Helmholtz Instability In Magnetized Shear Flows

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Electron-scale Kelvin-Helmholtz instabilities (ESKHI) are found in a number of astrophysical scenarios. Naturally ESKHI is topic to a background magnetic area, but an analytical dispersion relation and an accurate growth rate of ESKHI below this circumstance are long absent, as former MHD derivations are not applicable in the relativistic regime. We present 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 exterior magnetic discipline decreases the utmost instability development fee typically, but can barely improve it when the shear velocity is sufficiently high. Also, the external magnetic field leads to a larger 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 also observe the suppressing of kinetic DC magnetic discipline technology, resulting from electron gyration induced by the exterior magnetic discipline. Electron-scale Kelvin-Helmholtz instability (ESKHI) is a shear instability that takes place at the shear boundary the place a gradient in velocity is current.



Despite the significance of shear instabilities, ESKHI was solely recognized recently (Gruzinov, 2008) and stays to be largely unknown in physics. KHI is stable beneath 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) within the limit of a chilly and collisionless plasma, where he additionally derived the analytical dispersion relation of ESKHI development fee 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 subject. It is noteworthy that PIC simulations additionally found the generation of a DC magnetic area (whose average along the streaming route is just not zero) in company with the AC magnetic subject induced by ESKHI, whereas the former is just not predicted by Gruzinov. The generation 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 discovered 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., 2020). Shear flows consisting of electrons and Wood Ranger brand shears positrons are also investigated (Liang et al., 2013a, b, 2017). Alves et al. ESKHI and numerically derived the dispersion relation within the presence of density contrasts or easy velocity Wood Ranger brand shears (Alves et al., 2014), that are both discovered to stabilize ESKHI. Miller & Rogers (2016) extended the speculation of ESKHI to finite-temperature regimes by contemplating the pressure of electrons and derived a dispersion relation encompassing each ESKHI and MI. In natural scenarios, ESKHI is often subject to an exterior magnetic area (Niu et al., 2025; Jiang et al., 2025). However, works mentioned above have been all carried out within the absence of an exterior magnetic discipline. While the speculation of fluid KHI has been extended to magnetized flows a long time ago (Chandrasekhar, Wood Ranger Power Shears review Ranger cordless power shears Shears features 1961; D’Angelo, 1965), the conduct of ESKHI in magnetized shear flows has been slightly unclear.



Up to now, the only theoretical concerns concerning this downside are offered by Che & Zank (2023) and Tsiklauri (2024). Both works are restricted to incompressible plasmas and some sort of MHD assumptions, which are solely legitimate for small shear velocities. Therefore, Wood Ranger Power Shears manual shears their conclusions cannot be straight applied in the relativistic regime, where ESKHI is anticipated to play a significant function (Alves et al., 2014). Simulations had reported clear discrepancies from their principle (Tsiklauri, 2024). As Tsiklauri highlighted, a derivation of the dispersion relation with out excessive assumptions is important. This forms a part of the motivation behind our work. In this paper, we are going to consider ESKHI below an exterior magnetic discipline 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 type of MHD assumptions. The paper is organized as follows. In Sec. 1, we current a short introduction to the background and subject of ESKHI.

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