Electron-scale Kelvin-Helmholtz Instability In Magnetized Shear Flows

Electron-scale Kelvin-Helmholtz instabilities (ESKHI) are present in a number of astrophysical scenarios. Naturally ESKHI is subject to a background magnetic subject, however an analytical dispersion relation and an correct development price of ESKHI below this circumstance are long absent, as former MHD derivations aren't applicable in the relativistic regime. We current 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 maximum instability development price most often, however can barely increase it when the shear velocity is sufficiently high. Also, the external magnetic subject ends in a larger cutoff wavenumber of the unstable band and increases the wavenumber of essentially the most unstable mode. PIC simulations are carried out to confirm our conclusions, where we also observe the suppressing of kinetic DC magnetic area generation, ensuing from electron gyration induced by the external magnetic area. Electron-scale Kelvin-Helmholtz instability (ESKHI) is a shear instability that takes place at the shear boundary the place a gradient in velocity is present.



Despite the importance of shear instabilities, Wood Ranger Power Shears coupon Wood Ranger Power Shears features Wood Ranger Power Shears sale garden power shears specs ESKHI was solely recognized just lately (Gruzinov, 2008) and remains to be largely unknown in physics. KHI is stable under a such situation (Mandelker et al., 2016). These make ESKHI a promising candidate to generate magnetic fields within the relativistic jets. ESKHI was first proposed by Gruzinov (2008) within the limit of a cold and collisionless plasma, where he also 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 area. It's noteworthy that PIC simulations additionally discovered the generation of a DC magnetic subject (whose average alongside the streaming path just isn't zero) in firm with the AC magnetic subject induced by ESKHI, while the former just isn't 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 also discovered in PIC simulations regarding 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 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 cordless pruning shears (Alves et al., 2014), buy Wood Ranger Power Shears which are both discovered to stabilize ESKHI. Miller & Rogers (2016) extended the speculation of ESKHI to finite-temperature regimes by considering the strain of electrons and derived a dispersion relation encompassing both ESKHI and MI. In natural situations, ESKHI is often topic 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 area. While the theory of fluid KHI has been prolonged to magnetized flows a very long time in the past (Chandrasekhar, 1961; D’Angelo, 1965), the habits of ESKHI in magnetized shear flows has been slightly unclear.



Thus far, the one theoretical concerns regarding this downside are presented by Che & Zank (2023) and Tsiklauri (2024). Both works are restricted to incompressible plasmas and some type of MHD assumptions, which are only valid for small shear velocities. Therefore, their conclusions cannot be straight utilized within the relativistic regime, the place ESKHI is predicted to play a big function (Alves et al., 2014). Simulations had reported clear discrepancies from their theory (Tsiklauri, 2024). As Tsiklauri highlighted, a derivation of the dispersion relation without extreme assumptions is necessary. This forms a part of the motivation behind our work. In this paper, we will consider ESKHI below an exterior magnetic subject by immediately extending the works of Gruzinov (2008) and Alves et al. 2014). Which means that our work is carried out in the limit of chilly and collisionless plasma. We adopt the relativistic two-fluid equations and avoid any type of MHD assumptions. The paper is organized as follows. In Sec. 1, cordless pruning shears we present a brief introduction to the background and topic of ESKHI.