Electron-scale Kelvin-Helmholtz Instability In Magnetized Shear Flows
Electron-scale Kelvin-Helmholtz instabilities (ESKHI) are found in several astrophysical scenarios. Naturally ESKHI is topic to a background magnetic field, but an analytical dispersion relation and an accurate progress fee of ESKHI underneath this circumstance are long absent, as former MHD derivations aren't applicable within the relativistic regime. We present a generalized dispersion relation of ESKHI in relativistic magnetized shear flows, with few assumptions. ESKHI linear progress charges in certain circumstances are numerically calculated. We conclude that the presence of an external magnetic field decreases the utmost instability growth price most often, but can slightly increase it when the shear velocity is sufficiently high. Also, the exterior magnetic field 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 verify our conclusions, the place we also observe the suppressing of kinetic DC magnetic field technology, ensuing from electron gyration induced by the exterior Wood Ranger Power Shears shop magnetic subject. 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 importance of shear instabilities, ESKHI was only recognized lately (Gruzinov, 2008) and Wood Ranger Power Shears shop remains to be largely unknown in physics. KHI is stable underneath a such condition (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 restrict of a cold and collisionless plasma, where he also derived the analytical dispersion relation of ESKHI development charge for symmetrical shear flows. PIC simulations later confirmed the existence of ESKHI (Alves et al., 2012), discovering the technology of typical electron vortexes and magnetic subject. It's noteworthy that PIC simulations additionally found the generation of a DC magnetic area (whose average alongside the streaming course isn't zero) in company with the AC magnetic discipline induced by ESKHI, whereas the former shouldn't be 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 within the settings of ESKHI.
A transverse instability labelled mushroom instability (MI) was also 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., garden power shears 2013a, b, 2017). Alves et al. ESKHI and numerically derived the dispersion relation in the presence of density contrasts or easy velocity Wood Ranger Power Shears shop (Alves et al., 2014), that are both found to stabilize ESKHI. Miller & Rogers (2016) prolonged the idea of ESKHI to finite-temperature regimes by contemplating the pressure of electrons and Wood Ranger Power Shears price Wood Ranger Power Shears website electric power shears wood shears for sale derived a dispersion relation encompassing both ESKHI and MI. In natural scenarios, Wood Ranger Power Shears shop ESKHI is often topic to an external magnetic discipline (Niu et al., 2025; Jiang et al., 2025). However, works talked about above have been all carried out in the absence of an exterior magnetic subject. While the idea of fluid KHI has been prolonged to magnetized flows a long time ago (Chandrasekhar, 1961; D’Angelo, 1965), the behavior of ESKHI in magnetized shear flows has been somewhat unclear.
To this point, the only theoretical considerations regarding this downside are presented by Che & Zank (2023) and Tsiklauri (2024). Both works are limited to incompressible plasmas and a few form of MHD assumptions, which are only valid for small shear velocities. Therefore, their conclusions cannot be instantly utilized within 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 without extreme assumptions is important. This types part of the motivation behind our work. In this paper, we'll consider ESKHI beneath an external magnetic area by straight extending the works of Gruzinov (2008) and Alves et al. 2014). Because of this our work is carried out in the restrict of chilly and collisionless plasma. We adopt 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 subject of ESKHI.