Electron-scale Kelvin-Helmholtz Instability In Magnetized Shear Flows

Electron-scale Kelvin-Helmholtz instabilities (ESKHI) are present in several astrophysical situations. Naturally ESKHI is topic to a background magnetic subject, but an analytical dispersion relation and an correct growth fee of ESKHI under this circumstance are lengthy absent, as former MHD derivations are not applicable in the relativistic regime. We current a generalized dispersion relation of ESKHI in relativistic magnetized shear flows, with few assumptions. ESKHI linear development charges in sure circumstances are numerically calculated. We conclude that the presence of an exterior magnetic area decreases the utmost instability development fee typically, however can slightly increase it when the shear velocity is sufficiently excessive. Also, the exterior Wood Ranger Power Shears price magnetic area leads to 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 additionally observe the suppressing of kinetic DC magnetic discipline technology, 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 the place a gradient in velocity is present.



Despite the importance of shear instabilities, ESKHI was solely acknowledged lately (Gruzinov, 2008) and stays 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 in the relativistic jets. ESKHI was first proposed by Gruzinov (2008) in the limit of a cold 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), discovering the generation of typical electron vortexes and magnetic discipline. It's noteworthy that PIC simulations additionally found the era of a DC magnetic area (whose common along the streaming course shouldn't be zero) in company with the AC magnetic discipline induced by ESKHI, whereas the former is not predicted by Gruzinov. The era of DC magnetic fields is because of electron thermal diffusion or mixing induced by ESKHI throughout the shear interface (Grismayer et al., 2013), Wood Ranger Power Shears order now 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 in the aircraft 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 in the presence of density contrasts or clean velocity Wood Ranger Power Shears order now (Alves et al., 2014), which are both found to stabilize ESKHI. Miller & Rogers (2016) extended the speculation of ESKHI to finite-temperature regimes by contemplating the strain of electrons and derived a dispersion relation encompassing each ESKHI and MI. In natural situations, ESKHI is often topic to an exterior magnetic field (Niu et al., 2025; Jiang et al., 2025). However, works talked about above were all carried out within the absence of an exterior magnetic area. While the speculation of fluid KHI has been extended to magnetized flows a long time ago (Chandrasekhar, 1961; D’Angelo, 1965), the conduct of ESKHI in magnetized shear flows has been somewhat unclear.



To this point, the only theoretical considerations regarding this problem 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 solely legitimate for small shear velocities. Therefore, their conclusions cannot be immediately applied within the relativistic regime, where ESKHI is predicted to play a major position (Alves et al., 2014). Simulations had reported clear discrepancies from their idea (Tsiklauri, 2024). As Tsiklauri highlighted, a derivation of the dispersion relation with out extreme assumptions is critical. This kinds a part of the motivation behind our work. On this paper, Wood Ranger Power Shears order now we will consider ESKHI under an external magnetic discipline by instantly extending the works of Gruzinov (2008) and Alves et al. 2014). Which means that our work is carried out in the limit of cold and Wood Ranger Power Shears order now 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 current a quick introduction to the background and subject of ESKHI.