Electron-scale Kelvin-Helmholtz Instability In Magnetized Shear Flows

Electron-scale Kelvin-Helmholtz instabilities (ESKHI) are found in a number of astrophysical eventualities. Naturally ESKHI is topic to a background magnetic field, however an analytical dispersion relation and an correct development charge of ESKHI below this circumstance are lengthy absent, as former MHD derivations usually are not relevant within the relativistic regime. We present a generalized dispersion relation of ESKHI in relativistic magnetized shear flows, with few assumptions. ESKHI linear development rates in sure cases are numerically calculated. We conclude that the presence of an external magnetic subject decreases the maximum instability growth charge generally, however can slightly increase it when the shear velocity is sufficiently excessive. Also, the exterior magnetic discipline leads to a larger cutoff wavenumber of the unstable band and will increase the wavenumber of the most unstable mode. PIC simulations are carried out to confirm our conclusions, the place we additionally observe the suppressing of kinetic DC magnetic subject era, resulting from electron gyration induced by the exterior 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 significance of shear instabilities, ESKHI was solely acknowledged recently (Gruzinov, 2008) and stays 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 in the relativistic jets. ESKHI was first proposed by Gruzinov (2008) within the limit of a cold and collisionless plasma, tree branch shears where he additionally derived the analytical dispersion relation of ESKHI progress price 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 is noteworthy that PIC simulations also discovered the generation of a DC magnetic field (whose average along the streaming path is just not zero) in company with the AC magnetic discipline induced by ESKHI, while the previous just isn't predicted by Gruzinov. The technology 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 in the settings of ESKHI.



A transverse instability labelled mushroom instability (MI) was additionally discovered 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 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 clean velocity tree branch shears (Alves et al., Wood Ranger Power Shears features 2014), that are each found to stabilize ESKHI. Miller & Rogers (2016) prolonged the theory of ESKHI to finite-temperature regimes by contemplating the strain of electrons and derived a dispersion relation encompassing both ESKHI and MI. In natural eventualities, ESKHI is commonly topic to an exterior magnetic discipline (Niu et al., 2025; Jiang et al., 2025). However, works talked about above were all carried out in the absence of an exterior magnetic area. While the idea of fluid KHI has been extended to magnetized flows a long time ago (Chandrasekhar, 1961; D’Angelo, 1965), the habits of ESKHI in magnetized shear flows has been rather unclear.



So far, the one theoretical concerns concerning this problem are presented by Che & Zank (2023) and Tsiklauri (2024). Both works are restricted to incompressible plasmas and a few kind of MHD assumptions, which are solely valid Wood Ranger Power Shears for sale small shear velocities. Therefore, their conclusions cannot be directly applied in the relativistic regime, where ESKHI is predicted to play a big function (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 excessive assumptions is necessary. This types part of the motivation behind our work. On this paper, we'll consider ESKHI beneath an external magnetic discipline by instantly extending the works of Gruzinov (2008) and Alves et al. 2014). Which means our work is carried out in the limit of cold and collisionless plasma. We undertake the relativistic two-fluid equations and avoid any type of MHD assumptions. The paper is organized as follows. In Sec. 1, we present a brief introduction to the background and topic of ESKHI.