Electron-scale Kelvin-Helmholtz Instability In Magnetized Shear Flows

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Electron-scale Kelvin-Helmholtz instabilities (ESKHI) are found in several astrophysical eventualities. Naturally ESKHI is topic to a background magnetic subject, however an analytical dispersion relation and an correct development fee of ESKHI beneath this circumstance are lengthy absent, as former MHD derivations should not applicable in the relativistic regime. We current a generalized dispersion relation of ESKHI in relativistic magnetized shear flows, with few assumptions. ESKHI linear growth rates in certain cases are numerically calculated. We conclude that the presence of an exterior magnetic field decreases the maximum instability growth rate normally, however can slightly improve it when the shear velocity is sufficiently excessive. Also, the external magnetic subject ends in a bigger cutoff wavenumber of the unstable band and will increase the wavenumber of probably the most unstable mode. PIC simulations are carried out to confirm our conclusions, where we additionally observe the suppressing of kinetic DC magnetic area era, ensuing 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 present.



Despite the importance of shear instabilities, ESKHI was solely recognized recently (Gruzinov, 2008) and stays to be largely unknown in physics. KHI is stable below 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) in the restrict of a chilly and collisionless plasma, the place 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), finding the generation of typical electron vortexes and magnetic field. It's noteworthy that PIC simulations additionally discovered the generation of a DC magnetic discipline (whose common along the streaming direction isn't zero) in company with the AC magnetic subject induced by ESKHI, whereas 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 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 easy velocity Wood Ranger Power Shears website (Alves et al., 2014), which are each found to stabilize ESKHI. Miller & Rogers (2016) extended the speculation of ESKHI to finite-temperature regimes by considering the pressure of electrons and derived a dispersion relation encompassing each ESKHI and MI. In natural situations, ESKHI is usually subject to an exterior magnetic field (Niu et al., 2025; Jiang et al., Wood Ranger Power Shears website 2025). However, works talked about above have been all carried out within the absence of an exterior magnetic discipline. While the idea of fluid KHI has been prolonged to magnetized flows a long time in the past (Chandrasekhar, 1961; D’Angelo, 1965), the conduct of ESKHI in magnetized shear flows has been fairly unclear.



Thus far, the only theoretical considerations concerning this drawback are introduced by Che & Zank (2023) and Tsiklauri (2024). Both works are restricted to incompressible plasmas and some type of MHD assumptions, that are only valid for small shear velocities. Therefore, their conclusions can't be instantly applied within the relativistic regime, where ESKHI is anticipated to play a significant role (Alves et al., 2014). Simulations had reported clear discrepancies from their concept (Tsiklauri, 2024). As Tsiklauri highlighted, a derivation of the dispersion relation with out extreme assumptions is critical. This varieties a part of the motivation behind our work. On this paper, we'll consider ESKHI underneath an external magnetic discipline by immediately extending the works of Gruzinov (2008) and Alves et al. 2014). This means that our work is carried out in the restrict of chilly and collisionless plasma. We undertake the relativistic two-fluid equations and keep away from any type of MHD assumptions. The paper is organized as follows. In Sec. 1, we present a quick introduction to the background and topic of ESKHI.