Electron-scale Kelvin-Helmholtz Instability In Magnetized Shear Flows

Electron-scale Kelvin-Helmholtz instabilities (ESKHI) are present in several astrophysical eventualities. Naturally ESKHI is subject to a background magnetic discipline, however an analytical dispersion relation and an correct development price of ESKHI beneath this circumstance are lengthy absent, as former MHD derivations are usually 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 sure circumstances are numerically calculated. We conclude that the presence of an exterior magnetic area decreases the maximum instability growth fee most often, however can slightly increase it when the shear velocity is sufficiently excessive. Also, the exterior magnetic field results 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, the place we also observe the suppressing of kinetic DC magnetic field technology, Wood Ranger Tools resulting from electron gyration induced by the exterior magnetic subject. Electron-scale Kelvin-Helmholtz instability (ESKHI) is a shear instability that takes place on the shear boundary where a gradient in velocity is present.



Despite the importance of shear instabilities, ESKHI was only acknowledged just lately (Gruzinov, 2008) and stays to be largely unknown in physics. KHI is stable under a such condition (Mandelker et al., Wood Ranger Tools 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 chilly and collisionless plasma, the place he also 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), finding the technology of typical electron vortexes and magnetic discipline. It is noteworthy that PIC simulations additionally found the era of a DC magnetic area (whose average alongside the streaming course will not be zero) in company with the AC magnetic subject induced by ESKHI, while the former will not be predicted by Gruzinov. The technology of DC magnetic fields is because of electron thermal diffusion or mixing induced by ESKHI across 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 additionally discovered in PIC simulations concerning 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 within the presence of density contrasts or easy velocity shears (Alves et al., 2014), which are both discovered to stabilize ESKHI. Miller & Rogers (2016) prolonged the idea of ESKHI to finite-temperature regimes by contemplating the pressure of electrons and derived a dispersion relation encompassing both ESKHI and MI. In pure scenarios, ESKHI is commonly topic to an exterior magnetic subject (Niu et al., 2025; Jiang et al., 2025). However, works mentioned above were all carried out in the absence of an exterior magnetic area. While the theory 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 fairly unclear.



Up to now, the one theoretical considerations regarding this drawback are presented by Che & Zank (2023) and Tsiklauri (2024). Both works are restricted to incompressible plasmas and some type of MHD assumptions, which are solely valid for small shear velocities. Therefore, their conclusions cannot be straight applied within the relativistic regime, where ESKHI is expected to play a significant function (Alves et al., Wood Ranger Power Shears review Wood Ranger Power Shears shop Wood Ranger Power Shears coupon Wood Ranger Power Shears specs price 2014). Simulations had reported clear discrepancies from their idea (Tsiklauri, 2024). As Tsiklauri highlighted, a derivation of the dispersion relation without excessive assumptions is important. This forms part of the motivation behind our work. On this paper, we are going to consider ESKHI underneath an exterior magnetic field by immediately extending the works of Gruzinov (2008) and Alves et al. 2014). This means that our work is carried out within the limit of cold and collisionless plasma. We adopt the relativistic two-fluid equations and keep away from any form of MHD assumptions. The paper is organized as follows. In Sec. 1, we current a brief introduction to the background and subject of ESKHI.