<p>Electron-scale Kelvin-Helmholtz instabilities (ESKHI) are present in a number of astrophysical scenarios. Naturally ESKHI is topic to a background magnetic subject, but an analytical dispersion relation and an accurate development charge of ESKHI under this circumstance are long absent, as former MHD derivations usually are not applicable in the relativistic regime. We present a generalized dispersion relation of ESKHI in relativistic magnetized shear flows, <a href=https://marketingme.wiki/wiki/Comprehensive_Study_Report_On_Wood_Ranger_Power_Shears_And_Garden_Pruning_Tools>portable cutting shears</a> with few assumptions. ESKHI linear development rates in sure instances are numerically calculated. We conclude that the presence of an external magnetic area decreases the utmost instability progress fee most often, but can slightly increase it when the shear velocity is sufficiently excessive. Also, the external magnetic area results in a bigger 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, where we also observe the suppressing of kinetic DC magnetic field technology, resulting from electron gyration induced by the external magnetic subject. 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.</p><br><br><span style="display:block;text-align:center;clear:both"><iframe width="640" height="360" src="https://www.youtube.com/embed/De4QkTmwxMA?controls=2" frameborder="0" allowfullscreen title="Top 5 Electric Pruning Shears - Trim and Shape Your Garden with Precision! (c) by N/A"></iframe></span><p>Despite the significance of shear instabilities, ESKHI was solely acknowledged lately (Gruzinov, 2008) and remains to be largely unknown in physics. KHI is stable underneath 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 restrict of a chilly and collisionless plasma, the place he also derived the analytical dispersion relation of ESKHI progress fee 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 is noteworthy that PIC simulations additionally discovered the era of a DC magnetic discipline (whose average along the streaming route just isn't zero) in company with the AC magnetic field induced by ESKHI, while the former is not 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 in the settings of ESKHI.</p><br><br><p>A transverse instability labelled mushroom instability (MI) was also found in PIC simulations regarding 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 in the presence of density contrasts or smooth velocity <a href="https://jamiaummulqura.com/blog/study-report-wood-ranger-power-shears-and-their-applications-in-gardening-and-landscaping/">Wood Ranger Power Shears website</a> (Alves et al., 2014), that are both discovered to stabilize ESKHI. Miller & Rogers (2016) prolonged the idea 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 subject (Niu et al., 2025; Jiang et al., 2025). However, works talked about above have been all carried out within the absence of an external magnetic area. While the speculation 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 relatively unclear.</p><br><br><p>So far, the only theoretical issues regarding this problem are introduced by Che & Zank (2023) and Tsiklauri (2024). Both works are limited to incompressible plasmas and a few type of MHD assumptions, which are solely legitimate for small shear velocities. Therefore, their conclusions cannot be instantly applied in the relativistic regime, <A HREF='https://sakumc.org/xe/vbs/2790530'>Wood Ranger Power Shears website</A> the place ESKHI is predicted to play a big role (Alves et al., <a href=https://source.yysfan.com/tahliawhitman>Wood Ranger Power Shears</a> 2014). Simulations had reported clear discrepancies from their theory (Tsiklauri, <a href="https://gitea.mxthome.ru/bufordtorot553">Wood Ranger Power Shears website</a> 2024). As Tsiklauri highlighted, a derivation of the dispersion relation without excessive assumptions is critical. This kinds part of the motivation behind our work. On this paper, we'll consider ESKHI under an exterior magnetic area by immediately extending the works of Gruzinov (2008) and Alves et al. 2014). Which means that our work is carried out in the restrict of cold 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 current a quick introduction to the background and topic of ESKHI.</p>
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