Electron-scale Kelvin-Helmholtz instabilities (ESKHI) are found in a number of astrophysical eventualities. Naturally ESKHI is topic to a background magnetic area, however an analytical dispersion relation and an accurate growth price of ESKHI beneath this circumstance are long absent, as former MHD derivations usually are not relevant within the relativistic regime. We current a generalized dispersion relation of ESKHI in relativistic magnetized shear flows, with few assumptions. ESKHI linear development rates in certain instances are numerically calculated. We conclude that the presence of an exterior magnetic area decreases the maximum instability development rate generally, Wood Ranger Power Shears shop however can barely improve it when the shear velocity is sufficiently high. Also, the exterior magnetic area results in a bigger cutoff wavenumber of the unstable band and Wood Ranger Power Shears shop increases the wavenumber of probably the most unstable mode. PIC simulations are carried out to confirm our conclusions, where we also observe the suppressing of kinetic DC magnetic area generation, resulting from electron gyration induced by the external magnetic area. 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 significance of shear instabilities, ESKHI was only acknowledged lately (Gruzinov, Wood Ranger Power Shears shop 2008) and remains to be largely unknown in physics. KHI is stable beneath 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) within the restrict of a chilly and collisionless plasma, Wood Ranger Power Shears shop 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), finding the era of typical electron vortexes and magnetic subject. It is noteworthy that PIC simulations additionally found the technology of a DC magnetic field (whose average along the streaming direction is just not zero) in firm with the AC magnetic area induced by ESKHI, while the former just isn't predicted by Gruzinov. The generation of DC magnetic fields is because of electron thermal diffusion or mixing induced by ESKHI throughout 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 also found in PIC simulations regarding the dynamics within 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, Wood Ranger Power Shears official site 2017). Alves et al. ESKHI and numerically derived the dispersion relation within the presence of density contrasts or clean velocity Wood Ranger Power Shears shop (Alves et al., 2014), that are each found to stabilize ESKHI. Miller & Rogers (2016) prolonged the idea of ESKHI to finite-temperature regimes by contemplating the stress of electrons and Wood Ranger Power Shears shop derived a dispersion relation encompassing both ESKHI and MI. In natural situations, ESKHI is usually subject to an external magnetic field (Niu et al., 2025; Jiang et al., 2025). However, works mentioned above were all carried out within the absence of an exterior magnetic field. While the speculation of fluid KHI has been extended to magnetized flows a long time in the past (Chandrasekhar, 1961; D’Angelo, 1965), the habits of ESKHI in magnetized shear flows has been rather unclear.

Up to now, rechargeable garden shears the only theoretical issues concerning this downside are presented by Che & Zank (2023) and Tsiklauri (2024). Both works are restricted to incompressible plasmas and gardening shears some type of MHD assumptions, which are solely legitimate for small shear velocities. Therefore, their conclusions can't be directly applied in the relativistic regime, where ESKHI is anticipated to play a significant role (Alves et al., Wood Ranger brand shears 2014). Simulations had reported clear discrepancies from their concept (Tsiklauri, 2024). As Tsiklauri highlighted, a derivation of the dispersion relation with out excessive assumptions is important. This forms part of the motivation behind our work. In this paper, we will consider ESKHI under an external magnetic discipline by immediately extending the works of Gruzinov (2008) and professional landscaping shears Alves et al. 2014). This means that our work is carried out within the restrict 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 present a brief introduction to the background and subject of ESKHI.