Instabilities in a current sheet with plasma jet

Abstract

We study the stability problem of a magnetohydrodynamic current sheet with the presence of a plasma jet. The flow direction is perpendicular to the normal of the current sheet and we analyse two cases: (1) the flow is along the antiparallel component of the magnetic field; (2) the flow is perpendicular to the antiparallel component of the magnetic field. A generalized equation set with the condition of incompressibility is derived and solved as a boundary value problem. For the first case we show that the streaming kink mode is stabilized by the magnetic field at $V_0/B_0 \lesssim 2$ , where $V_0$ and $B_0$ are the jet speed and upstream Alfvén speed, and it is not affected by resistivity significantly. The streaming sausage mode is stabilized at $V_0/B_0 \lesssim 1$ , and it can transit to the streaming tearing mode with a finite resistivity. The streaming tearing mode has larger growth rate than the pure tearing mode, though the scaling relation between the maximum growth rate and the Lundquist number remains unchanged. When the jet is perpendicular to the antiparallel component of the magnetic field, the most unstable sausage mode is usually perpendicular (wavevector along the jet) without a guide field. But with a finite guide field, the most unstable sausage mode can be oblique, depending on the jet speed and guide field strength.

LAPS: An MPI-parallelized 3D pseudo-spectral Hall-MHD simulation code incorporating the expanding box model

“…It is well known that a resistive current sheet is susceptible to the tearing mode instability (Furth et al, 1963), the growth of which can break an elongated current sheet into a chain of plasmoids rapidly. The theory of tearing instability in incompressible MHD was well established, and its growth rate can be calculated in a semianalytic way (Pucci and Velli, 2013;Shi et al, 2020a;Shi, 2022). Thus, incompressible tearing instability is a very good benchmark for resistive-MHD code.…”

“…Derivation of Eq. 15 can be found in many previous studies (e.g., Shi et al, 2020a;Shi, 2022). Here, we use the boundary-value-problem solver implemented in the package SciPy (Virtanen et al, 2020) to solve Eq.…”