Kelvin–Helmholtz instability in a cool solar jet in the framework of Hall magnetohydrodynamics: A case study [SSA]

http://arxiv.org/abs/1706.03683


We investigate the conditions under which the magnetohydrodynamic (MHD) modes in a cylindrical magnetic flux tube moving along its axis become unstable against the Kelvin–Helmholtz (KH) instability. We employ the dispersion relations of MHD modes derived from the linearized Hall MHD equations for cool (zero beta) plasma. We assume real wave numbers and complex angular wave frequencies, notably complex wave phase velocities. The dispersion equations are solved numerically at fixed input parameters and varying values of the ratio $l_\mathrm{Hall}/a$, where $l_\mathrm{Hall} = c/\omega_\mathrm{pi}$ ($c$ being the speed of light, and $\omega_\mathrm{pi}$ the ion plasma frequency) and $a$ is the flux tube radius. It is shown that the stability of the MHD modes depends upon four parameters: the density contrast between the flux tube and its environment, the ratio $l_\mathrm{Hall}/a$, and the value of the Alfv\’en Mach number (the ratio of the tube axial velocity to Alfv\’en speed inside the flux tube). It is found that at high density contrasts, for small values of $l_\mathrm{Hall}/a$, the kink ($m = 1$) mode can become unstable against KH instability at some critical Alfv\’en Mach number (or equivalently at critical flow speed), but a threshold $l_\mathrm{Hall}/a$ can suppress the onset of KH instability. At small density contrasts, however, the magnitude of $l_\mathrm{Hall}/a$ does not affect noticeably the condition for instability occurrence—even though it can reduce the critical Alfv\’en Mach number. It is established that the sausage mode ($m = 0$) is not subject to the KH instability.

Read this paper on arXiv…

I. Zhelyazkov and Z. Dimitrov
Tue, 13 Jun 17
19/92

Comments: 15 pages, 7 figures