A linear MHD instability analysis of solar mass ejections with gravitation

Solar mass ejections seem, on the basis of many observations, to be divided into two categories: stable and unstable. We use linear magnetohydrodynamic (MHD) instability of a cylindrical plasma in an attempt to search for a theoretical explanation for this phenomenon. The dispersion relation is obtained and solved numerically. It is found that the initial plasma-flow velocity has a significant effect on the instability criteria and growth rate. Also found is that the instability growth-rate is much larger in those cases where plasma flow exists in comparison with the static case. The wave number range where the instability may occur also becomes wider with plasma flow. Further, it is shown that the region of the instability shifts to the short wavelength region with increasing plasma-flow velocity. Therefore, the plasma column may break into small pieces, resembling the melon seed phenomenon that has been suggested as a mechanism for mass ejection in the solar atmosphere. Under the assumption of a thin-tube approximation we show that gravity has little effect on the instability of quasi-horizontal ejection, but it has considerable effect for the vertical ejection. In order to deal with the gravitational force it is convenient to divide the problem into three cases: horizontal, vertical, and oblique. The exact analytical solution exists only in the vertical case. Asymptotic solutions are given in the horizontal and oblique cases.