The magnetohydrodynamic instability of a vertically ejected cylinder from the solar surface

Abstract

The linear MHD instability of a magnetized cylinder ejected perpendicularly to the solar surface is investigated and the general dispersion relation and its simplified form under the quasi-homogeneous condition are given. A concrete example is computed to compare with the case of horizontal ejection. It is found that 1) in the vertical case, the growth rate ω″ increases linearly with k, while in the horizontal case, ω″ fluctuates around some mean value. In both cases short-wavelength instability occurs easily and the cylinder tends to be broken into small pieces and the m=0 and m=1 modes are of equal importance. 2) In the vertical case the cylinder resonates at high frequencies; in the horizontal case, the reverse is true. 3) Skin effect phenomena seem to be present in various disturbed quantities in the vertical case but not in the horizontal case. 4) In both cases three nodes, pure oscillating, damping and growing, simultaneously exist. 5) In both cases ω″ is very sensitive to the magnetic field ψ-component H e 0 ψ , and as H e0 ψ →0, ω″ can decrease by several orders of magnitude. This indicates that the twisted magnetic field component is the primary factor causing the instability while ejection and gravity play only a helping role.