On application of the Arnold's stability method to the problem of magnetohydrodynamic stability with helical symmetry

The problem of magnetohydrodynamic stability is examined within the content of the Arnold's Stability method. In order to take full advantage of the well-developed theory derived for the stability analysis of various stratified flows by virtue of this method, we devise a mathematical isomorphism between the equations of ideal magnetohydrodynamics and those governing stratified flows, i.e. Euler equations. This isomorphism proves possible if, in brief, the lines of force of the prevailing magnetic field is helical initially. The resulting analogous (or isomorphic) stratified flows obtained in this regard is used to deduce the linear and nonlinear stability criteria for the original magnetohydrodynamic systems in an indirect manner. Helical symmetry is assumed throughout the present treatment. Five different classes of steady solutions are to be studied