Hall magnetohydrodynamic effects for current sheet flapping oscillations related to the magnetic double gradient mechanism

Abstract

Hall magnetohydrodynamic model is investigated for current sheet flapping oscillations, which implies a gradient of the normal magnetic field component. For the initial undisturbed current sheet structure, the normal magnetic field component is assumed to have a weak linear variation. The profile of the electric current velocity is described by hyperbolic functions with a maximum at the center of the current sheet. In the framework of this model, eigenfrequencies are calculated as functions of the wave number for the "kink" and "sausage" flapping wave modes. Because of the Hall effects, the flapping eigenfrequency is larger for the waves propagating along the electric current, and it is smaller for the opposite wave propagation with respect to the current. The asymmetry of the flapping wave propagation, caused by Hall effects, is pronounced stronger for thinner current sheets. This is due to the Doppler effect related to the electric current velocity.