Theory of a Forced Hydromagnetic Cavity (I)

In this paper, we study a one-dimensional hydromagnetic cavity into which A1fvi.n waves are fed by harmonic shear motion of its boundaries, where they interact with slow magnetosonic waves. The nonlinear equations governing the space slow-varying amplitudes of the forward and backward Alfven waves are derived and are subsequently solved under the characteristic conditions for the A1fvèn waves excited at the boundaries where the magnetosonic oscillations are required to vanish. The forced hydromagnetic cavity is shown to exhibit rnultistable behaviors under certain circumstances.