THEORY OF A FORCED HYDROMAGNETIC CAVITY .1.

In this paper, we study a one-dimensional hydromagnetic cavity into wh ich Alfven waves are fed by harmonic shear motion of its boundaries, w here they interact with slow magnetosonic waves. The nonlinear equatio ns governing the space slow-varying amplitudes of the forward and back ward Alfven waves are derived and are subsequently solved under the ch aracteristic conditions for the Alfven waves exited at the boundaries where the magnetosonic oscillations are required to vanish. The forced hydromagnetic cavity is shown to exhibit multistable behaviors under certain circumstances.