A description is given of a general method of deriving dynamic equations for the amplitudes of interacting waves (both volume and surface waves) in a bounded plasma. The treatment is based on the study of the interaction of magnetohydrodynamic waves in a plasma cylinder confined by a strong magnetic field. Decay instabilities were studied in order to find the probabilities and evaluate the characteristic times of the corresponding three-plasmon processes. It is shown that the non-linearity of the boundary conditions can have a substantial effect on three-plasmon interactions involving surface waves.The linear problem was solved in advance. It is shown, in particular, that in addition to the Alfvén surface waves, acoustic-type surface waves with frequencies approximately equal (ωA being the Alfvén frequency) can propagate in the plasma cylinder.
Electrostatic surface waves in a magnetized two-fluid plasma