Eigenmodes of an ion plasma sheath

Summary form only given. We investigate the structure and stability of transverse (in the sheath plane) eigenmodes of a collisionless ion sheath occurring at the plasma boundary. An ion sheath represents a particular example of nonlinear ion-sound waves, which, in general include solitons and periodic waves structures. All these nonlinear waves can be found by formulating plasma equations in a form of the oscillator eigenvalue problem in a generic nonlinear potential (Sagdeev potential). Solitons and periodic waves correspond to trapped (localized) states, while the sheath solution is an untrapped state with the local maximum as the wall. To investigate the transverse stability and eigenmodes of the sheath solution we employ a method previously used to study transverse oscillations of solitons (e.g. within the Kadomtsev-Petviashvili equation). We have generalized this technique for the sheath solution. We have obtained the dispersion relation for transverse oscillations and found stable eigenmodes with a frequency lower than the ion plasma frequency.