Dispersion relations for electrostatic surface waves in a homogeneous plasma-layer which interacts with an external electric pumping field parallel to the boundaries are derived in the framework of the kinetic theory. The parametrically excited and purely growing instabilities are investigated. Electric threshold fields and growth rates for the instable surface modes are given. It can be shown that the minimum threshold for parametric excitation occurs for those modes which are symmetric about the midplane of the layer.

Zur Theorie der parametrischen Anregung von elektrostatischen Oberflächenwellen in einer Plasmaschicht

Onedimensional fluid theory of Tonks-Dattner resonances in inhomogeneous, bounded plasmas is extended to stronger exciting electric fields. The relation of parametric instabilities and harmonic generation with Tonks-Dattner resonances will be worked out in a more direct way than in previous work. Electric field thresholds and growth rates for parametric instabilities will be obtained from theory of homogeneous Mathieu equation. Stationary excitation at the driving frequency and its harmonics follows from a particular solution of an inhomogeneous Mathieu equation.

S. Wolschke

Papers

Theory of Parametric Instabilities and Harmonic Generation in Tonks-Dattner Resonances