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

Abstract

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 To&-Dattner reaonances 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 a t the driving frequency and its harmonics follows from a particular solution of an inhomogeneoiis Mathieu equation.