Parametric excitation

General aspects of the theory of parametric instabilities are surveyed. First, the basic concept of the parametric excitation is explained and its characteristic features are described with the use of the Mathieu equation model. Two specific types of instabilities - resonant type and non-resonant type purely growing instabilities - are specifically discussed. The theory is then extended to a general three-mode coupling problem in a uniform medium and a physical mechanism of the instability is presented. A brief classification of various instabilities is also presented. Finally, some geometrical effects on the resonant decay instability are discussed based on physical rather than mathematical arguments, with particular reference to the absolute versus convective types of instabilities. (author)