Modulational instabilities of electromagnetic and electrostatic waves in plasmas

A general discussion of modulational instabilities in plasmas is presented. It is shown that the basic mechanism is a four-wave interaction which tends to increase the wavenumber k of the wave in contrast to the usual three-wave decay or scattering processes which tend to reduce the k-spectrum of the waves. Examples include the Langmuir modulational instability, filamentation of both electrostatic and electromagnetic waves and the oscillating two stream instability. General equations for the modulation of finite amplitude, high frequency waves in unmagnetised plasmas are given. The stability properties of the linearised equations and the conservation relations of the nonlinear equations are obtained. Finally modulational instabilities relevant to beat wave studies are discussed.