A VARIATIONAL APPROACH TO PARAMETRIC-INSTABILITIES IN INHOMOGENEOUS PLASMAS .4. THE MIXED POLARIZATION HIGH-FREQUENCY INSTABILITY

The theories of the two plasmon decay (TPD) instability and stimulated Raman scattering (SRS) are unified and-presented using a variational formulation. The mixed polarization high-frequency instability is the resulting generalization which has SRS and TPD as special cases. The m ost unstable mode's properties are derived and shown as a function of perpendicular wave number. For vanishing wave number we recover the Ra man backscattering result and for wave numbers a few times larger than the square root of the homogeneous plasma growth rate normalized to t he pump frequency, the two plasmon decay instability modes are recover ed. This transition is accompanied by a change of polarization from a purely electromagnetic transversely polarized wave in the case of Rama n to a strictly electrostatic or longitudinally polarized wave in the case of TPD, and admixtures in between. Experimental signatures of the se modes are given and a method is proposed by which the density scale length and electron temperature would be simultaneously inferred from the width and height of the spectral signature corresponding to these hybrid modes in an ideal experiment.