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 most unstable mode's properties are derived and shown as a function of perpendicular wave number. For vanishing wave number we recover the Raman backscattering result and for wave numbers a few times larger than the square root of the homogeneous plasma growth rate normalized to the pump frequency, the two plasmon decay instability modes are recovered. This transition is accompanied by a change of polarization from a purely electromagnetic transversely polarized wave in the case of Raman to a strictly electrostatic or longitudinally polarized wave in the case of TPD, and admixtures in between. Experimental signatures of these 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.