A variational approach to parametric instabilities in inhomogeneous plasmas III: Two-plasmon decay

The theory of the two-plasmon decay instability is recast in the form of a variational principle for the pump strength or intensity of the incident laser. This allows the calculation of growth rates, frequency shifts, and threshold conditions for two-plasmon decay modes that occur in integer power law density profiles, including the effects of oblique incidence of the laser and both S and P polarizations. The transition between parabolic profiles occurring at the peak of an exploding foil target and linear profiles on its flanks is treated as well.