A VARIATIONAL APPROACH TO PARAMETRIC-INSTABILITIES IN INHOMOGENEOUS PLASMAS .2. STIMULATED RAMAN-SCATTERING

The theory of temporally unstable modes or bound states associated wit h stimulated Raman scattering in inhomogeneous plasmas is recast in th e form of a variational principle for the pump strength or intensity o f the incident laser. This Minimum Pump Strength-Variational Principle (MPS-VP) formalism allows the unification of disparate;results on gro wth rates, frequency shifts, and threshold conditions, which in the pa st relied on specific and restrictive assumptions on the density profi le, scattering geometry, temperature, and damping rates. The variation al approach leads to generalizations of these results in a uniform man ner. Various levels of sophistication in the choice of trial and dual functions are explored. Simplifications and short cuts that will be us ed throughout this series of papers are tested here, and their regions of validity explored. The principle new result of some practical inte rest is the growth rate of Raman sidescattering occurring anywhere at the peak or on the flanks of a parabolic density profile such as can b e found in an exploding foil experiment. This new calculation includes any density at or below quarter-critical,at any temperature, and at l ow or high damping rate limits.