Purely-growing parametric instabilities in plasmas at near-critical densities

The oscillating-two-stream instability (OTSI) is shown to be a zero-frequency absolute instability of the backward-wave parametric type. The instability is shown to be distinct from the concurrent parametric-decay-instability (PDI), even for sub-critical pump frequencies very near the critical value. The analogous ‘purely-growing Brissllouin instability’ (POBI) is shown not to exist, in a collinear interaction, with a travelling-wave pump. In fact we conclude that no such backward-wave, zero frequency, absolute instability could occur in any case where the two interacting, frequency shifted waves are on the same mode of propagation as the travelling-wave pump. Finally, the possibility of a PGBI by means of a standing-wave pump, as suggested earlier by Lashmore-Davies, is confirmed for a collinear interaction, through the identification on the Brilbum diagram of a zero-frequency, back-wave parametric interaction resulting from the coupling of Stokes and anti-Stokes light waves by the standing-wave pumb light wave.