Parametric instabilities in two-dimensional non-uniform plasma in the range of linear conversion of an oblique Langmuir wave

Theory of parametric decay instability in two-dimensional nonuniform plasma was constructed. It is shown, that instability is of convective character, when pumping wave represents the main radial Traivelpis-Guld (TG) mode (single-mode pumping wave). It results to amplification of equilibrium ion-acoustic noise and excitation of back scattered TG modes. It is shown, that feedback loop, specific for two-dimensional nonuniform plasma, can occur in the case of multi-mode pumping wave in plasma. Propagation of five waves, participating in interaction in feedback loop was calculated, and dispersion equation for eigenfrequencies and increments of excited ion-sound wave was obtained