Nonlinear theory of parametric kinetic instabilities in a plasma

For parametric kinetic-type instabilities, caused by resonance particle oscillation builup, the weak turbulence theory for a general case of finite particle shifts in a sinusoidal pumping wave field is generalized. Generalization of quasilinear kinetic equations for the case of finite particle shifts is obtained. Based on the generalized theory the nonlinear stage is investigated and the saturation level of the ion cyclotron kinetic parametric instability is determined in case when a relative ion and electron velocity is less than or the order of the ion thermal velocity. Rates of turbulent heating of plasma components are estimated