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Nonlinear regimes of one-dimensional parametric instabilities of long-waveplasma waves are considered for the cases when the average plasma field energydensity is less (Zakharov's model) or greater (Silin's model) than the plasmathermal energy density. The hybrid models presented in this paper treat theelectrons as a fluid by way of an equation for the high-frequency wave andtreat the ions kinetically with a super-particle simulation. This makespossible consideration of non-resonant particles trapped by high-frequencyoscillations and the influence of trajectory crossing on the development of theparametric instability. The evolution of ion energy distribution is studied. Itis shown that after saturation of the instability, the ion kinetic energydensity normalized to the initial field energy density is of the order of theratio of linear growth rate to the plasma frequency, for the case when theinitial field energy far exceeds the plasma thermal energy. In this case, theion energy distribution is different from the Maxwellian.In the opposite caseof hot plasma, the ions acquire a part of initial field energy, which isapproximately equal to the half of ratio of initial Langmuir field energy tothe plasma thermal energy. At this, the ion kinetic energy distribution isclose to the Maxwellian, and it is reasonably to speak about ion temperature.The crossing of ion trajectories in the surrounding of density cavities is areason of instability quenching in both cases.

Kinetics of ions during the development of parametric instability of intensive Langmuir waves in plasma