Ion heating, burnout of the high-frequency field, and ion sound generation under the development of a modulation instability of an intense Langmuir wave in a plasma

The development of one-dimensional parametric instabilities of intense long plasma waves is considered in terms of the so-called hybrid models, with electrons being treated as a fluid and ions being regarded as particles. The analysis is performed for both cases when the average plasma field energy is lower (Zakharov's hybrid model—ZHM) or greater (Silin's hybrid model—SHM) than the plasma thermal energy. The efficiency of energy transfer to ions and to ion perturbations under the development of the instability is considered for various values of electron-to-ion mass ratios. The energy of low-frequency oscillations (ion-sound waves) is found to be much lower than the final ion kinetic energy. We also discuss the influence of the changes in the damping rate of the high-frequency (HF) field on the instability development. The decrease of the absorption of the HF field inhibits the HF field burnout within plasma density cavities and gives rise to the broadening of the HF spectrum. At the same time, the ion velocity distribution tends to the normal distribution in both ZHM and SHM.