Energy mode distribution at the very beginning of parametric instabilities of monochromatic Langmuir waves

Starting from a general form of the Zakharov equations the relations for electric fields and wave energy distributions at the very beginning of parametric instabilities are derived in dependence on initial Langmuir wave parameters. The corresponding dispersion equations in general and approximative forms are presented. These equations of the order up to eleven, with a different level of physical effects included (hydrodynamic-like, L2 and L3 distributions, non-linear denominators, quasi-neutrality violation approximations) are solved numerically. The growth rates, real frequencies and energy mode distributions are obtained in five regimes of the modulational and decay instabilities. A new description which is expressed by the energy mode distribution clearly shows energies transferred into upand down-converted Langmuir and electromagnetic modes. Results confirming those from previous studies as well as new and more general ones are presented. Furthermore, it is found that in some commonly used approximations of the dispersion equation, in the decay regime, non-physically high real frequencies appear. It is shown that for more general approximations this problem is effectually reduced. The role of wave damping is considered, too. Finally, for a constant parent Langmuir wave, it is found that the conversion efficiency into the electromagnetic mode sharply increases with the temperature increase.