Coupled Nonlinear Schrodinger (CNLS) Equations for two interacting electrostatic wavepackets in a non-Maxwellian fluid plasma model

Abstract The nonlinear dynamics of two co-propagating electrostatic wavepackets in a one-dimensional non-magnetized plasma fluid model is considered, from first principles. The coupled waves are characterized by different (carrier) wavenumbers and amplitudes. A plasma consisting of non-thermalized (κ−distributed) electrons evolving against a cold (stationary) ion background is considered. The original model is reduced, by means of a multiple-scale perturbation method, to a pair of coupled nonlinear Schr¨odinger (CNLS) equations for the dynamics of the wavepacket envelopes. For arbitrary wavenumbers, the resulting CNLS equations exhibit no known symmetry and thus intrinsically differ from the Manakov system, in general. Exact analytical expressions have been derived for the dispersion, self-modulation (nonlinearity) and cross-modulation (coupling) coefficients involved in the CNLS equations, as functions of the wavenumbers (k1, k2) and of the spectral index κ characterizing the electron profile. An analytical investigation has thus been carried out of the modulational instability (MI) properties of this pair of wavepackets, focusing on the role of the intrinsic (variable) parameters. Modulational instability is shown to occur in most parts of the parameter space. The instability window(s) and the corresponding growth rate are calculated numerically in a number of case studies. Two-wave interaction favors MI by extending its range of occurrence and by enhancing its growth rate. Growth rate patterns obtained for different κ index (values) suggest that deviation from thermal (Maxwellian) equilibrium, for low κ values, leads to enhances MI of the interacting wave pair. Although we have focused on electrostatic wavepacket propagation in nonthermal (non-Maxwellian) plasma, the results of this study are generic and may be used as basis to model energy localization in nonlinear optics, in hydrodynamics or in dispersive media with Kerr-type nonlinearities where modulational instability is relevant.