Dissipative high-frequency envelope soliton modes in nonthermal plasmas

The linear and nonlinear properties of modulated high-frequency (electron-acoustic) electrostatic wave packets are investigated via a fluid-dynamical approach. A three-component plasma is considered, composed of two types of electrons at different temperatures (“cold” and “hot” electrons) evolving against a cold stationary ion background. A weak dissipative effect is assumed, due to electron-neutral collisions. While the cold electrons are treated as an inertial fluid, the hot electrons are assumed to be in a non-Maxwellian state, described by a kappa ($\kappa$) type distribution. The linear characteristics of electron-acoustic waves are analyzed in detail, and a linear dispersion relation is obtained. Weakly damped electrostatic waves are shown to propagate above a wave number k threshold, whose value is related to dissipation (and reduces to zero in its absence). Long-wavelength values (i.e., for k below that threshold) are heavily damped and no propagation occurs. The nonlinear dynamics (modulational self-interaction) of wave packets in the propagating region is modeled via a dissipative nonlinear Schr{\"{o}}dinger type equation, derived via a multiscale perturbation technique for the wave envelope, which includes a dissipative term associated with the finite imaginary part of the nonlinearity term. The dynamical and structural characteristics (speed, amplitude, width) of dissipative localized modes representing the amplitude of modulated electron-acoustic wave packets in a collisional plasma are thus investigated for various values of relevant plasma (configuration) parameters, namely the superthermality index $\kappa$, the cold-to-hot electron density ratio, and collisionality (strength). Our analytical predictions are tested by computer simulations. A quasilinear perturbation method for near-integrable systems leads to a theoretical prediction for the wave amplitude decay, which is shown to match our numerical result. The results presented in this paper should be useful in understanding the dynamics of localized electrostatic disturbances in space plasmas, and also in laboratory plasmas, where the combined effect(s) of excess energetic (suprathermal) electrons and (weak) electron-neutral collisions may be relevant.