On the occurrence of freak waves in negative ion plasmas

Abstract

A theoretical investigation of the existence of electrostatic freak waves (FWs), also known as rogue waves (RWs), in a multicomponent plasma with negative ions is presented, from first principles. A three component plasma is considered, consisting of positive ions, negative ions and electrons. Both ion species (distinguished by their different mass and absolute charge) are modeled as cold inertial fluids, for simplicity, while the electrons are assumed to be thermalized, given the dynamical scale of interest. Based on a multiscale perturbation technique, a nonlinear Schrödinger (NLS) type equation is derived, describing the evolution of an electrostatic wavepacket amplitude (envelope). By means of a modulational stability analysis, we have determined the conditions for bright envelope solitons (breathers) or, alternatively, for dark-type envelope solitons (envelope holes) to exist. The region of existence of freak waves in configurational parameter space is elucidated, in terms of the negative-ion component (concentration and charge). The parametric dependence of the spatiotemporal characteristics of FWs on the negative-ion parameters is also discussed. It is established that freak waves may occur in a wide region in parameter space. Our analytical predictions are corroborated by numerical simulations, showing that FWs may occur spontaneously in the dynamics. Our results extend earlier studies and also enable an efficient interpretation of past and future experiments.