Nonlinear theory of the modulational instability at the ion–ion hybrid frequency and collapse of ion–ion hybrid waves in two-ion plasmas

We study the dynamics of two-dimensional (2D) nonlinear ion–ion hybrid waves propagating perpendicular to an external magnetic field in plasmas with two ion species. We derive nonlinear equations for the envelope of electrostatic potential at the ion–ion hybrid frequency to describe the interaction of ion–ion hybrid waves with low-frequency acoustic-type disturbances. The resulting nonlinear equations also take into account the contribution of the second harmonics of the ion–ion hybrid frequency. A nonlinear dispersion relation is obtained, and, for a number of particular cases, modulational instability growth rates are found. By neglecting the contribution of second harmonics, the phenomenon of the collapse of ion–ion hybrid waves is predicted. It is shown that taking into account the interaction with the second harmonic results in the existence of a stable two-dimensional soliton.