Modulational instability of electrostatic ion cyclotron wave in a two-electron-temperature plasma

A three-dimensional nonlinear Schrüdinger equation for an electrostatic ion cyclotron wave coupled to an ion-acoustic wave in a collision-free plasma consisting of cold ions and two-temperature electrons is derived using the reductive perturbation method. It is shown that a range of wavenumbers corresponding to the instability of a plane electrostatic ion cyclotron wave against a two-dimensional modulation depends on the ratio of temperature of hot and cold electron components.