Multidimensional freak waves in electron depleted dusty magnetoplasmas having superthermal ion with two temperatures

The three-dimensional modulational instability (MI) and the associated electrostatic freak waves in electron depleted dusty magnetoplasmas having two temperature ions obeying Kappa distribution with transverse plane perturbations are investigated. For this purpose, the three-dimensional (3D) nonlinear Schrödinger equation (NLSE) is derived using the multi-scale perturbation technique. The regions of stable and unstable structures are determined precisely depending on a new criterium different from that of the one-dimensional (1D) NLSE. In the unstable regions the first- and second-order rogue waves are examined. The dependence of MI and freak waves on the relevant plasma parameters, namely, modulational obliqueness, cold ion concentration, cold-to-hot ion temperature ratio, dust gyrofrequency, and the spectral indices of the cold and hot ions are investigated. The present investigation is useful in space and laboratory magnetoplasmas, for instance, Geotail spacecraft observations seen in Earth’s magnetotail, solar wind, interstellar medium, and in the magnetosphere of Jupiter.