Semi-analytical study of variable charge dust acoustic solitary waves in a dusty plasma with a q-nonextensive ion velocity distribution

An attempt is made to study variable charge dust acoustic (DA) solitons within the theoretical framework of the Tsallis statistical mechanics. The correct nonextensive ion charging current is presented for the first time based on the orbit motion limited (OML) approach. The variable dust charge is then expressed in terms of the Lambert function and we take advantage of this transcendental function to investigate nonlinear localized DA waves in a charge varying dusty plasma with nonextensive ions more rigorously. Our results reveal that the ion nonextensivity makes the dust acoustic solitary structure more spiky. As the ions deviate from their thermodynamic equilibrium, the dust grain charge becomes least negative and the dust accumulation more effective. In addition, the nonextensive character of the ions contributes to the electron depletion. The latter is more pronounced as the ions evolve far away from their thermal equilibrium. Our results should help in providing a good fit between theoretical and experimental results.