Effect of dust non‐linear charge and size‐distribution on dust-acoustic double‐layers in dusty plasmas

The investigation of the existence of arbitrarily large amplitude electrostatic dust-acoustic double layers is conducted in a four‐component plasma consisting of electrons, two distinct positive ion species of different temperatures, and massive negatively‐charged dust particles that are assumed spheres of different radii distributed according to a power‐law. The dependence of the dust grain charge on its size is considered to be nonlinear. The number densities of electrons and ions are assumed to follow a Boltzmann distribution, whereas the dynamics of charged dust grains is described by fluid equations. Comparison is conducted between plasmas containing size‐distributed dust grains and those containing monosize dust grains, while examining the criteria for the existence of dust-acoustic double layers along with the dependence of their amplitudes and Mach numbers on plasma parameters.