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Nonplanar quantum dust ion-acoustic Gardner double layers

Nonplanar (cylindrical and spherical) double layers (DLs) in a quantum dusty plasma (composed of inertial ions, Fermi electrons and negatively charged immobile dust particles) are studied by employing the reductive perturbation method. The modified Gardner equation describing the nonlinear propagation of the quantum dust ion-acoustic (QDIA) waves is derived, and its nonplanar DL solutions are numerically analyzed. The parametric regimes for the existence of the DLs, which are found to be associated with both positive and negative potentials, are obtained. It has been found that the existence of small but finite-amplitude electrostatic DLs depends on μ = Zdnd0/ni0 (where Zd is the number of electrons residing onto the dust grain surface, and nd0 and ni0 are, respectively, the dust and ion number density at equilibrium) as well as the quantum diffraction parameter H. It has also been found that the propagation characteristics of nonplanar QDIA DLs are significantly different from those of the planar ones.