Planar and nonplanar quantum dust ion-acoustic Gardner double layers in multi-ion dusty plasma

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 double layer solutions are numerically analyzed. The parametric regimes for the existence of the DLs, which are found to be associated with both positive and negative potential, are obtained. It has been found that the existence of small but finite amplitude electrostatic double layers depends on β=Zpnp0/Znnn0 (where Zp (Zn) is the charge states for positive ions (negative ions) and np0 (nn0) is the equilibrium positive ions (negative ions) number density) as well as the quantum diffraction parameter, H. It has been also found that the propagation characteristics of nonplanar QDIA DLs are significantly differ from those of planar ones.