Double-wells and double-layers in dusty Fermi-Dirac plasmas: Comparison with the semiclassical Thomas-Fermi counterpart

Based on the quantum hydrodynamic model, a new relationship between the electrostatic-potential and the electron-density in the ultra-dense plasma is derived. Propagation of arbitrary amplitude nonlinear ion waves is, then, investigated in a completely degenerate dense dusty electron-ion plasma, using this new energy relation, for the relativistic electrons in the ground of quantum hydrodynamics model and the results are compared to the case of semiclassical Thomas-Fermi dusty plasma. Using the standard pseudo-potential approach it is remarked that the Fermi-Dirac plasma, in contrast to the Thomas-Fermi counterpart, accommodates a wide variety of nonlinear excitations such as positive-/negative-potential ion solitary and periodic waves, double-layers and double-wells. It is also remarked that, the relativistic degeneracy parameter which relates to the mass-density of plasma has significant effects on the allowed matching-speed range in dusty Fermi-Dirac plasmas.