Dust ion-acoustic shocks in quantum dusty pair-ion plasmas

Abstract

The formation of dust ion-acoustic shocks in a four-component quantum plasma whose constituents are electrons, both positive and negative ions, and immobile charged dust grains, is studied. The effects of both the dissipation due to kinematic viscosity and the dispersion caused by the charge separation as well as the quantum tunneling associated with the Bohm potential are taken into account. The propagation of small but finite amplitude dust ion-acoustic waves is governed by the Korteweg–de Vries–Burger equation, which exhibits both oscillatory and monotonic shocks depending not only on the viscosity parameters η±=μ±ωp−/cs2 (where μ± are the coefficients of kinematic viscosity, ωp− is the plasma frequency for negative ions, and cs is the ion-sound speed), but also on the quantum parameter H (the ratio of the electron plasmon to the electron Fermi energy) and the positive to negative ion density ratio β. Large amplitude stationary shocks are recovered for a Mach number (M) exceeding its critical value (Mc). Unlike the small amplitude shocks, quite a smaller value of η+, η−, H and β may lead to the large amplitude monotonic shock structures. The results could be of importance in astrophysical and laser produced plasmas.