Interaction of Dust-Ion Acoustic Shocks in Quantum Dusty Plasma

Abstract

Over the last many years, study of nonlinear phenomena in quantum plasmas is a prime focus of the researcher due to its wide ranging applications in microelectronic devices, in nano-scale systems, in laser fusion plasmas, in next generation high intensity laser sources, in quantum plasma echoes, in quantum plasma instabilities and in dense astrophysical environments. The quantum effects in plasmas become significant, when the associated de Broglie wavelength of the particles is comparable to the inter-particle distance Dust grains are universal in various parts of our cosmic environment, such as in the planetary ring system of Saturn, in Jupiter's moon and in the dust rings of the Martian moon etc. The presence of highly charged dust grains in plasmas give rise to different kinds of wave modes; dust-ion acoustic mode (DIA) is one of such modes under present study. The Quantum Hydrodynamic (QHD) model is useful approximation to study various kind of nonlinear phenomena in quantum dusty plasmas. In present investigation, we have analyzed the interaction of dust ion-acoustic (DIA) shock waves in quantum plasma whose constituents are electrons and ions showing quantum behavior and negatively charged dust grains. The ions and dust grains are assumed to be mobile and quantum electrons are considered to be inertialess. Using an extended Poincare-Lighthill-Kuo perturbation method, two sided KdV-Burgers equations for shock waves are derived. The analytical phase shifts of DIA shock waves after collision have also been deduced. The impacts of physical parameters such as the quantum diffraction parameter for electrons and ions, kinematic viscosity which arises due to dust charge variation, the unperturbed dust to ion density ratio, and temperature ratio on the phase shifts occurred during the head-on collision between DIA shock waves are analyzed. Only positive potential shocks are observed. Amplitude and width of DIA shocks are enhanced with change in number density ratio. The phase shift is also increased with increase in number density and ion viscosity parameter. The findings of this investigation may be of great importance to understand the characteristics and phase shift in trajectories due to the collision of DIA shock waves in different space and astrophysical environments.