Instability of Ion Acoustic Wave in a Quantum Dusty Plasma Bounded in Finite Geometry

The instability of  ion-acoustic wave in quantum dusty plasma propagating in a cylindrical waveguide filled with strongly magnetized plasma consisting of oblique streaming of holes and stationary negatively charged dust particles has been theoretically investigated using   the quantum hydro-dynamical (QHD) model which includes both quantum statistical effect and the quantum diffraction effect. It is shown that ion acoustic wave become unstable in the  bounded quantum dusty plasma. The growth rate of unstable wave  depends   on the stream velocity of holes, quantum diffraction parameter,  charge imbalance parameter, inclination of stream velocity and  dimension of cylindrical wave guide.  Moreover, the phase velocity of the wave  depends on the plasma parameters and the dimension of wave guide. Growth rate of the instability  and phase velocity  of wave  in bounded quantum plasma are shown  graphically  and discussed.