Two stream instabilities in unmagnetized nonrelativistic quantum plasma

The objective of this study is to analyse instabilities and growth rate in unmagnetized dense non-relativistic collisionless quantum plasma under the impact of dynamics of ions. Model of quantum hydrodynamics is used to observe the streaming instabilities in highly dense inhomogeneous unmagnetized quantum plasma at low temperature. The model includes continuity and momentum equations for degenerate electrons and nondegenerate ions which interact with each other due to electrostatic field. Using normal mode analysis and linearization, perturbed potential is obtained in terms of unperturbed parameters with the help of first order perturbation in densities and velocities of electrons and ions while neglecting higher order perturbations. Variation in growth rates for detected instabilities is observed by using appropriate quantum plasma parameters.