Investigation of the quantum electrostatic streaming instabilities in the presence of a Fermi pressure

In this paper, quantum two-stream and multi-stream instabilities have been studied by taking into account the effect of Fermi pressure term. The dispersion relation is calculated by means of a quantum non-relativistic hydrodynamic model. It is shown that there is no any free energy for velocities shorter than Fermi velocity in the system and hence the plasma system is stable in this condition. On the other hand, it has been observed, taking into account the effect of Fermi pressure decreases the maximum growth rate of instabilities but cut-off wave number increases. It is found that the growth rate and cut-off wave number of two-stream instability is larger than multi-stream instability due to Focusing of energy.