Quantum instability of two non-parallel flows: Parallel wave propagation

The streaming instability for two non-paralleled plasma shells propagating through a background quantum plasma has been studied. The dispersion relation is calculated, assumed that the perturbation wave vector is in the direction of one of the plasma shell, by linearizing and solving fluid-Maxwell equations. The resulting dispersion equation is analyzed numerically in a wide range of system parameters. Investigation of cut-off wave number and growth rate are shown that, the instability for a wide range of wave number when the velocity of shells reaches to a specific value, β=βc.