Excitation of longitudinal waves in a degenerate isotropic quantum plasma

A dispersion equation, which describes the interaction of low-density electron beam with a degenerate electron quantum plasma, is derived and examined for some interesting cases. In addition to the instabilities similar to those for classical plasma, due to the quantum effect, a new type of instability is found. Growth rates of these new modes, which are purely quantum, are obtained. Furthermore, the excitation of Bogolyubov's type of spectrum by a strong electric field is discussed.