Excitation of Quantized Longitudinal Electric Waves in a Degenerate Fermi Gas

The system of electron beam - degenerate Fermi gas in a magnetic field is investigated. Instabilities of the quantized longitudinal electric waves are studied by a newly derived dispersion equation. Novel branches of longitudinal waves are found, which have no analogies without the Landau quantization. Growth rates of these new modes are obtained. The excitation of the zero sound by an electron beam is discussed and found that the quantization of the energy of electrons imposes a new condition. Furthermore, the excitation of Bogolyubov's type of spectrum by a strong electric field is considered.