  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.
