Dispersion of multi-stream instability in quantum magnetized hot plasmas

Using the quantum hydrodynamic (QHD) equations with magnetic field on the Wigner-Maxwell system, the general dielectric tensor and dispersion equation for quantum plasmas were derived. Dispersion relations of one-, two-stream and beam-plasma instabilities in uniform quantum magnetized plasmas are investigated through the new dielectric tensor. The magnetic field which is parallel to the fluid velocity does not work on stream instabilities. The quantum and thermal effects have remarkable impact on two-stream instability. The critical wave number for beam-plasma instability with quantum effects correction is given too.