A novel approach to the quantum Buneman instability

Consider a non collisional quantum plasma, where electrons stream with a velocity u0 relative to the ions, which are assumed to be initially at rest due to their mass. A quantum dispersion relation is obtained having considered the Bohm interpretation of Quantum Mechanics by means of Quantum Magnetohydrodynamics. This quantum dispersion relation contains the classical non dimensional parameter Kappa and the quantum non dimensional parameter H. A quartic equation ( Aw 4+Bw 3+Cw 2+Dw+E =0, where w is the normalized frequency ) is obtained from the quantum dispersion relation. So the novel approach to the quantum Buneman instability consists in having solved for the first time this quartic equation in order to obtain the instability intervals. My next paper will show how the values of kappa and H can be replaced by the initial velocity u0 in the quantum instability intervals obtained in this paper.