On the Bernstein mode in a degenerate anisotropic quantum plasma

Abstract

By employing quantum Vlasov–Maxwell set of equations, we have derived a general dispersion relation for perpendicularly propagating electrostatic waves in a degenerate anisotropic quantum plasma. Specifically, we discuss the Bernstein mode and examine how the effects of quantum diffraction and degenerate anisotropy influence its propagation characteristics. We find that the spectrum of the mode becomes more oscillatory. Further, we observe that while the anisotropy significantly affects the mode for β = ωpe/ωce > 1, the quantum effect prevails for β < 1. These effects become more prominent at higher harmonics. It is also pointed out that our results may prove helpful to understand the phenomena of plasma heating and particle acceleration in astrophysical environments like white dwarf.