Linear Waves in Magnetized Quantum Plasma

Summary form only given. We have investigated the dispersion properties of some kinds of linear waves in uniform, cold quantum magnetoplasmas. Our analysis is based on the quantum magnetohydrodynamic equations. We derive new dispersion relations of the Langmuir wave and X wave by solving the plasma dielectric permeability tensor and find that the dispersion relations of the ordinary wave, the left-handed wave, and the right-handed wave show no quantum effect corrections. The results indicate that the quantum corrections have significant effects on the dispersion property of the Langmuir wave when the wave number k is big enough. The quantum effects also make the electrostatic oscillation into the Langmuir wave, which now has weak dispersion and whose group velocity increases with increasing frequency. The quantum corrections to the dispersion relation of the X wave have also been studied. Compared to the Langmuir wave, quantum effects have weaker corrections to the dispersion of the X wave and actually can be neglected in general conditions. For the Langmuir wave, our conclusion is that quantum effect corrections are significant when the electron quantum wavelength becomes comparable to the linear waves wavelengths. For simplicity, we consider only two types of wave vectors: the one that is parallel to the magnetic field and the one that is perpendicular to the magnetic field. Once the expression of the plasma dielectric permeability tensor is obtained, the dispersion relations of more complicated kinds of waves can be obtained with smaller efforts.