Parallel propagating Electromagnetic Waves in Magnetized Quantum Electron Plasma

Abstract

The quantum Vlasov equation has been derived with the use of quasi probability distribution named as the Wigner function and the electromagnetic Schrodinger equation. By using this quantum kinetic model the parallel propagating electromagnetic waves have been studied and the susceptibility tensor for R (right handed circularly polarized) and L (right handed circularly polarized wave) wave has been derived. The dispersion relation of R and L waves is obtained by using Fermi Dirac distribution at zero temperature. By comparing the curves obtained by plotting quantum dispersion relation of R and L wave with that of the classical R and L wave, it has been observed that the upper branch of the R wave in quantum plasma has slightly higher group velocity than that of the R wave in a classical plasma. While for the lower R wave branch the quantum mechanical group velocity is slower than the classical group velocity and the anomalous dispersion is observed. Moreover, the quantum mechanical L wave is almost the same as the classical L wave but minor corrections are observed at higher values of k which indicates the faster group velocity of quantum mechanical waves as compared to the classical L wave.