Vlasov equation for magnetized quantum plasmas and its application to plasma waves

Abstract

In this thesis, I derived the kinetic equation of quantum plasmas, the quantum Vlasov equation, and applied it to calculate the susceptibility tensor of the quantum plasma waves. The dispersion relations for the linear waves propagating parallel to the ambient magnetic field were derived analytically for partially and fully degenerate plasmas. For the electrostatic wave, Langmuir wave, its group and phase velocities were found to be faster in the quantum plasma than in the classical plasma since the quantum correction gives additional effect that resembles a thermal term to the wave. Hence, the Langmuir wave propagates in the quantum plasma even in the ideal case of zero temperature, whereas the wave becomes a pure oscillation in the cold plasma limit. In the case of electromagnetic waves, quantum effects were seen to be of two origins: one from the Fermi distribution and the other from the use of the Schrodinger equation (the quantum recoil effect). The Fermi distribution effect is generally larger than the quantum recoil effect, though both of them gives only minor correction to the upper branches of L and R waves. On the other hand, a unique feature of quantum origin was seen in the lower branch of R wave: a region of anomalous dispersion appears as a result of the Fermi distribution and it is divided into two, separated by a region of normal dispersion, due to the quantum recoil effect. Additionally, the quantum fluid equations and quantum magnetohydrodynamic equations are derived by using the quantum Vlasov equation and the adiabatic equation in the quantum plasma is derived analytically.