Quantum corrections for fundamental plasma behaviors

Abstract

Quantum plasmas have received considerable attention in recent years. The quantum effects become important if the typical distance separating particles in a plasma system becomes comparable or less than the de Broglie wavelength of the particles. This condition will be satisfied when the Fermi temperature is greater than thermal temperature of plasmas; thus quantum effects become important. The electrons in the plasmas approach to a Fermi gas, their statistical behavior is described by Fermi-Dirac distribution instead of classical Boltzman distribution. Quantum hydrodynamics (QHD) is the most widely used hydrodynamic model, which deals with transport processes of particles, the momentum of particle and macroscopic physical quantities like energy. Together with the status equation, they form a complete set of equations to describe quantum plasmas from the fluid dynamics’ point of view. Besides, Quantum Magnetohydrodynamic (QMHD) model is established based on QHD equations and takes into account of magnetic field. This research is based on QMHD model to investigate the different waves and fluid instabilities in magnetized plasmas. This thesis includes some parts as described in the following. First, based on the quantum hydrodynamic equations with magnetic field, we investigated the dispersion relation of some types of linear waves in quantum magnetized plasmas. Our results indicate that the quantum corrections have significant effects on the dispersion properties of the Langmuir wave. Second, we studied the general dispersion equation for quantum magnetized warm plasmas. Using the plasma dielectric tensor, we obtained the dispersion relations of magnetoelectric waves and multi-stream instability by solving the dispersion equation. The parallel magnetic field has no effects on stream instability, while twostream instability is altered remarkably by quantum effects and thermal effects. Third, the electromagnetic drift waves of nonuniform quantum magnetized EPI plasmas on the basis of the QMHD model were discussed by taking the thermal and Fermi pressure terms into account. We found that the drift wave is unstable when the wave vector has a component along the axis and the growth rate is approximately proportional to the square of the electron number density gradient. Fourth, the electrostatic drift waves (EDWs) in nonuniform quantum pair plasmas placed in an external magnetic field were investigated. We derived the analytic expression of the dispersion relation of EDWs with the presence of equilibrium magnetic field inhomogeneity and show that a new, purely quantum, branch appears. This new electrostatic drift mode does not exist in classical pair plasmas and has no vital relation with quantum statistic effects. Next, the Rayleigh-Taylor (RT) instability in an ideal incompressible quantum magnetized plasma system was researched. Using the exponential density distribution and fixed boundary conditions, we derive the analytical expression of the growth rate of RT instability. The RT instability is affected significantly by quantum effects. Quantum mechanical effects suppress the RT instability in proper circumstances. Moreover, we calculated the electrostatic drift waves (EDW) in nonuniform threedimensional Fermi plasma placed in an external magnetic field. The dispersion relation of EDWis obtained. The new quantum diamagnetic drift velocity and quantum ion-acoustic velocity are introduced and shown to be much greater than their respective value under classical circumstances. The dispersion relation is affected and altered obviously by quantum mechanical effects. At the last, we consider the possible electrostatic drift waves (EDWs) in quantum dusty plasmas. The dust self-gravitational effects are taken into account. One can see that the Jeans terms induced by the dust gravitation perturbation exert significant effects on the dispersion relation. Under these environment, a drift-like instability is induced by the Jeans terms.