Linear Analysis of Electrostatic Modes in Quantum Plasmas

Abstract

The quantum vlasov equation is derived in this work as a differential equation based on Wigner’s representation and used for a magnetised degenerate electron plasma. The dispersion relations resulting from the quantum version of the Vlasov equation and the degeneracy effect include correction terms. The dispersion characteristics of electrostatic waves, propagating in both parallel and perpendicular direction, in quantum plasmas are investigated for various parameters, from semi-conductor plasmas to typically metallic densities and densities related to compressed matter and dense astrophysical objects. The results obtained will be helpful in understanding the important characteristics of electrostatic waves in dense plasma environments like white dwarf and neutron stars, which contain degenerate electrons.