Dispersion relations in weakly degenerate plasmas

Abstract

From a quantum mechanical point of view, electrons in laser produced plasmas can be regarded as weakly degenerate. For instance, for a plasma with electron density of 10 22 cm −3 and electron temperature of 1 eV, Sommerfeld's parameter is between 1 and 2. Under these conditions the usual dispersion relations for waves in plasmas need be corrected to account for degeneracy. In the present work, starting from the transport equation with a simplified version of the Boltzmann–Uehling–Uhlenbeck collision kernel the propagation of waves impinging on a plasma with weakly degenerate electrons is investigated and dispersion relations accounting for degeneracy are derived. These dispersion relations give the classical ones in the limit for Sommerfeld's parameter approaching zero. A shift of the wavenumber value and a non-collisional damping due to degeneracy effects are predicted which render a weakly degenerate plasma more opaque to radiation than a non-degenerate one.