Parallel propagating modes and anomalous spatial damping in the ultra-relativistic electron plasma with arbitrary degeneracy

The dispersion relations of parallel propagating modes (Langmuir mode, right and left handed circular polarized waves) in the weak magnetic field limit| ω-k·v |>> Ω are considered for ultra-relativistic arbitrary degenerate electron plasma. The results are presented in terms of moments of Fermi-Dirac distribution. The increase in the electron equilibrium number density from negative large (weakly degenerate) to positive large (highly degenerate) values of μ/T_e is observed (where μ is the electron chemical potential and T_e is the electron thermal energy). As a result, shifting of the cutoff points in all the real dispersion branches towards the higher values and increasing in the band gap between unmagnetized longitudinal and transverse modes in k-space are examined. Also, the suppression of the weak magnetic field effects in weakly magnetized right handed and left handed circular polarized waves and a decrease in the longitudinal and transverse screening effects are observed in the graphical patterns due to an increase in the equilibrium number density.