Parallel Propagating Waves in Weakly Magnetized Relativistic Electron Plasma

The parallel propagating waves (Langmuir, R and L waves) are studies in different plasma environments by choosing the different values of η = (mc
²
/k
_B
T) and (ω
_pe
²
/ω
_ce
²
). The dispersion relations of these waves are derived under a weak magnetic field limit for a fully relativistic plasma environment. The analytical solution of the integrals in the dispersion relations is not possible, so we use a numerical quadrature approach for their solution. We observe that in both relativistic and weakly relativistic plasmas, these modes shifted to lower values of frequency. The cutoff points of Rand L-waves shifted to further lower values in high-density plasma compared to low density.