On the frequency spectra of the electrostatic upper hybrid wave and linear Landau damping in a weakly magnetized relativistic electron plasma

On the basis of Vlasov-Kinetic model and using Maxwell-Juttner distribution function, dispersion relation of electrostatic wave in a collisionless homogeneous relativistic electron plasma is derived. The analysis of the oscillation spectra is carried out in a weak magnetic field limit ω−kvth ≥ Ω. Approximate analytic expression for the weakly damped mode is obtained in the subluminal limiting range. It is shown that the relativistic weakly damped mode can be estimated analytically in the range where the wave phase velocity v φ becomes greater than relativistic thermal velocity of the electron but less than speed of light. Results in the non-relativistic and the ultrarelativistic cases are also discussed.