Waves propagating parallel to the magnetic field in relativistically hot plasmas: A hydrodynamic model

The high-frequency part of spectrum of electromagnetic waves propagating parallel to the external magnetic field is considered for the macroscopically motionless plasmas with the relativistic temperatures $T\sim m_{e}c^{2}$, where $m_{e}$ is the mass of electron, $c$ is the speed of light. The analysis is based on the novel hydrodynamic model based on four equations for the material fields which can be combined in two four vectors. These material fields are the concentration and the velocity field \emph{and} the average reverse relativistic $\gamma$ functor and the flux of the reverse relativistic $\gamma$ functor. In the nonrelativistic regime we have three waves (the ions are assumed to be motionless). Strong thermal effects lead to a coefficient in front of cyclotron frequency which decreases the effective contribution of the cyclotron frequency. At $T=0.1m_{e}c^{2}$ we have a decrease of area of existence of fast magneto-sound wave from the area of the large frequencies. While the area of existence of extraordinary waves becomes larger towards smaller frequencies. The strong magnetic field limit $\mid\Omega_{e}\mid > \omega_{Le}$ additional wave appears with frequency below thermally decreased cyclotron frequency, where $\mid\Omega_{e}\mid$ is the electron cyclotron frequency, and $\omega_{Le}$ is the Langmuir frequency. Further increase of temperature leads to the disappearance of fast magneto-sound wave and to the considerable increase of area of existence of extraordinary towards smaller frequencies.