Waves propagating parallel to the magnetic field in relativistically hot plasmas: A hydrodynamic model with the average reverse gamma factor evolution

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