Hydrodynamic description of waves in a relativistic plasma with allowance for radiative deceleration

Linear oscillations of a relativistic plasma are investigated with consideration of radiative deceleration in the hydrodynamic approximat ion. A relativistically invariant dispersion relation is obtained and analyzed for a stationary plasma in the absence of external fields, for a plasma moving at a constant average velocity, and for waves propagating parallel and perpendicular to an external magnetic field. It is shown that the energy losses in collective emission of electrons results in damping of all types of plasma oscillations. This damping exceeds the Landau damping for waves in a plasma with density $n≥10^9$ cm^3, whose phase velocities are at least an order of magnitude higher than the electron thermal velocity.