Microscopic model for relativistic hydrodynamics of ideal plasmas

Relativistic hydrodynamics of classic plasmas is derived from the microscopic model in the limit of ideal plasmas, while the microscopic description assumes the level of dynamics of individual particles and the kinetic models look as the macroscopic models in this approach. The chain of equations is constructed step by step starting from the concentration evolution. It happens that the energy density and the momentum density do not appear at such approach, but new relativistic hydrodynamic variables appear in the model. These variables has no nonrelativistic analogs, but they are reduced to the concentration, the particle current, the pressure (the flux of the particle current) if relativistic effects are dropped. These variables are reduced to functions of the concentration, the particle current, the pressure if the thermal velocities are dropped in compare with the relativistic velocity field. Final equations are presented in the monopole limit of the mean-field (the self-consistent field) approximation. Hence, the contributions of the electric dipole moment, magnetic dipole moment, electric quadrupole moment, etc., of the macroscopically infinitesimal element of volume appearing in derived equations are dropped. Graphical abstract