Microscopic model for relativistic hydrodynamics of ideal plasmas

TL;DR

This paper derives a relativistic hydrodynamic model for ideal plasmas from microscopic principles, introducing new variables without nonrelativistic analogs, and presents the final equations in a mean-field approximation.

Contribution

It develops a microscopic derivation of relativistic hydrodynamics for ideal plasmas, revealing new variables unique to the relativistic regime.

Findings

New relativistic-hydrodynamic variables identified

Derived equations reduce to classical variables in nonrelativistic limit

Final model presented in the monopole mean-field approximation

Abstract

Relativistic hydrodynamics of classic plasmas is derived from the microscopic model in the limit of ideal plasmas. 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 meanfield (the selfconsistent 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.