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A non-relativistic multi-fluid plasma axisymmetric equilibrium model wasdeveloped recently to account for the presence of an energetic electron fluidin addition to thermal electron and ion fluids. The equilibrium formulation ofa multi-fluid plasma with relativistic energetic electrons is developed andreported in this paper. Relativistic effects in a fluid model approximation canappear in two ways: due to a large macroscopic fluid velocity comparable to thespeed of light and large particle's microscopic random motion which becomessignificant if the temperature becomes comparable to or larger than theelectron rest mass-energy. It is found that the axial component of relativisticgeneralized angular momentum can be used to describe relativistic axisymmetricequilibrium. The formulation is applied to a four-fluid plasma composed of arelativistic energetic electron fluid, a thermal electron fluid, and fluids oftwo thermal ion species (e.g. proton and boron ions). The four-fluid densityexpression which is consistent with the electrostatic potential is obtained andapplied in the computation. An example equilibrium approximating a four-fluidplasma recently observed in a solenoid-free ECRH sustained spherical torusplasma is calculated and presented. A second equilibrium that extends theenergetic electron temperature of the first example to 679keV is calculatedrevealing significant relativistic effects.

Four-Fluid Axisymmetric Plasma Equilibrium Model Including Relativistic Electrons and Computational Method and Results