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