A non-relativistic multi-fluid plasma axisymmetric equilibrium model [A. Ishida et al., “Three-fluid axisymmetric equilibrium model and application to spherical torus plasmas sustained by RF electron heating,” Plasma Fusion Res. 10, 1403084 (2015)] 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 a 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 [Y.-K. M. Peng et al., “Initial results of the EXL-50 experiment,” (to be published)] is calculated and presented. A second equilibrium that extends the energetic electron temperature of the first example to 679 keV is calculated revealing significant relativistic effects.

中文翻译：

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包含相对论电子的四流体轴对称等离子体平衡模型及计算方法和结果

非相对论性多流体等离子体轴对称平衡模型[A. 石田等。，“三流体轴对称平衡模型及其在通过射频电子加热维持的球形环面等离子体中的应用”，Plasma Fusion Res。10，1403084（2015）]的开发是为了解决除热电子和离子流体外还存在高能电子流体的问题。本文开发并报道了具有相对论性高能电子的多流体等离子体的平衡公式。流体模型近似中的相对论效应可能以两种方式出现：由于大的宏观流体速度可与光速媲美，并且大粒子的微观随机运动在温度等于或大于电子静止质量能时变得非常重要。 。发现相对论广义角动量的轴向分量可用于描述相对论轴对称平衡。将该配方应用于由相对论高能电子流体组成的四流体等离子体，热电子流体，以及两种热离子物质（例如，质子和硼离子）的流体。得到与静电势一致的四流体密度表达式，并将其应用于计算中。最近在无螺线管ECRH持续球形环面等离子体中观察到的近似四流体等离子体的示例平衡[Y.-KM Peng等。，“ EXL-50实验的初始结果”（即将出版）]被计算并显​​示出来。计算了将第一示例的高能电子温度扩展到679 keV的第二平衡，从而揭示了显着的相对论效应。