Development of a reduced multi-fluid equilibrium model and its application to proton–boron spherical tokamaks

Proton–Boron (p- 11 B) fusion represents a promising pathway toward aneutronic clean energy but requires extremely high ion temperatures and robust magnetic confinement. Spherical Tokamaks/Torus (ST) driven by high-power neutral beam injection are a primary candidate for this regime. In such devices, the combination of strong toroidal rotation and the significant mass disparity between protons and boron ions leads to complex multi-fluid effects—specifically centrifugal species separation and electrostatic polarization—which standard single-fluid magnetohydrodynamic models fail to capture. Conversely, comprehensive multi-fluid models that include poloidal flows often suffer from numerical stiffness and excessive complexity, hindering their use in routine engineering analysis. To address these challenges, we have developed a reduced multi-fluid equilibrium model designed to balance physical fidelity with computational robustness. By retaining the dominant toroidal rotation and self-consistent electrostatic potential while neglecting secondary effects such as poloidal flow inertia and pressure anisotropy, the model is formulated as a generalized Grad–Shafranov equation coupled with species-specific Bernoulli relations and a quasi-neutrality constraint. The model is applied to analyze the equilibrium configurations of two representative p- 11 B ST devices designed by the ENN Group: the experimental EHL-2 and the reactor-scale EHL-3B. Simulation results demonstrate that the equilibrium modification is governed by the ion Mach number ( M ). In the low-rotation regime ( M < 0.5 ), multi-fluid effects are weak, and the solution converges toward the single-fluid limit. However, in the high-rotation regime ( M > 2 ), strong centrifugal forces drive significant boron accumulation at the low-field side and generate an internal electrostatic potential on the order of 10 kV. These results confirm the necessity of multi-fluid modeling for accurate p- 11 B reactor design within the assumptions quantified in this work.