Investigation of Toroidal Rotation Effects on Spherical Torus Equilibria using the Fast Spectral Solver VEQ-R

Standard reduced models often fail to adequately describe the complex geometric response of tokamak plasmas to strong toroidal rotation. In this work, we present VEQ-R, a computationally efficient spectral solver designed to calculate fixed-boundary equilibria with arbitrary toroidal flow. In contrast to computationally intensive grid-based codes, our model employs a 12-parameter shifted Chebyshev spectral expansion to explicitly resolve radial variations in high-order shaping profiles–such as dynamic elongation and triangularity. This capability allows the solver to accurately capture differential flux surface distortions (non-rigid effects) even in challenging sonic regimes ($M\sim 1.0$). By synergizing this compact variational formulation with a novel ``Matrix-Kernel’’ acceleration technique, we transform the problem into pre-computed algebraic matrix operations. This approach achieves convergence in approximately 5 ms, maintaining exceptional geometric fidelity compared to high-resolution benchmarks while balancing speed and accuracy. Our analysis reveals that rotation-induced flux compression leads to a monotonic decrease in the core safety factor $q_0$, pushing it dangerously close to unity–a structural deformation mechanism effectively captured by this approximate yet robust solver.