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

TL;DR

This paper introduces VEQ-R, a fast spectral solver for calculating spherical torus equilibria with arbitrary toroidal rotation, capturing complex geometric effects efficiently and accurately in challenging sonic regimes.

Contribution

The paper presents VEQ-R, a novel spectral solver that efficiently computes equilibria with arbitrary toroidal flow using a shifted Chebyshev expansion and a Matrix-Kernel acceleration technique.

Findings

VEQ-R achieves convergence in about 5 ms.

It accurately captures differential flux surface distortions.

Rotation-induced flux compression affects the safety factor q0.

Abstract

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.