ECOM: a fast and accurate solver for toroidal axisymmetric MHD equilibria

TL;DR

ECOM is a novel, high-precision solver for toroidal axisymmetric MHD equilibria that leverages conformal mapping and spectral methods to outperform traditional finite element codes in accuracy and speed.

Contribution

The paper introduces ECOM, a fast and accurate equilibrium solver combining conformal mapping with spectral methods, achieving exponential convergence for MHD equilibrium calculations.

Findings

ECOM computes safety factor and magnetic shear with higher accuracy than CHEASE.

ECOM achieves exponential convergence for the poloidal flux function.

ECOM outperforms finite element codes in accuracy at similar computational times.

Abstract

We present ECOM (Equilibrium solver via COnformal Mapping), a fast and accurate fixed boundary solver for toroidally axisymmetric magnetohydrodynamic equilibria with or without a toroidal flow. ECOM combines conformal mapping and Fourier and integral equation methods on the unit disk to achieve exponential convergence for the poloidal flux function as well as its first and second partial derivatives. As a consequence of its high order accuracy, for dense grids and tokamak-like elongations ECOM computes key quantities such as the safety factor and the magnetic shear with higher accuracy than the finite element based code CHEASE [H. L\"utjens \textit{et al.}, Computer physics communications 97, 219 (1996)] at equal run time. ECOM has been developed to provide equilibrium quantities and details of the flux contour geometry as inputs to stability, wave propagation and transport codes.