ATEQ: Adaptive Toroidal Equilibrium code

TL;DR

The paper introduces ATEQ, an adaptive numerical code for solving the Grad-Shafranov equation in tokamak equilibrium studies, featuring improved accuracy and reduced computational complexity through innovative decomposition and adaptive schemes.

Contribution

The paper presents a novel adaptive shooting scheme and matrix reduction technique that enhance the efficiency and accuracy of axisymmetric MHD equilibrium solutions.

Findings

Significantly improved accuracy in equilibrium solutions.

Matrix size reduced by about an order of magnitude.

Enhanced flexibility in handling Fourier components.

Abstract

A radially adaptive numerical scheme is developed to solve the Grad-Shafranov equation for axisymmetric magnetohydrodynamic equilibrium. A decomposition with independent solutions is employed in the radial direction and Fourier decomposition is used in the poloidal direction. The independent solutions are then obtained using an adaptive shooting scheme together with the multi-region matching technique in the radial direction. Accordingly, the Adaptive Toroidal Equilibrium (ATEQ) code is constructed for axisymmetric equilibrium studies. The adaptive numerical scheme in the radial direction improves considerably the accuracy of the equilibrium solution. The decomposition with independent solutions effectively reduces the matrix size in solving the magnetohydrodynamic equilibrium problem. The reduction of the matrix size is about an order of magnitude as compared with the conventional radially grid-based numerical schemes. Also, in this ATEQ numerical scheme, no matter how accuracy in the radial direction is imposed, the size of the matrices basically does not change. The small matrix size scheme gives ATEQ more flexibility to address the requirement of the number of Fourier components in the poloidal direction in the tough equilibrium problems. These two unique features, the adaptive shooting and small matrix size, make ATEQ useful to improve tokamak equilibrium solutions.