Development of a free boundary Tokamak Equilibrium Solver (TES) for Advanced Study of Tokamak Equilibria

TL;DR

This paper introduces a free-boundary Tokamak Equilibrium Solver (TES) with novel features for resolving axisymmetric instabilities and accommodating complex divertor geometries, validated through rigorous tests and applied to snowflake equilibrium analysis.

Contribution

The paper presents a new TES capable of handling axisymmetric instabilities and complex divertor geometries, validated against analytical solutions and applied to snowflake equilibrium modeling.

Findings

Solver confirms solution uniqueness independent of domain variations.

Equilibrium profiles match analytical generalized Solovev equilibrium.

Force balance and stability are validated through instability tests.

Abstract

A free-boundary Tokamak Equilibrium Solver (TES), developed for advanced study of tokamak equilibra, is described with two distinctive features. One is a generalized method to resolve the intrinsic axisymmetric instability, which is encountered after all in equilibrium calculation with a free-boundary condition. The other is an extension to deal with a new divertor geometry such as snowflake or X divertors. For validations, the uniqueness of a solution is confirmed by the independence on variations of computational domain, the mathematical correctness and accuracy of equilibrium profiles are checked by a direct comparison with an analytic equilibrium known as a generalized Solovev equilibrium, and the governing force balance relation is tested by examining the intrinsic axisymmetric instabilities. As a valuable application, a snowflake equilibrium that requires a second order zero of the poloidal magnetic field is discussed in the circumstance of KSTAR coil system.