Sawtooth crash in tokamak as a sequence of Multi-region Relaxed MHD equilibria

TL;DR

This paper models the sawtooth crash in tokamaks as a sequence of Multi-region Relaxed MHD equilibria, revealing the process of reconnection and state transitions with insights from numerical simulations and comparisons.

Contribution

It introduces a novel approach using MRxMHD equilibria to model sawtooth crashes, providing a new perspective complementary to traditional MHD simulations.

Findings

System prefers lower energy non-axisymmetric equilibria with islands.

Reconnection process leads to a return to axisymmetric state.

MRxMHD results agree with nonlinear MHD code M3D-C1 on key features.

Abstract

This study examines the sawtooth crash phenomenon in tokamak plasmas by modelling it as a sequence of Multi-region Relaxed Magnetohydrodynamic (MRxMHD) equilibria. Using the Stepped-Pressure Equilibrium Code (SPEC), we constructed a series of equilibria representing intermediate states during the sawtooth crash, with progressively increasing reconnection regions. Numerical results demonstrated that the system prefers the lower energy non-axisymmetric equilibria with islands and is eventually back to an axisymmetric state, capturing key features of the reconnection process. Comparisons with the nonlinear MHD code M3D-C1 showed remarkable agreement on the field-line topology, the safety factor, and the current profile. However, the simplified MRxMHD model does not resolve the detailed structure of the current sheet. Despite this limitation, MRxMHD offers an insightful approach and a complementary perspective to initial-value MHD simulations.