Direct prediction of saturated neoclassical tearing modes in slab using an equilibrium approach

TL;DR

This paper introduces a novel equilibrium approach using a variational principle to directly predict the nonlinear saturation of neoclassical tearing modes in slab geometry, eliminating the need for resistive MHD simulations.

Contribution

The authors develop a method based on Taylor relaxation and the SPEC equilibrium solver to accurately and efficiently predict saturated island widths of NTMs without intermediate resistive dynamics simulation.

Findings

Saturated island widths agree with resistive MHD simulations.

The approach matches predictions from the Modified Rutherford Equation.

It effectively captures both classical and neoclassical tearing modes.

Abstract

We demonstrate for the first time that the nonlinear saturation of neoclassical tearing modes (NTMs) can be found directly using a variational principle based on Taylor relaxation, without needing to simulate the intermediate, resistivity-dependent dynamics. As in previous investigations of classical tearing mode saturation (Loizu et al. 2020; Loizu & Bonfiglio 2023), we make use of SPEC (Hudson et al. 2012), an equilibrium solver based on the variational principle of the Multi-Region relaxed MHD, featuring stepped pressure profiles and arbitrary magnetic topology. We work in slab geometry and employ a simple bootstrap current model $J_\textrm{bs} = C \nabla p$ to study the bootstrap-driven tearing modes, scanning over the asymptotic matching parameter $\Delta'$ and the bootstrap current strength. Saturated island widths produced by SPEC agree well with the predictions of an initial value resistive MHD code (Huang & Bhattacharjee 2016) while being orders of magnitude faster to calculate. Additionally, we observe good agreement with a simple analytical Modified Rutherford Equation, without requiring any fitting coefficients. The match is obtained for both linearly unstable classical tearing modes in the presence of bootstrap current, and neoclassical tearing modes, which are linearly stable but nonlinear-unstable due to the effects of the bootstrap current