Nonlinear Saturation of Ballooning Modes in Stellarators

TL;DR

This paper investigates the nonlinear saturation of ballooning modes in stellarators using a flux tube approach, revealing metastable saturated states and potential for explosive MHD behavior similar to ELMs.

Contribution

It develops a variational flux tube energy calculation method adapted for stellarator equilibria, enabling analysis of nonlinear ballooning mode saturation.

Findings

Saturated flux tube states exist crossing 10-20% of plasma minor radius.

Features of nonlinear flux tube structures match full MHD simulations of Wendelstein 7X.

Saturated states are metastable, close to linear instability threshold.

Abstract

Ballooning mode saturation is investigated in realistic stellarator configurations using the flux tube approach of Ham et. al. [1] [2]. The method is adapted to account for the lack of exact force balance in stellarator equilibrium solvers that assume existence of nested flux surfaces. A variational approach for calculating flux tube energy is developed to overcome this force error problem in stellarator numerical equilibria. Saturated (equilibrium) flux tube states that cross 10-20% of the plasma minor radius are shown to exist for linearly ballooning unstable profiles. It is shown that several features of the displaced flux tube structure in a full nonlinear MHD simulation of Wendelstein 7X are reproduced by our model. Saturated states are found in a compact stellarator equilibrium close but below the marginal ballooning linear instability, i.e. the unperturbed equilibrium is metastable. This suggests that Edge-Localized-Mode-like explosive MHD behavior may be possible in stellarators.