On the possibility of helicity oscillations in the saturation of the Tayler instability

TL;DR

This paper investigates the potential for helicity oscillations in the saturation of the Tayler instability, using a Landau-Ginzburg model, and concludes such oscillations are unlikely due to symmetry considerations.

Contribution

The study introduces a higher-order Landau-Ginzburg effective Lagrangian approach to analyze helicity oscillations in the Tayler instability saturation.

Findings

Helicity oscillations are unlikely if mirror symmetry between modes is spontaneously broken.

Adding higher-order terms or explicit symmetry breaking does not favor oscillating states.

The interaction of chiral modes does not seem to produce oscillating saturation states.

Abstract

Recent numerical results of current-driven instabilities at low magnetic Prandtl number and high Hartmann number support the possibility of a saturation state characterized by helicity oscillations. We investigate the underlying mechanism by analyzing this possibility using an higher-order Landau-Ginzburg effective Lagrangian for the weakly non-linear amplitude dynamics, where the magnetic and velocity perturbations are linearly dependent. We find that, if the mirror symmetry between left- and right-handed modes is spontaneously broken, it is impossible to achieve an oscillating helical state. We argue that the result is likely to hold also adding higher-order terms and in the presence of an explicit symmetry breaking. We conclude that an oscillating saturating state for the Tayler instability is unlikely to depend on the interaction of chiral modes.