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

Alfio Bonanno, Filippo Guarnieri

Published 2016-09-14Version 1

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 analyze this possibility using an higher-order Landau-Ginzburg effective Lagrangian for the weakly non-linear amplitude dynamics. 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 in the presence of an explicit symmetry breaking. We conclude that an oscillating saturating state for the Tayler instability is unlikely to occurr in realistic physical situations.