The Tayler instability at low magnetic Prandtl numbers: between chiral symmetry breaking and helicity oscillations

The Tayler instability is a kink-type, current driven instability that plays an important role in plasma physics but might also be relevant in liquid metal applications with high electrical currents. In the framework of the Tayler-Spruit dynamo model of stellar magnetic field generation, the question of spontaneous helical (chiral) symmetry breaking during the saturation of the Tayler instability has received considerable interest. Focusing on fluids with low magnetic Prandtl numbers, for which the quasistatic approximation can be applied, we utilize an integro-differential equation approach in order to investigate the saturation mechanism of the Tayler instability. Both the exponential growth phase and the saturated phase are analyzed in terms of the action of the α and β effects of mean-field magnetohydrodynamics. In the exponential growth phase we always find a spontaneous chiral symmetry breaking which, however, disappears in the saturated phase. For higher degrees of supercriticality, we observe helicity oscillations in the saturated regime. For Lundquist numbers in the order of one we also obtain chiral symmetry breaking of the saturated magnetic field.