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The Tayler instability is a kink-type, current driven instability that playsan important role in plasma physics but might also be relevant in liquid metalapplications with high electrical currents. In the framework of theTayler-Spruit dynamo model of stellar magnetic field generation, the questionof spontaneous helical (chiral) symmetry breaking during the saturation of theTayler instability has received considerable interest. Focusing on fluids withlow magnetic Prandtl numbers, for which the quasistatic approximation can beapplied, we utilize an integro-differential equation approach in order toinvestigate the saturation mechanism of the Tayler instability. Both theexponential growth phase and the saturated phase are analyzed in terms of theaction of the alpha and beta effects of mean-field magnetohydrodynamics. In theexponential growth phase we always find a spontaneous chiral symmetry breakingwhich, however, disappears in the saturated phase. For higher degrees ofsupercriticality, we observe helicity oscillations in the saturated regime. ForLundquist numbers in the order of one we also obtain chiral symmetry breakingof the saturated magnetic field.

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