| Summary: | 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 (Spruit 2002 Astron. Astrophys. http://dx.doi.org/10.1051/0004-6361:20011465 381 http://dx.doi.org/10.1051/0004-6361:20011465 ), the question of spontaneous helical (chiral) symmetry breaking during the saturation of the Tayler instability has received considerable interest (Zahn et al 2007 Astron. Astrophys. http://dx.doi.org/10.1051/0004-6361:20077653 474 http://dx.doi.org/10.1051/0004-6361:20077653 ; Gellert et al 2011 Mon. Not. R. Astron. Soc. http://dx.doi.org/10.1051/0004-6361:20011465 414 http://dx.doi.org/10.1051/0004-6361:20011465 ; Bonanno et al 2012 Phys. Rev. E http://dx.doi.org/10.1103/PhysRevE.86.016313 86 http://dx.doi.org/10.1103/PhysRevE.86.016313 ). Focusing on fluids with low magnetic Prandtl numbers, for which the quasistatic approximation can be applied, we utilize an integro-differential equation approach (Weber et al 2013 New J. Phys. http://dx.doi.org/10.1088/1367-2630/15/4/043034 15 http://dx.doi.org/10.1088/1367-2630/15/4/043034 ) in order to investigate the saturation mechanism of the Tayler instability. Both the exponential growth phase and the saturated phase are analysed 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.
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