  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 alpha and beta 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.
