  Helicity and \alpha effect driven by the nonaxisymmetric Tayler instability
of toroidal magnetic fields in stellar radiation zones are computed. In the
linear approximation a purely toroidal field always excites pairs of modes with
identical growth rates but with opposite helicity so that the net helicity
vanishes. If the magnetic background field has a helical structure by an extra
(weak) poloidal component then one of the modes dominates producing a net
kinetic helicity anticorrelated to the current helicity of the background
field.
  The mean electromotive force is computed with the result that the \alpha
effect by the most rapidly growing mode has the same sign as the current
helicity of the background field. The \alpha effect is found as too small to
drive an \alpha^{2} dynamo but the excitation conditions for an \alpha\Omega
dynamo can be fulfilled for weak poloidal fields. Moreover, if the dynamo
produces its own \alpha effect by the magnetic instability then problems with
its sign do not arise. For all cases, however, the \alpha effect shows an
extremely strong concentration to the poles so that a possible \alpha\Omega
dynamo might only work at the polar regions. Hence, the results of our linear
theory lead to a new topological problem for the existence of large-scale
dynamos in stellar radiation zones on the basis of the current-driven
instability of toroidal fields.
