  Analytical solution of first order torsion ${\alpha}$-effect in twisted
magnetic flux tubes representing a flux tube dynamo in Riemannian space is
presented. Toroidal and poloidal component of the magnetic field decays as
$r^{-1}$, while grow exponentially in time. The rate of speed of the helical
dynamo depends upon the value of Frenet curvature of the tube. The $\alpha$
factor possesses a fundamental contribution from constant torsion tube
approximation. It is also assumed that the curvature of the magnetic axis of
the tube is constant. Though ${\alpha}$-effect dynamo equations are rather more
complex in Riemann flux tube coordinates, a simple solution assuming force-free
magnetic fields is shown to be possible. Dynamo solutions are possible if the
dynamo action is able to change the signs of torsion and curvature of the
dynamo flux tube simultaneously.
