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Here, an analytical version of numerical results is obtained in case ofconsidering the laminar non-turbulent limit, of a twisted Riemannian thin fluxtube. It is shown that the magnetic field is amplified, when electric currenthelicity and Riemann curvature are both negative. Thus spaces of positive andnegative Riemannian curvatures seems to support dynamo action inside the torus,and not only negative Riemannian curvature surfaces as happens in 2D dynamos.New features appear in ${\alpha}^{2}$-dynamo twisted flow, using theapproximation of thin tubes flux tubes. These solutions are obtained in theresonant profile of the toroidal and poloidal frequencies modes of the dynamoforce-free flow.

Mean-field helicity in random ${\alpha}^{2}$-dynamo twisted flows