Mean-field helicity in random α-dynamo twisted flows

Recent results by Shukurov, Stepanov and Sokoloff [Phys. Rev. E 78,025301,(2008)] on dynamo action in Moebius strip flows, indicate that strong magnetic fields appear in regions where, electric current and flow kinetic helicities have the same sign. Here, an analytical version of their numerical result is obtained by a simpler method of considering the laminar non-turbulent limit, of a twisted Riemannian thin flux tube. It is shown that the magnetic field is amplified, when electric current helicity and Riemann curvature are both negative. Thus spaces of positive and negative 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 α-dynamo twisted flow, using the approximation of thin tubes flux tubes. These solutions are obtained in the resonant profile of the toroidal and poloidal frequencies modes of the dynamo force-free flow. To a certain extent our solution seems to extend Shukurov, Stepanov and Sokoloff, solution to more general twisted flows than their Moebius strip flow. From Perm liquid sodium torus dynamo experimental data, torsion of the geometrical axis of the twisted torus is computed. For an external radius of the torus ofR ≈ 8.0×10−2m yields a strong torsion of the order of 10m. Knowledge of the topological structure of flows helps to design future dynamo experiments. Negative Riemannian curvature flows may appear in solar inflexionary flux tubes, where internal curvature is positive while external curvature is negative, and therefore the scalar Gaussian or two-dimensional curvature is negative. Simple Arnold-Beltrami-Childress (ABC) dynamo flows are obtained. Mean-field ABC dynamos were developed by Kleeorin et al [Phys Rev E79,046302,(2009)] for anisotropic turbulence.PACS numbers: 47.65.Md,Hw.47.65.-d