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Recently Ricca and Maggione [MHD (2008)] have presented a very simple andinteresting model of stretch-twist-fold dynamo in diffusive media based onnumerical simulations of Riemannian flux tubes. In this paper we present a yetsimpler way of analytically obtaining fast and slow dynamo, generated by by thecurvature energy of magnetic filaments in diffusive media. geometrical modelfor the galactic or accretion disk dynamo in shear flows is presented. In thefast dynamo case it is shown that the absence of stretching leads to theabsence of fast dynamos and when torsion of filaments vanishes the dynamoaction cannot be support as well. This is the Cowling-Zeldovich theorem forplanar flows. Isotropy of the magnetic fields hypothesis is used to compute thefast nature of dynamo. A similar result using non-holonomic Frenet frame hasbeen recently obtained for filamentary dynamos [Garcia de Andrade, AN (2008)].The stretch-twist-fold (STF) filamented models discussed here may serve toformulate future experiments in the Madison Dynamo Experiment (MDE) facility[Nornberg et al, Phys Plasmas (2008)]. Though their running experiments dealwith magnetic fields that are orthogonal to the flow, other topologies are alsoused here, with an eye in future experiments. Unstretched filaments in MDEshows Vishik anti-fast dynamo action applies [Garcia de Andrade[Phys Plasmas(2008)].

Stretch-Twist-Fold and slow filamentary dynamos in liquid sodium Madison Dynamo Experiments