A two-scale homogeneous dynamo an extended analytical model and an experimental demonstration under development

F. H. Busse¹ - U. Muller² - R. Stieglitz² - A. Tilgner¹

¹ University of Bayreuth, Physikalisches Institut, Postfach 30 08, 95499 Bayreuth, Germany
² Institute for Applied Thermo- and Fluiddynamics (IATF), Forshungscentrum Karlsruhe, Postfach 36 40, D-76021 Karlsruhe, Germany

Abstract
A laboratory experiment for a homogeneous dynamo based on a forced sodium flow in a cylindrical container is being developed. The design utilizes the efficient dynamo models based on scale separation which have found their simplest forms in the peri-odic dynamos of G.O. Roberts (1972) and which in principle are based on the alfa-effect of Steenbeck, Krause and Rädler (1966). This is realized by arranging quasi-periodic small-scale helical motions in a sodium filled cylindrical box. Because of technical and cost limitations the scale ratio can hardly exceed an order of 4 in a feasible experi-ment. Therefore, a more detailed study of the onset of dynamo action is required compared to the technical proposal of Busse (1992). The improved theory takes especially into account higher order terms of the length scale ratio and moreover, the diffusion and advection of the induced magnetic field into the outer insulating do-main of the cylinder. Additionally it assesses errors due to an enhanced electromagnetic diffusivity by turbulent flow motion and deviations of the technically obtained velocity field compared to the ideal periodic laminar velocity distribution. The extended theory results in higher critical magnetic Reynolds numbers than the previous simplified calculations of Busse (1992). This in turn requires larger volumetric sodium flow rates for the experimental facility. The new critical condition, the experimental design and the envisaged technical modifications are outlined in the pres-entation. Figs 7, Refs 8.