Dynamos on stream surfaces of a highly conducting fluid

This paper discusses dynamo action in generalisations of the Ponomarenko dy namo at large magnetic Reynolds number. The original Ponomarenko dynamo con sists of a spiralling flow in which the stream surfaces are concentric cyli nders of circular cross section, and the flow depends only on distance from the axis in cylindrical polar coordinates. In this study, the stream surfaces are allowed to be cylinders of arbitrary cross section, and the flow is only required to be independent of the coor dinate along the cylinder axes. For smooth flows alpha and eddy diffusion e ffects are identified, in terms of the geometry of the stream surfaces, and asymptotic formulae for growth rates in the limit of large magnetic Reynol ds number are obtained. Numerical support for these results is presented us ing direct simulation of dynamo action in selected flows at high conductivi ty. Finally the case is considered when in spherical polar coordinates the flow is independent of the azimuthal coordinate and the stream surfaces, wh ich are tori, have arbitrary cross sections.