ON A CLASS OF NON-AXISYMMETRICAL FLUX ROPE SOLUTIONS TO THE ELECTROMAGNETIC INDUCTION EQUATION

We display non-axisymmetric generalisations of a known exact axisymmet ric Bus rope solution to the induction equation. The assumed velocity field is a simple axisymmetric stagnation point Bow. Solutions for mag netic fields with non-zero azimuthal wavenumber are given. These provi de local models for fluxrope features seen in numerical computations o f probable fast dynamos. Remarkably, they can have positive growth rat es for any magnetic Reynolds number, and have finite energy (per unit length along the axis) provided only that the growth rate is less than one, in velocity-based units. Thus although not chaotic, this flow fu nctions as a fast dynamo, albeit one with the unphysical feature that its velocity tends to infinity far from the origin. It is therefore de sirable to exclude such a feature when choosing velocity fields as can didates for a realistic fast dynamo, to avoid finding one for a spurio us reason.