NEW RESULTS FOR THE HERZENBERG DYNAMO - STEADY AND OSCILLATORY SOLUTIONS

The Herzenberg dynamo, consisting of two rotating electrically conduct ing spheres with non-parallel spin axes, immersed in a finite spherica l conducting medium, is simulated numerically for a variety of paramet ers not accessible to the original asymptotic theory. Our model places the spheres in a spatially periodic box. The largest growth rate is o btained when the angle, cp, between the spin axes is somewhat larger t han 125 degrees. In agreement with the asymptotic analysis, it is foun d that the critical dynamo number is approximately proportional to the cube of the ratio of the common radius of the spheres and their separ ation. The asymptotic prediction, strictly valid only in the limit of small spheres, remains approximately valid even when the diameter of t he spheres becomes comparable to their separation. For /phi/ < 90 degr ees we also find oscillatory solutions, which were not predicted by He rzenberg's analysis. To understand such solutions we present a modifie d asymptotic analysis in which the separation of the two spheres is es sentially replaced by the skin depth which, in turn, depends on the di ameter of the spheres. The magnetic field consists of magnetic flux ri ngs wrapped around the two spheres. Applications to local models of tu rbulent dynamos and to dynamo action in binary stars are discussed.