Non-linear dynamos in torus geometry: transition to chaos

We present results from integrating the non-linear mean field dynamo equations in the $\alpha\omega$-regime in a toroidal conducting volume. We assume a Keplerian rotation law, and impose axisymmetry. The non-linearity is a simple $\alpha$-quenching. For ‘fat’ tori, where the ratio of minor to major axis is not small, we find that solutions with negative dynamo number and dipolar parity are singly periodic for slightly supercritical dynamo numbers, and then undergo a further Hopf bifurcation to become doubly periodic, before becoming chaotic at dynamo numbers greater than about three times supercritical.