Fast Magnetic Dynamos in Chaotic Flows

A generic structure is proposed for rapidly growing magnetic fields in a class of steady, incompressible flows which are everywhere chaotic with positive Liapunov exponent. In such a flow at high magnetic Reynolds number $R_m$, the magnetic field is approximately aligned everywhere with the dilating direction of the flow, and may have extremely complicated spatial structure. In the limit of infinite $R_m$, the leading-order growth rate is bounded below by the positive Liapunov exponent of the flow; thus the field is a fast dynamo.