STEADY FAST DYNAMO FLOWS

The problem of whether or not steady fast kinematic dynamos exist for typical smooth velocity fields has remained an open question in the origin of magnetic fields in nature (e.g., the observed magnetic fields in stars and in galaxies). [Here by a steady flow it is meant that the fluid velocity v depends on position x but is independent of time t, i.e., v = v (x).] Recently it has been conjectured that fast kinematic dynamos are produced by flows that satisfy a certain condition. Flows satisfying this condition are called D flows. In this paper it is shown how to construct a class of steady D flows, and the properties of this class of flows are investigated. The results indicate that fast dynamo action is typical for steady chaotic flows.