Applied Mathematics Seminar

The magnetic fields observed in many astrophysical objects are thought to be generated by motions in the electrically conducting fluid making up the object. The study of this process is called the dynamo problem. In the initial phase of a dynamo the field is weak enough that its effects on the motion can be neglected, and any resulting dynamo is termed kinematic. In this phase the field grows exponentially, and if the growth time is of order the fluid turnover time the dynamo is fast. If it is of order the ohmic decay time, the dynamo is slow. Eventually the field becomes strong enough to modify the motion, and some kind of steady or statistically steady state results.

In this talk the above background will be explained in more detail, and two specific numerical calculations will be described. The first treats kinematic dynamo action in a layer of hexagons, and is joint work with V.A. Zheligovsky. The results have relevance for the magnetic field observed in the surface layers of the Sun, the so-called ``magnetic carpet''. The second considers the dynamical processes limiting the growth of a fast dynamo based on the so-called ``ABC'' flows acting on an infinite cubical lattice. This is joint work with Olga Podvigina. The results can be used to infer scaling laws for the maximum field strength; if they apply in astrophysics, these cast doubt on the effectiveness of the dynamo process. I will speculate on possible ways out of this dilemma.