Fast dynamo theory attempts to explain how magnetic fields arise in astrophysical objects such as the Sun, other stars, and galaxies. Such fields are manifest on the Sun as sunspots, and are inferred in other objects from various kinds of Zeeman splitting and polarisation measurements. The fields are thought to be generated by motions in the electrically conducting fluids (ionised gases) that comprise the objects, and the resulting phenomena are termed self-exciting dynamos. In most cases the dynamo has to be able to operate on the turnover timescale of the flow in order for significant growth to have been achieved in the lifetime of the Universe; such a dynamo is then called fast, and it has been shown that the flow has to be mathematically chaotic to achieve this result.
The so-called kinematic version of the dynamo problem investigates whether some particular flow can initiate growth of a magnetic field; in particular it calculates the rate of growth, which is positive if the flow acts as a dynamo. Several examples of fast kinematic dynamos are now known, and interest has switched to the problem where the magnetic forces are allowed to modify the motion, a process which stops further growth of field and leads to equilibration at a finite level. The crucial question is whether this level is high enough to correspond to observed field strengths. This project concerns the numerical computation of solutions to this nonlinear problem, using a class of chaotic flows known as the ABC flows. Currently we have found strong field solutions in various limiting cases, and have used them to infer scaling laws over a wider range of physical parameters.
For pictures of magnetic isosurfaces, see
Two 25% Dynamo Isosurfaces around 40 turnovers apart>
