Axisymmetric Dynamo from Theory to Experiment

Abstract:

Cowling's theorem on the impossibility of dynamo action producing an axisymmetric magnetic field has shaped the development of dynamo theory. The configurations where dynamo action exists are necessarily complex and no realistic solution can be obtained analytically. However, Cowling's theorem applies under the explicit condition that the electrical conductivity is isotropic. Recently, we have produced a theoretical dynamo model with axisymmetric self-induced magnetic field, using an anisotropic conductivity. The velocity field is that of a rotating cylinder in a fixed stator. Besides, the solution can be obtained analytically and the properties of this dynamo can be studied easily. I will show that this dynamo is very fast and quite efficient, requiring a moderate value of magnetic Reynolds number. Because the dynamo threshold seems accessible, we have decided to build an experimental setup based on that theoretical model. With 37 kg of copper and a bit more than 100 Watts, it should be enough to enter the regime of self-induced dynamo. I will report of our progress at the time of the conference. Besides its conceptual and educational interests, one may wonder whether the anisotropic dynamo could be a model for natural dynamos. The anisotropy of conductivity does not need to be very strong and one can think of possible sources of anisotropy. For instance, in the inner core of the Earth, the elastic tensor is suspected to be anisotropic and the electrical conductivity could well be so. In stars, the plasma can have an anisotropic electrical conductivity, usually due to the magnetic field itself, making the problem non-linear.