Abstract

We first present basic results about advection, diffusion and amplification of a magnetic field by the flow of an electrically conducting fluid. This topic has been initially motivated by the study of possible mechanisms to explain the magnetic fields of astrophysical objects. However, self-generation of a magnetic field by an electrically conducting fluid, the so-called dynamo effect, is also a typical bi-furcation problem that involves many interesting aspects from the viewpoint of dynamical system theory: the effect of the flow geometry on the nature of the bi-furcation, the effect of turbulent fluctuations on the threshold value, the saturation mechanisms above threshold, the dynamics of the generated magnetic field and the statistical properties of its fluctuations with respect to the ones of the turbulent flow. We have tried to emphasize some of these problems within the general pre-sentation of the subject and more particularly in sections 6 and 7. These notes should not be considered as a review article. There exist many well known books and reviews on dynamo theory 1,2,3,4,5,6. For a general presentation of the sub-ject, we refer to “Magnetic field generation in electrically conducting fluids ” by Moffatt 7. The generation of large scale magnetic fields by small scale turbulent motions is reviewed in “Mean-field magnetohydrodynamics and dynamo theory” by Krause and Rädler 8. The problem of “fast dynamos ” in the limit of large magnetic Reynolds number is studied by Childress and Gilbert in “Stretch, twist, fold: the fast dynamo ” 9. Finally, we refer to “Magnetic fields in astrophysics ” by Zeldovich, Ruzmaikin and Sokoloff 10 for a detailed review on magnetic fields of astrophysical objects and their possible role in the early evolution of the universe.