This book contains the lectures given at the workshop "Dynamo and dynamics, a mathematical challenge" held in Cargese from August 21 to 26, 2000. The workshop differed from most previous conferences on the dynamo effect in two important respects. First, it was at this international conference that the experimental observation of homogeneous fluid dynamos was first reported. Second, the conference gathered scientists from very different fields, thus showing that thepynamo problem has become an interdisciplinary subject involving not only astrophysicists and geophysicists, but also scientists working in dynamical systems theory, hydrodynamics, and numerical simulation, as well as several groups in experimental physics. This book thus reports important results on various dynamo studies in these different contexts: - Decades after the discovery of the first analytic examples of laminar fluid dynamos, the self-generation of a magnetic field by a flow ofliquid sodium has been reported by the Karlsruhe and Riga groups. Although there were no doubts concerning the self generation by the laminar Roberts-type or Ponomarenko-type flows that were used, these experiments have raised interesting questions about the influence of the turbulent fluctuations on the dynamo threshold and on the saturation level of the magnetic field.

The increasing power of computer resources along with great improvements in observational data in recent years have led to some remarkable and rapid advances in astrophysical fluid dynamics. The subject spans three distinct but overlapping communities whose interests focus on (1) accretion discs and high-energy astrophysics; (2) solar, stellar, and galactic magnetic fields; and (3) the geodynamo, planetary magnetic fields, and associated experiments. This book grew out of a special conference sponsored by the London Mathematical Society with the support of EPSRC that brought together leading researchers in all of these areas to exchange ideas and review the status of the field. The many interesting problems addressed in this volume concern:

Although the origin of Earth's and other celestial bodies' magnetic fields remains unknown, we do know that the motion of electrically conducting fluids generates and maintains these fields, forming the basis of magnetohydrodynamics (MHD) and, to a larger extent, dynamo theory. Answering the need for a comprehensive, interdisciplinary introduction

Nonlinear dynamo theory is central to understanding the magnetic structures of planets, stars and galaxies. In chapters contributed by some of the leading scientists in the field, this text explores some of the recent advances in the field. Both kinetic and dynamic approaches to the subject are considered, including fast dynamos, topological methods in dynamo theory, physics of the solar cycle and the fundamentals of mean field dynamo. Advances in Nonlinear Dynamos is ideal for graduate students and researchers in theoretical astrophysics and applied mathematics, particularly those interested in cosmic magnetism and related topics, such as turbulence, convection, and more general nonlinear physics.

Treats the origin of magnetic fields in planets, stars and galaxies, and the manner of their evolution over time.

Dynamos is a collection of lectures given in July 2007 at the Les Houches Summer School on "Dynamos". Provides a pedagogical introduction to topics in Dynamos Addresses each topic from the basis to the most recent developments Covers the lectures by internationally-renowned and leading experts

"This book is the second volume of a compilation of lecture notes on various topics in nonlinear physics delivered by specialists during the summer schools organized by the Institut Non Linaeaire de Nice ... in Peyresq ... since 1998. The first volume, edited by R. Kaiser and J. Montaldi, contains courses from the years 1998 and 1999. This volume collects notes of the lectures given from the summers of 2000, 2001 and 2002"--Preface, v. 2.