Dynamo theory

Abstract: Recent years have witnessed dramatic progress in our understanding of how turbulence arises and transports angular momentum in astrophysical accretion disks. The key conceptual point has its origins in work dating from the 1950s, but its implications have been fully understood only in the last several years: the combination of a subthermal magnetic field (any nonpathological configuration will do) and outwardly decreasing differential rotation rapidly generates magnetohydrodynamic (MHD) turbulence via a remarkably simple linear instability. The result is a greatly enhanced effective viscosity, the origin of which had been a long-standing problem. The MHD nature of disk turbulence has linked two broad domains of magnetized fluid research: accretion theory and dynamos. The understanding that weak magnetic fields are not merely passively acted upon by turbulence, but actively generate it, means that the assumptions of classical dynamo theory break down in disks. Paralleling the new conceptual understanding has been the development of powerful numerical MHD codes. These have taught us that disks truly are turbulent, transporting angular momentum at greatly enhanced rates. We have also learned, however, that not all forms of disk turbulence do this. Purely hydrodynamic turbulence, when it is imposed, simply causes fluctuations without a significant increase in transport. The interplay between numerical simulation and analytic arguments has been particularly fruitful in accretion disk theory and is a major focus of this article. The authors conclude with a summary of what is now known of disk turbulence and mention some knotty outstanding questions (e.g., what is the physics behind nonlinear field saturation?) for which we may soon begin to develop answers.

Abstract: The current understanding of astrophysical magnetic fields is reviewed, focusing on their generation and maintenance by turbulence. In the astrophysical context this generation is usually explained by a self-excited dynamo, which involves flows that can amplify a weak 'seed' magnetic field exponentially fast. Particular emphasis is placed on the nonlinear saturation of the dynamo. Analytic and numerical results are discussed both for small scale dynamos, which are completely isotropic, and for large scale dynamos, where some form of parity breaking is crucial. Central to the discussion of large scale dynamos is the so-called alpha effect which explains the generation of a mean field if the turbulence lacks mirror symmetry, i.e. if the flow has kinetic helicity. Large scale dynamos produce small scale helical fields as a waste product that quench the large scale dynamo and hence the alpha effect. With this in mind, the microscopic theory of the alpha effect is revisited in full detail and recent results for the loss of helical magnetic fields are reviewed.