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.Comment: 285 pages, 72 figures, accepted by Phys. Re

The nonlinear evolution of magnetized Keplerian shear ows is simulated in a local, three-dimensional model, including the e ects of compressibility and strati cation. Supersonic ows are initially generated by the Balbus-Hawley magnetic shear instability. The resulting ows regenerate a turbulent magnetic eld which, in turn, reinforces the turbulence. Thus, the system acts like a dynamo that generates its own turbulence. However, unlike usual dynamos, the magnetic energy exceeds the kinetic energy of the turbulence by a factor of 3{10. By assuming the eld to be vertical on the outer (upper and lower) surfaces we do not constrain the horizontal magnetic ux. Indeed, a large scale toroidal magnetic eld is generated, mostly in the form of toroidal ux tubes with lengths comparable to the toroidal extent of the box. This large scale eld is mainly of Present address: Nordita, Blegdamsvej 17, DK-2100 Copenhagen , Denmark y The National Center for Atmospheric Research is sponsored by the National Science Foundation 1 even (i.e. quadrupolar) parity with respect to the midplane and changes direction on a timescale of about 30 orbits, in a possibly cyclic manner. The e ective Shakura-Sunyaev alpha viscosity parameter is between 0.001 and 0.005, and the contribution from the Maxwell stress is about 3-7 times larger than the contribution from the Reynolds stress.

We discuss current observational and theoretical knowledge of magnetic fields, especially the large-scale structure in the disks and halos of spiral galaxies. Among other topics, we consider the enhancement of global magnetic fields in the interarm regions, magnetic spiral arms, and representations as superpositions of azimuthal modes, emphasizing a number of unresolved questions. It is argued that a turbulent hydromagnetic dynamo of some kind and an inverse cascade 1 Now at Department of Mathematics and Statistics, University of Newcastle upon Tyne, NE1 7RU, United Kingdom. 155 0066-4146/96/0915-0155$08.00 156 BECK ET AL of magnetic energy gives the most plausible explanation for the regular galactic magnetic fields. Primordial theory is found to be unsatisfactory, and fields of cosmological origin may not even be able to provide a seed field for a dynamo. Although dynamo theory has its own problems, the general form of the dynamo equations appears quite robust. Finally, detailed models of magnetic field generation in galaxies, allowing for factors such as spiral structure, starbursts, galactic winds, and fountains, are discussed and confronted with observations.

A numerical model of isotropic homogeneous turbulence with helical forcing is investigated. The resulting Ñow, which is essentially the prototype of the a2 dynamo of mean Ðeld dynamo theory, produces strong dynamo action with an additional large-scale Ðeld on the scale of the box (at wavenumber k \ 1 ; forcing is at k \ 5). This large-scale Ðeld is nearly force free and exceeds the equipartition value. As the magnetic Reynolds number increases, the saturation Ðeld strength and the growth rate of the R m dynamo increase. However, the time it takes to build up the large-scale Ðeld from equipartition to its Ðnal superequipartition value increases with magnetic Reynolds number. The large-scale Ðeld generation can be identiÐed as being due to nonlocal interactions originating from the forcing scale, which is characteristic of the a-e †ect. Both a and turbulent magnetic di †usivity are determined simultaneously using g t numerical experiments where the mean Ðeld is modiÐed artiÐcially. Both quantities are quenched in an fashion. The evolution of the energy of the mean Ðeld matches that predicted by an a2 R m -dependent dynamo model with similar a and quenchings. For this model an analytic solution is given that g t matches the results of the simulations. The simulations are numerically robust in that the shape of the spectrum at large scales is unchanged when changing the resolution from 303 to 1203 mesh points, or when increasing the magnetic Prandtl number (viscosity/magnetic di †usivity) from 1 to 100. Increasing the forcing wavenumber to 30 (i.e., increasing the scale separation) makes the inverse cascade e †ect more pronounced, although it remains otherwise qualitatively unchanged.

Nonhelical hydromagnetic forced turbulence is investigated using large scale simulations on up to 256 processors and 1024 3 meshpoints. The magnetic Prandtl number is varied between 1/8 and 30, although in most cases it is unity. When the magnetic Reynolds number is based on the inverse forcing wavenumber, the critical value for dynamo action is shown to be around 35 for magnetic Prandtl number of unity. For small magnetic Prandtl numbers we find the critical magnetic Reynolds number to increase with decreasing magnetic Prandtl number. The Kazantsev k 3/2 spectrum for magnetic energy is confirmed for the kinematic regime, i.e. when nonlinear effects are still unimportant and when the magnetic Prandtl number is unity. In the nonlinear regime, the energy budget converges for large Reynolds numbers (around 1000) such that for our parameters about 70% is in kinetic energy and about 30% is in magnetic energy. The energy dissipation rates are converged to 30% viscous dissipation and 70% resistive dissipation. Second order structure functions of the Elsasser variables give evidence for a k −5/3 spectrum. Nevertheless, the three-dimensional spectrum is close to k −3/2 , but we argue that this is due to the bottleneck effect. The bottleneck effect is shown to be equally strong both for magnetic and nonmagnetic turbulence, but it is far weaker in one-dimensional spectra that are normally studied in laboratory turbulence. Structure function exponents for other orders are well described by the She-Leveque formula, but the velocity field is significantly less intermittent and the magnetic field is more intermittent than the Elsasser variables.

We further explore nondimensional relationships between the magnetic dynamo cycle period the P cyc

Arguments for and against the widely accepted picture of a solar dynamo being seated in the tachocline are reviewed and alternative ideas concerning dynamos operating in the bulk of the convection zone, or perhaps even in the near-surface shear layer, are discussed. Based on the angular velocities of magnetic tracers it is argued that the observations are compatible with a distributed dynamo that may be strongly shaped by the near-surface shear layer. Direct simulations of dynamo action in a slab with turbulence and shear are presented to discuss filling factor and tilt angles of bipolar regions in such a model.

We investigate hydromagnetic turbulence of primordial magnetic fields using magnetohydrodynamics ͑MHD͒ in an expanding universe. We present the basic, covariant MHD equations, find solutions for MHD waves in the early universe, and investigate the equations numerically for random magnetic fields in two spatial dimensions. We find the formation of magnetic structures at larger and larger scales as time goes on. In three dimensions we use a cascade ͑shell͒ model that has been rather successful in the study of certain aspects of hydrodynamic turbulence. Using such a model we find that after ϳ10 9 times the initial time the scale of the magnetic field fluctuation ͑in the comoving frame͒ has increased by 4-5 orders of magnitude as a consequence of an inverse cascade effect ͑i.e., transfer of energy from smaller to larger scales͒. Thus at large scales primordial magnetic fields are considerably stronger than expected from considerations which do not take into account the effects of MHD turbulence. ͓S0556-2821͑96͒02712-9͔ PACS number͑s͒: 95.30.Qd, 04.40.Nr, 98.62.En