The dark spots on the solar disk, some of them are visible with the naked eye, and the aurorae, especially those strectching down to the tropics, are the best visible manifestations of the solar activity. Since more than one century, we know that this activity follows a regular periodic cycle of 11-years (Heinrich Schwabe 1844), but with an intensity, which is sufficiently variable, to speak of “small” and “large” solar cycles.

Mean-field and direct simulations of the hydrodynamics and hydromagnetics of the solar convection zone are discussed with the ultimate aim to understand the generation of differential rotation and magnetic fields. Various arguments constraining the values of the various turbulent diffusion coefficients are presented. It is suggested that the turbulent magnetic diffusivity is much smaller than the eddy viscosity which, in turn, is by up to a factor of ten smaller than the eddy conductivity. The magnetic field obtained from direct simulations is highly intermittent, and there is no clear systematic orientation of bipolar regions emerging from the convection zone. Various mechanisms that might cause such a field orientation are considered. Finally, the application of direct simulations to the determination of mean-field transport coefficients is emphasised.

Three-dimensional simulations of convection are studied with specific attention to the effects of rotation and latitude on different quantities. The latitude-dependence of the strength of convection is found to decrease with increasing strength of the turbulence. The λ-effect is, however, still present also in a more turbulent case.

Models of spherical dynamos are considered which involve the full interaction between the magnetic field and the motion of an incompressible conducting fluid. In the basic equations magnetic field and fluid velocity are expanded in series of certain decay modes. In this way these equations are reduced to an infinite set of ordinary first-order differential equations for the coefficients of these expansions. The behaviour of dynamos can then be studied by integrating a finite set of these equations numerically. Some first results obtained in this way are presented for mean-field models in which the growth of the magnetic field due to the α–effect is limited by large-scale motions generated by Lorentz forces.

Starting from the ideal MHD equations written in spherical coordinates, using the regular perturbation method, quasiheliostrophic equations are derived as generalisation of quasigeostrophic models for atmospheric flow. From the fourth order momentum and induction equations, two prognostic equations for the stream function and magnetic flux function are derived. The magnetohydrodynamic model based on these equations is a suitable framework for describing the interaction between large-scale dynamic and magnetic features and the presence of specific patterns like active longitudes in the solar activity cycle.

It is shown that the scaling of rotation periods by a color-dependent parameter (turnover time) improves substantially the observed activity-period relations only for single, main sequence, solar type stars with 0.5 ≲ B – V ≲ 0.8. For other single main sequence stars and for single giants activity indices correlate equally well with rotation period and the Rossby number, or show no correlation with either parameter.

We present calculations showing how stable nonaxisymmetric magnetic fields may be excited in an alpha-quenched mean field dynamo in a deep spherical shell. The large scale velocity fields (differential rotation, meridional circulation) are determined by solving the axisymmetric Navier-Stokes equation, neglecting the Lorentz force but including a term parameterizing the turbulent Reynolds stresses.

This report deals with the rotational history of late-type stars subsequent to their reaching the main sequence. The question of relevance to this Symposium is whether detailed comparison of magnetic braking theory with observations of young stellar clusters will yield any constraints on dynamo activity, in particular on the relation between the surface field strength Bs and the angular velocity ω.

Ev Lac = Gliese 873 (dM4.5e) is a well-known flare star with hydrogen Balmer lines as well as with Ca II lines in emission. Rotational modulation by starspots has been discovered by Pettersen (1980) who determined the photometric (rotational) period P = 4.378 d. Spot photometry of EV Lac was obtained with the 60 cm telescope of the Bulgarian National Astronomical Observatory in the years 1983–87 and 1989–91. For these years (except for 1989 and 1990) light curves are available in the V and B bands. From the BNAO-data and the data published by Pettersen (1980) a new ephemerishas been derived which shows a slight revision of the period.

Emission spectra of the flare star EV Lac in several nights of September 1989 are studied. Their variations due to the stellar rotational modulation are found and permit to define the most active longitudes on the stellar surface.

Magnetically active late-type stars have inhomogeneities on their surfaces that cause various observable effects in the spectral lines and light curves. Such inhomogeneities are magnetic starspots, plages etc. in active regions on the photospheric and chromospheric level. The variations of the spectral lines and light curves originating in these inhomogeneities undergo modulations following stellar rotation.

The theory of fossil magnetic fields shows that new born stars may have internal magnetic fields of more than 1 million gauss. Convection inside young solar type stars will tangle any strong fossil magnetic field. The small scale magnetic field rises to the surface and determines the young stars activity attenuating with their age. When a fossil field is diminished a turbulent dynamo may begin to work in the condition of nonlinear stabilization. The scaling relations for the turbulent αω dynamo show that the strength of the generated “fossil” magnetic field inside the main sequence stars is stabilized on the level one tenth — 10 millions gauss, depending on the mass of the stars.

A model of a local magnetic field within a white dwarf is constructed by the use of quantum statistics. The polarized Fermi, Bose and Maxwell statistics is calculated within a Heisenberg magnetism model by the use of Jones calculus. With a mesoscopic description the quantum mechanical dynamo can be discussed. The result is an efficient excitation mechanism, based on Lorentz time transformations and magnetic interactions. An Ap star as progenitor of a polarized white dwarf may loose its field and can generate a stronger one due to an intrinsic dynamo on a time scale of 107 years.

A mechanism for bipolar flows during early and late phases of star evolution is given, based on recently detected cold dark matter.

Accretion disks are approximated by thin tori and the generation of magnetic fields by torus–dynamos is investigated. Solutions for the general α2ω–dynamo embedded into vacuum and into an ideally conducting medium are presented. Whereas the former solutions are qualitatively similar to those obtained for thin disks, there is a mode for the latter peculiar to torus–geometry. Excitation conditions for torus–dynamos are compared to those realized in accretion disks in cataclysmic variables, around T Tauri stars and in AGN's.

We study magnetic field topologies and magnetic field strength in a thin accretion disk around a rotating black hole. The magnetic field is assumed to enter the disk at the outer edge and is amplified in the accretion process by differential rotation. This scenario seems likely for AGN, where magnetized plasma from a molecular torus flows into an inner accretion disk.

In nonideal Newtonian magnetohydrodynamics the presence of a rotating central black hole is taken into account by using the form of the Keplerian rotation law valid for Kerr geometry outside the marginally stable orbit and a boundary layer, caused by the frame dragging effect, within. In the unstable region close to the hole the turbulent timescale is much larger than the accretion timescale so that the effective magnetic diffusivity, which is large in the disk due to turbulence, is low. As a consequence the poloidal magnetic field lines cross the horizon almost radially in agreement with [1].

We present stationary axisymmetric solutions of the induction equation for vanishing α-effect. Dipolar field structures are most favourable for the generation of fast jets and can effectively contribute to the heating of a corona or some X-ray source. Quadrupolar field structures may also drive jets, however the field strength is considerably lower and therefore also the energy that can be supplied into a corona or a jet.

Generation of the magnetic field during procces of disc accretion onto black hole or magnetize neutrin star may form current structures in a polar region. The instability and disruption of this currents must lead to effective acceleration of the particles to ultra high energy as it observe by GRO and UHE-astronomy experiments.

Many circumstellar disks associated with objects ranging from protoplanetary nebulae to accretion disks around compact stars allow for the generation of magnetic fields by an αω dynamo. We have applied kinematic dynamo formalism to geometrically thin accretion disks. We calculate, in the framework of an adiabatic approximation, the normal mode solutions for dynamos operating in disks around compact stars. We then describe the criteria for a viable dynamo in protoplanetary nebulae, and discuss the particular features that make accretion disk dynamos different from planetary, stellar, and galactic dynamos.

Employing the standard theory for thin accretion disks I estimate the relevant parameters for a dynamo in an accretion disk. These estimates could then be compared to the results of numerical simulations. Some preliminary results of such simulations (Torkelsson & Brandenburg 1992) are presented too.

We present the results of recent work on a model of angular momentum transport in thin, ionized, accretion disks. In particular, we consider three physical effects, each of which can be represented in terms of a local MHD mode in such a disk. First, we discuss the generation and propagation of internal modes within accretion disks, pointing out certain features which make them particularly promising as the driving force behind a strong, fast dynamo in accretion disks. Second, we point ou that the magnetic shearing instability (MSI) first discussed by Velikhov, and more recently by Balbus and Hawley in the specific context of these disks, provides a natural saturation mechanism for any disk dynamo, leading to an approximate equality between the dimensionless viscosity and the ratio of the dynamo growth rate to the local shear. Third, we argue that magnetic buoyancy is largely suppressed by the turbulence generated by the shearing instability. This prevents it from removing magnetic flux from the disk any faster than random turbulent diffusion. We find that the dimensionless viscosity α scales as (H/r)4/3, where H is the disk height and r is its radius.