The generation of the solar magnetic field is generally ascribed to dynamo processes in the convection zone. The dynamo effects, differential rotation (ω–effect) and helical turbulence (α–effect) are explained, and the basic properties of the mean–field dynamo equations are discussed in close comparison with the observed solar cycle.

Especially the question of the seat of the dynamo is addressed. Problems of a dynamo in the convection zone proper could be magnetic buoyancy, the nearly strict observance of the polarity rules and the migration pattern of the magnetic fields which are difficult to understand in the light of recent studies of the field structure in the convection zone and by observations of the solar acoustic oscillations. To overcome some of these problems it has been suggested that the solar dynamo operates in the thin overshoot region at the base of the convection zone instead. Some aspects of such an interface dynamo are discussed. As an alternative to the turbulent α–effect a dynamic α-effect based on magnetostrophic waves driven by a magnetic buoyancy instability of a magnetic flux layer is introduced. Model calculations for both pictures, a convection zone and an interface dynamo, are presented which use the internal rotation of the sun as deduced from helioseismology. Solutions with solar cycle behaviour are only obtained if the magnetic flux is bounded in the lower convection zone and the α–effect is concentrated near the equator.

Another aspect briefly addressed is the nonlinear saturation of the magnetic field. The necessity of the dynamic nature of the dynamo processes is emphasized, and different processes, e.g. magnetic buoyancy and α-quenching, are mentioned.

The effect of anisotropic transport of the mean magnetic field by turbulence in a stratified rotating fluid is briefly discussed to find its qualitative correspondence to the observed field redistribution over a solar cycle. A kinematic model of a dynamo in a spherical shell is developed with the transport effect included to assess its importance in a more consistent way. The anisotropic transport brings the simulated field behavior closer to that observed on the Sun.

The idea behind the use of ensemble averaging and the finite magnetic energy method of van Geffen and Hoyng (1992) is briefly discussed. Applying this method to the solar dynamo shows that the turbulence — an essential ingredient of traditional mean field dynamo theory — poses grave problems: the turbulence makes the magnetic field so unstable that it becomes impossible to recognize any period.

We applied the results of recent derivations of the α-effect to the solar convection zone model by Stix (1989) to find the depth and latitude dependences of the α-tensor. Pronounced inhomogeneity and anisotropy are revealed: the α-coefficients for different directions are quite different and strongly latitude-dependent.

The structure of solar surface magnetic fields, the way they erupt from the the convection zone below, and processes like flux expulsion and fragmentation instabilities support the view that magnetic flux in a stellar convection zone is in an intermittent, fragmented state which can be described as an ensemble of magnetic flux tubes. Depending on size and field strength, the dynamics of magnetic flux tubes can strongly differ from the behavior of a passive, diffuse field which is often assumed in conventional mean-field dynamo theory. Observed properties of active regions like emergence in low latitudes, Hale's polarity rules, tilt angles, and the process of sunspot formation from smaller fragments, together with theoretical considerations of the dynamics of buoyant flux tubes indicate that the magnetic structures which erupt in an emerging active region are not passive to convection and originate in a source region (presumably an overshoot layer below the convection zone proper) with a field strength of at least 105 G, far beyond the equipartition field strength with respect to convective flows. We discuss the consequences of such a situation for dynamo theory of the solar cycle and consider the possibility of dynamo models on the basis of flux tubes. A simple, illustrative example of a flux tube dynamo is presented.

The combined action of the subadiabatic ambient stratification in the overshoot region below the convection zone and the inertial forces associated with the solar rotation is shown to lead to the suppression of the escape of magnetic flux in the form of toroidal flux tubes both toward the surface and toward higher latitudes. We show that a flux ring initially in thermal equilibrium with its environment and rotating with the ambient angular velocity moves radially and latitudinally towards an equilibrium configuration of lower internal temperature and larger internal rotation rate with respect to the surrounding, field-free gas. We conclude that flux rings with B≲ 105 G can be kept within the overshoot region if the superadiabaticity is sufficiently negative, i.e. δ = ▿ – ▿ad ≲–10−5; below that field strength the poleward drift is also reduced to a latitudinal oscillation of moderate amplitude, δθ ≲ 20 deg. Flux rings with significantly larger field strength cannot be kept in the equatorial parts of the overshoot region: their equilibrium configuration is located at high latitudes far outside the solar activity belts and, at any rate, requires unrealistic values of δ.

We consider the linear stability of a toroidal flux tube lying in the equatorial plane of a differentially rotating star and investigate its dependence on superadiabaticity, magnetic field strength, and gradient of angular velocity.

The mean magnetic field transport due to inhomogeneity of the turbulence intensity is considered taking the field back reaction on motion into account. In spite of the magnetic quenching, the downward diamagnetic pumping is still powerful enough to keep the fields of 3 to 4 kG strength near the SCZ base against the magnetic buoyancy.

From the fluctuations of the velocity and magnetic field observed in different kinds of solar wind the fluctuating electric fields are derived, and their power spectra are constructed and analysed. The mean electromotive force ɛ generated by the turbulent motions depends upon the nature of the fluctuations. Simple dynamo theory predicts a linear relationship between ɛ and the mean magnetic field B0. Correlation studies carried out to establish the alpha effect in the solar wind have given negative results.

A short compilation of various radio methods of the determination of magnetic fields in the solar corona is given which, completed by observations in other spectral ranges (e.g. the optical and X-ray ranges), results in a complex picture of the magnetic field. Some topics of interest are the following:

1. (1) Comparison with a standard reference magnetic field in the solar corona,

2. (2) Possible evidence of substantial small-scale fluctuations of the magnetic field (e.g. in active regions),

3. (3) Indication of magnetic fields substantially in excess of the standard distribution (e.g. in limb flare events).

An observational example of nonlinear coupling between flows and magnetic field generated by dynamo action of the flows is found in the 110-year periodic modulations of the solar differential rotation and the solar cycle.

I consider the effect of rapid fluctuations in the mean helicity on a plane dynamo wave in the αω-approximation and in the weak forcing limit. The phase shift and the logarithmic amplitude of the wave exhibit a correlated random walk, so that weaker (stronger) cycles last longer (shorter). The solar cycle data follow this prediction rather well. Mean helicity fluctuations are concluded to be an important source of solar cycle variability.

The solar magnetized surface reveals a stable spin period — the Carrington period — and a stable oscillation period — the Hale period. The latter is traced by each of the low-order multipole moments, whereby the total magnetic energy (near the surface) is more or less constant. This highly non-stochastic structure is reminiscent of a permanent magnetic flux frozen into the Sun's radiative core, and dragged out into the heliosphere by the solar wind. The radius-dependent torque exerted by this magnetic flux can restore the observed system of torsional oscillations of the convection zone.

Two nonlinear dynamos have been analyzed by numerical means: 3D-simulation of the magneto-hydrodynamic equations and qualitative analysis of a simplified low-dimensional mean field model. It turns out that both are capable of deterministic chaos in a certain parameter range. As the basic tool the calculation of Lyapunov exponents has been used.

The correlation dimension D (2) as a characteristic measure of the regular or chaotic behaviour of the solar dynamical system has been calculated. The algorithm suggested by Grassberger and Procaccia (1983) has been applied to time series of relative sunspot numbers and of areas of sunspots and faculae. In the first case, a correlation dimension D (2) ≃ 1.5 has been found; in the other two cases, the algorithm was not convergent, the results obtained being not relevant, due to the too short series of data available.

From the analysis of a series of data concerning phenomena taking place in the high corona, in the interplanetary medium and in the magnetosphere, we came to the conclusion that we have to take into consideration a two-component solar cycle in which, with a 5–6 yr delay, the cycle of the dipole component of the solar magnetic field and the following sunspot cycle are closely correlated. In order to show the new mechanisms to incorporate into a model of a two-component solar cycle, we discuss several other relevant solar data.

The fundamental quantity for the total solar irradiance is the solar constant J which is determined by the mean Sun-Earth distance and by the energy budget in the interior of the sun. The mean distance is the major semi-axis of the earth orbit and therefore a constant of celestial mechanics. The energy production and transport in the interior of the sun must be constant at least during a Helmholtz-Kelvin period. Actually, the heat budget of the sun is constant during some billion years.