The large-scale magnetic field of the Sun and solar-type stars is probably generated near the interface of the radiative core and the convection zone. One of the well-known difficulties of interface-type and other dynamo models is to explain the latitudinal distribution of magnetic fields as observed on the Sun. In this contribution new results of numerical MHD simulations of transport coefficients of magnetic fields in the rapid rotation regime, relevant for the base of the solar convection zone, are presented that may contribute to explaining the latitudinal distribution of magnetic fields observed on the Sun. A brief outlook on further numerical simulations of transport coefficients and their relevance for mean-field dynamo theory is given.

The exact solution of the evolution equation for the magnetic field in ideal MHD, Callebaut (2006), with an azimuthal velocity which is function of $r$ and $\vartheta$ only (spherical coordinates) is applied to a bipolar magnetic seed field and to a quadripolar field. Resistivity and $\alpha$-effect are not yet taken into account, but the extensions are possible. From the surface observations we had derived an approximate analytic expression for the differential rotation in order to work fully analytically in the application. Qualitatively the results for a quadripolar field are as for a bipolar seed field. The main features are the same: for some latitudes the field may increase by two orders of magnitude, the separation between sunspots and polar faculae is clearcut, there is, relatively speaking, a too strong amplification in the polar regions (the latter occurs in other models too). The hypothesis that the seed fields are situated at the tachocline is not required: the amplification is active throughout the whole convective zone, albeit with different strengths, and thus during the transit of the flux tubes from tachocline to the solar surface too.

We review how the so-called flux-transport solar dynamos work and show that such models calibrate well with solar cycle observations, and simulate well the relative peaks of the past 8 cycles. This success provides a basis for forecasting a strong solar cycle 24. We also show that a previous forecast of the timing of onset of cycle 24 is being verified by recent sunspot area statistics and coronal structures.

The broad range of dynamics exhibited by plasma motions within the solar interior affects many aspects of the generation and transport of magnetic fields during the solar magnetic activity cycle. On the photosphere, such dynamics include the differential rotation, meridional flows, and a hierarchy of convection cells, and these fluid motions are observed to readily advect any small-scale magnetic fields embedded within them. While the effects of large-scale flows on the global activity cycle are well known, it is becoming increasingly apparent that small-scale dynamics can also affect global magnetic activity throughout the solar cycle. Such effects include variations in the strength of the magnetic dipole moment with time, and the timing of the reversals of the polar-cap flux. In this article, several aspects of this coupling between small and large scales will be illustrated, and the implications of such coupling on the solar activity cycle will be discussed.

Understanding the mechanism that causes the emergence of magnetic flux from the solar interior to the atmosphere, the drastic changes in the properties of the matter and magnetic fields along the rise and the interplay of dynamic and resistive phenomena that shape the emerged regions is one of the major open tasks in solar physics. Important advances are being made both in the theoretical modelling and in the observation of the emergence events. This review concentrates on recent advances through 3D numerical experiments carried out with massively parallel MHD and radiative transfer codes.

Based on photospheric vector magnetograms obtained at Huairou Observing Station and BBSO, we studied the evolution of magnetic nonpotentiality and energy transport in NOAA AR 10720. Daily changes of vector magnetic field was analyzed. Shear angle, helicity and free energy density which were deduced from the data were examined.

A New EFR on January 13 brought in magnetic nonpotentiality strong shear angle, free energy and complexity(multiple neutral line and opposite sign helicity) which touched off AR activity, support the idea that upper atmospheres critical state may be made by continues changes on the photosphere.

Kinematic solar dynamo models (KSDM) that use a solar like differential rotation profile usually fail to reproduce the latitudinal distribution of the toroidal magnetic fields. Usually, it is assumed that it is the larger radial shear present in the solar tachocline at higher latitudes that is the responsible for such results. We here consider variations in the shape and thickness of the tachocline and find that a better distribution of the toroidal fields is obtained when the thickness of the tachocline is $d_1=0.02R_{\odot}$, a smaller value than that conventionally used.

The Rayleigh-Taylor instability (RTI) of a continuously stratified fluid has implications on the stability of solar and planetary interiors. A nonlinear stage of the two-dimensional RTI is studied by including various effects. By using the multiple scale method, we derived a nonlinear Schrödinger equation (NLSE) in 2+1 dimensions. We show the general soliton solutions of the NLSE and this allows to discuss their stability.

The dynamic process of magnetic flux emergence from the solar interior to the outer atmosphere may well be related with eruptive phenomena and intense events of the Solar activity. However, the physics of the emergence is not still well understood. Thus, we have performed 3D MHD simulations to study the rising motion of a twisted flux tube from the convection zone of the Sun and its interaction with a preexisting coronal magnetic field. The results show that the reconnection process depends criticaly on the initial relative orientation between the two magnetic flux systems into contact. On the other hand, the overal process of emergence depends mostly on the dynamics of the sub-photospheric plasma.

We explain the generation of the large-scale unipolar magnetic field regions (global magnetic regions) by the same dynamo action as for the generation of the sunspots and the polar faculae butterfly diagrams as given by Callebaut (2006). The previous global magnetic regions through meridional circulation now serve as the main seed fields (flux-transport dynamo for the global field regions), possibly supplemented by leftovers from the sunspots and some weak fields generated at the tachocline.

Solar flares are of great fundamental and practical interest. In some events the energy release might exceed 1026J Tsurutani et al. (2003) and accompanying CME courses extremely severe magnetic storm. Because of very rare occurrence of such global flares a laboratory simulation appears to be an alternative that could provide experimental data necessary for physical understanding of this phenomenon and for verifying theoretical models. Flare involves processes on many widely varying spatial and time scales. In laboratory only some parts of the whole evolution could be attempted for simulation. The present work is focused on the last stage of eruption when a magnetic loop filled with heated plasma is ejected away from the Sun, either itself or pushed by an upcoming jet. The geometry of a flare loop suggests that a magnetic dipole and laser-produced plasma could be used to simulate this structure Nikitin & Ponomarenko (1995). In the present work similarity criteria that relate laboratory parameters to the natural phenomena, experimental set up and preliminary results are presented.

Longitudinal structure of the photospheric magnetic field over last tree solar cycles has been studied. The reconstruction of the longitudinal structure in the heliographic system rotating rigidly with Carrington rate was performed and compared with longitudinal distributions of random origin.

It was performed a study of the North-South asymmetry of the magnetic field distribution by comparison of the temporal behavior of long and short term variabilities of the photospheric field at the same latitudes in opposit hemispheres using WSO data sets covered the interval from 1976 to 2005.

Differential rotational rate of the magnetic field measured in the photosphere was calculated and its temporal dependence was studied using two independent methods. It was found that the rotational rate has a character of torsional waves running to the equator with 11 year periodicity. At high latitudes the rotation is getting slower during minimum of activity when the field measured there is stronger.

Observations of the large scale magnetic field in the photosphere taken at the Wilcox Solar Observatory since 1976 up to 2005 have been analyzed to deduce its latitudinal and longitudinal structures, its differential rotation, and their variability in time. Basic topology of solar magnetic field was reconstructed in coordinate system rotating with different rate.

The spectral and source characteristics of a complex radio burst observed with the spectrometers of China and the Nobeyama Radio Heliograph are analyzed. This burst presents two separate burst peaks occurred in different frequency range (broad-band microwave and narrow-band decimeter wavelengths). We stress that the late phase radio bursts in decimeter wavelength corresponding to the post-flare loops may be the radio homologous flare.

Transport of the solar background large-scale magnetic regions is followed between individual consecutive magnetic synoptic charts derived from observing data of Kitt Peak NSO. During many solar rotations the horizontal magnetic flux displacement was described by large-scale horizontal transport velocities, inferred in many points over the whole solar photosphere. Large-scale transport velocities contains from both axially symmetric and non-axially symmetric components. The first one describes zonal and meridional global transport studied in time interval during three last solar activity cycles. Cycle dependent global velocities are found as values varying in heliographic latitude and in the phase of the solar cycle.

Fourier local correlation tracking (FLCT) was applied to time series of the normal magnetic field in vector magnetograms of NOAA AR 8210, from 17:13–21:29 UT on 1998 May 1, to derive photospheric flows. These flows, combined with both the observed horizontal magnetic field and an inferred horizontal potential magnetic field, can be used to derive the flux of free magnetic energy across the photosphere. Here, we present the formalism used, as well as a map of the time-averaged free energy flux. Over the time interval covered by the magnetograms, ${\sim} 10^{31}\,$erg of free magnetic energy flowed upward across the photosphere, a significant fraction of the energy typically released in large flares coronal mass ejections (CMEs). A flare and coronal mass ejection began at 22:30 UT. We acknowledge the kind support of AFOSR's MURI program.

We analyze three solar active regions observed with the MDI instrument onboard SoHO (Scherrer et al. 1995). We apply the time-distance helioseismology formalism to derive the travel times of acoustic waves propagating through these active regions. The inversion of these acoustic travel times gives us access to the 3D sound-speed structure below the sunspots. We compare the main characteristics of these inversion results as a function of the active region size and magnetic field strength.

In the impulsive phase of solar flares, the electrostatic waves can be excited during magnetic reconnection. The proton and electron at reconnecting X points can be accelerated by perpendicular propagating electrostatic waves.