During minima of solar activity, it is possible to estimate the influence of convection zone turbulence on the magnetic flux tubes forming active regions (ARs), because the toroidal field of the old cycle weakens, and the new toroidal field is still weak. We analyzed ARs of solar minima between 23-24 and 24-25 solar cycles. ARs were classified as regular, irregular and unipolar spots. Regular ARs follow the empirical laws consistent with the Babcock–Leighton dynamo theory. We found that regular ARs dominate by flux and by number during the solar minima. Irregular ARs are mainly represented by bipolar structures of deformed orientation and contribute only one-third in the total flux and one-third in the total number. Very complex multipolar ARs are extremely rare. So, during solar minima the global dynamo still guides the formation of ARs, whereas the turbulence only slightly affects the toroidal flux tubes orientation.

The solar dynamo is a physical process of magnetic field generation due to conversion of kinetic energy of plasma flows into magnetic energy. However, in the mean-field dynamo theory, one needs to segregate scales and consider separately large-scale dynamo and small-scale dynamo. The large-scale dynamo produces the large-scale mean field and unavoidable fluctuations of the mean field. Both are cycle-dependent. The small-scale dynamo is supposed to produce only the small-scale field, and this field is cycle-independent. There is no sharp boundary between the intervals of the large-scale and small-scale dynamos. An unavoidable presence of a smooth transition implies that there is a region where the properties of the large-scale global dynamo and fluctuations inherent to small-scale dynamo co-exist on some intermediate scales. Recent achievements in observations of the small-scale dynamo operation on the smallest observable scales and on the intermediate scales of typical active regions are discussed in the review.

Statistical study of 3047 active regions (ARs) from 1996 to 2021 was performed using the catalog of the magneto-morphological classes (MMC) of ARs CrAO. According to the magneto-morphological classification of ARs proposed earlier, all ARs, except for unipolar spots, were sorted out between two categories: regular (bipolar groups obeying the Hale’s polarity law, the Joy’s law, etc.) and irregular ARs (all the rest). We analyzed the number and fluxes of ARs depending on their location in different (relative to the equator) hemispheres. We found that the trends for fluxes are more pronounced. For ARs of both MMC types, they demonstrate signs of both a multi-peak and double-peak structure. Some peaks coincide with the main maxima of the cycle. The second main maximum is mainly formed by the irregular ARs in the S-hemisphere. This might be due to the interaction of the dipole and quadrupole components of the global magnetic field.

Magnetic helicity (volume integral of the product of the magnetic field vector B and the vector potential A), or its proxy, the current helicity at the surface (surface integral of B·J or BzJz), is an important quantity which characterizes the helical nature of solar magnetic fields. The current helicity on the Sun shows a tendency, though with large dispersion, that it is positive in the southern hemisphere and negative in the northern hemisphere (the helicity sign rule). However, there are indications that the helicity sign rule may be reversed at activity minimum periods. We will discuss the significance of this property by focusing on the statistical distributions of helicity whether its dispersion follows Gaussian distribution or not.

We review the theoretical studies of the Alfvén wave model of spicules and coronal heating, mainly based on the papers by Kudoh & Shibata (1999), Saito et al. (2001) and Moriyasu et al. (2004) which performed MHD numerical simulations of nonlinear Alfvén waves propagating along a magnetic flux tube in the solar atmosphere. Kudoh & Shibata (1999) and Saito et al. (2001) found that, if the root mean square of the perturbation is greater than ~ 1 km s−1 in the photosphere, (1) the transition region is lifted up to more than ~ 5000 km (i.e., the spicule is produced), (2) the energy flux sufficient for heating the quiet corona (~ 3.0 × 105 ergs s−1 cm−2) is transported into the corona by Alfvén waves. Moriyasu et al. (2004) demonstrated that a hot corona is created in an initially cool loop as a result of the nonlinear Alfvén waves produced near the photosphere. We conclude that the nonlinear Alfvén wave model is the promising model of spicules and coronal heating.

A three-dimensional, time-dependent, magnetohydrodynamic (MHD) model is constructed for the study of active region (AR) evolution. The new physics included in this model is differential rotation, meridional flow, effective diffusion and cyclonic turbulence effects, which means, that the photospheric shear is automatically generated instead of prescribed as is usually done for modeling. To benchmark this newly developed model, we have used observed active region NOAA/AR-8100 (October 29 - November 3, 1997) to verify the model by computation of the total magnetic flux and magnetic field maps of that active region. Then, we apply this model to compute the non-potentiality magnetic field parameters for possible coronal mass ejection production. These parameters are: (i) magnetic flux content ($\Phi$), (ii) the length of strong shear, strong-field main neutral line, ($L_{ss}$), (iii) the net electric current ($I_N$) and (iv) the flux normalized measure of the field twist ($\alpha$ = $\mu$$\frac{I_N}{\Phi}$). These parameters are compared with the measured values which showed remarkable agreement.To search for other articles by the author(s) go to: http://adsabs.harvard.edu/abstract_service.html