The helicity of cellular convective flows in a horizontal layer of compressible fluid (gas) heated from below and rotating about a vertical axis is studied using finite-difference numerical simulations. The medium is assumed to be polytropically stratified. An initial thermal perturbation is introduced so as to produce a system of Bénard-type hexagonal convection cells. The flow gradually becomes less ordered, and the mean helicity grows initially and decreases sharply after the substantial chaotisation of the flow. Given the Rayleigh and Prandtl numbers, the maximum value reached by the mean helicity increases with the decrease of the polytrope index and has a maximum at a certain rotational velocity of the layer.

Convection is simulated numerically based on two-dimensional Boussinesq equations for a fluid layer with a specially chosen stratification such that the convective instability is much stronger in a thin subsurface sublayer than in the remaining part of the layer. The developing convective flow has a small-scale component superposed onto a basic large-scale roll flow.

The magnetorotational instability (MRI) of thin, vertically-isothermal Keplerian discs, under the influence of an axial magnetic field is investigated near the instability threshold. The nonlinear interaction of Alfven-Coriolis (MRI) modes with stable magnetoacoustic waves is considered. The transition of the Alfven-Coriolis modes to instability occurs when the linearized system has zero eigenvalue of multiplicity two. As a result the nonlinear ordinary differential equation that describes the evolution of the amplitude of the MRI mode near the threshold is of second order. Solutions of that amplitude equation reveal that the MRI is saturated to bursty periodical oscillations due to the transfer of energy to the stable magnetosonic modes.

The interaction of helical convective motions and differential rotation in the solar convection zone results in turbulent drift of a large-scale magnetic field. We discuss the pumping mechanism and its impact on the solar dynamo.

It is conjectured that magnetic configurations may be characterized by the embedded invariants which are extracted from their topological textures. Hence, experimentally observed magnetic structures can be classified by the invariants of the elementary building blocks of the 3-D structures - prime knots. These unique invariants may describe the magnetic configurations in ion drop-outs in solar impulsive events, in photospheric flux ropes carried into the interplanetary medium by the solar wind, and can affect the decay rates for complex magnetic configurations.

Ohm, Hall, and ambipolar diffusions in the partially ionized plasma are considered. The statement of Pandey & Wardle (2011,2012) that only Ohmic diffusion is capable of destroying the magnetic flux is not sufficiently correct due to the formal dependence of the magnetic diffusion on a frame of reference.

We give a short introduction to the subject and review advances in understanding the basic ingredients of the mean-field dynamo theory. The discussion includes the recent analytic and numerical work in developments for the mean electromotive force of the turbulent flows and magnetic field, the nonlinear effects of the magnetic helicity, the non-local generation effects in the dynamo. We give an example of the mean-field solar dynamo model that incorporates the fairly complete expressions for the mean-electromotive force, the subsurface shear layer and the conservation of the total helicity. The model is used to shed light on the issues in the solar dynamo and on the future development of this field of research.

An update is given on the current status of solar and stellar dynamos. At present, it is still unclear why stellar cycle frequencies increase with rotation frequency in such a way that their ratio increases with stellar activity. The small-scale dynamo is expected to operate in spite of a small value of the magnetic Prandtl number in stars. Whether or not the global magnetic activity in stars is a shallow or deeply rooted phenomenon is another open question. Progress in demonstrating the presence and importance of magnetic helicity fluxes in dynamos is briefly reviewed, and finally the role of nonlocality is emphasized in modeling stellar dynamos using the mean-field approach. On the other hand, direct numerical simulations have now come to the point where the models show solar-like equatorward migration that can be compared with observations and that need to be understood theoretically.

Meridional flow results from slight deviations from the thermal wind balance. The deviations are relatively large in the boundary layers near the top and bottom of the convection zone. Accordingly, the meridional flow attains its largest velocities at the boundaries and decreases inside the convection zone. The thickness of the boundary layers, where meridional flow is concentrated, decreases with rotation rate, so that an advection-dominated regime of dynamos is not probable in rapidly rotating stars. Angular momentum transport by convection and by the meridional flow produce differential rotation. The convective fluxes of angular momentum point radially inward in the case of slow rotation but change their direction to equatorward and parallel to the rotation axis as the rotation rate increases. The differential rotation of main-sequence dwarfs is predicted to vary mildly with rotation rate but increase strongly with stellar surface temperature. The significance of differential rotation for dynamos has the opposite tendency to increase with spectral type.

In the last decades, the experimental study of dynamo action has made great progress. However, after the dynamo experiments in Karlsruhe and Riga, the von-Kármán-Sodium (VKS) dynamo is only the third facility that has been able to demonstrate fluid flow driven self-generation of magnetic fields in a laboratory experiment. Further progress in the experimental examination of dynamo action is expected from the planned precession driven dynamo experiment that will be designed in the framework of the liquid sodium facility DRESDYN (DREsden Sodium facility for DYNamo and thermohydraulic studies).

In this paper, we briefly present numerical models of the VKS dynamo that demonstrate the close relation between the axisymmetric field observed in that experiment and the soft iron material used for the flow driving impellers. We further show recent results of preparatory water experiments and design studies related to the precession dynamo and delineate the scientific prospects for the final set-up.

Convective turbulent motions in the solar interior, as well as the mean flows resulting from them, determine the evolution of the solar magnetic field. With the aim to get a better understanding of these flows we study anelastic rotating convection in a spherical shell whose stratification resembles that of the solar interior. This study is done through numerical simulations performed with the EULAG code. Due to the numerical formulation, these simulations are known as implicit large eddy simulations (ILES), since they intrinsically capture the contribution of, non-resolved, small scales at the same time maximizing the effective Reynolds number. We reproduce some previous results and find a transition between buoyancy and rotation dominated regimes which results in anti-solar or solar like rotation patterns. Even thought the rotation profiles are dominated by Taylor-Proudman columnar rotation, we are able to reproduce the tachocline and a low latitude near-surface shear layer. We find that simulations results depend on the grid resolution as a consequence of a different sub-grid scale contribution.

The tachocline is important in the solar dynamo for the generation and the storage of the magnetic fields. A most plausible explanation for the confinement of the tachocline is given by the fast tachocline model in which the tachocline is confined by the anisotropic momentum transfer by the Maxwell stress of the dynamo generated magnetic fields. We employ a flux transport dynamo model coupled with the simple feedback formula of this fast tachocline model which basically relates the thickness of the tachocline to the Maxwell stress. We find that this nonlinear coupling not only produces a stable solar-like dynamo solution but also a significant latitudinal variation in the tachocline thickness which is in agreement with the observations.

Sunspot data and large-scale solar magnetic field data are used to demonstrate the operation of the Babcock-Leighton mechanism on the Sun. A dynamo model is developed that employs jointly a nonlocal alpha-effect of the Babcock-Leighton type and diamagnetic downward pumping. The pumping concentrates magnetic fields to the base of the convection zone. The magnetic cycle period, equatorial symmetry of the generated fields, their meridional drift, and the polar-to-toroidal field ratio obtained in the model agree with observations.

We investigate the relations between tachocline-based dynamos and the surface flux transport mechanisms in stars with outer convection zones. Using our combined models of flux generation and transport, we demonstrate the importance of the buoyant rise of magnetic flux, which physically determines the emergence latitudes and tilt angles of bipolar magnetic regions. The combined effects of the dynamo strength, flux rise, and surface transport lead to various cyclic and non-cyclic time series of total unsigned surface magnetic flux.

The occurrence of grand minima like the Maunder minimum is an intriguing aspect of the sunspot cycle. We use the flux transport dynamo model to explain the grand minima, showing that they arise when either the poloidal field or the meridional circulation falls to a sufficiently low value due to fluctuations. Assuming these fluctuations to be Gaussian and determining the various parameters from the data of the last 28 cycles, we carry on a dynamo simulation with both these fluctuations. The results are remarkably close to the observational data.

Having advance knowledge of solar activity is important because the Sun's magnetic output governs space weather and impacts technologies reliant on space. However, the irregular nature of the solar cycle makes solar activity predictions a challenging task. This is best achieved through appropriately constrained solar dynamo simulations and as such the first step towards predictions is to understand the underlying physics of the solar dynamo mechanism. In Babcock-Leighton type dynamo models, the poloidal field is generated near the solar surface whereas the toroidal field is generated in the solar interior. Therefore a finite time is necessary for the coupling of the spatially segregated source layers of the dynamo. This time delay introduces a memory in the dynamo mechanism which allows forecasting of future solar activity. Here we discuss how this forecasting ability of the solar cycle is affected by downward turbulent pumping of magnetic flux. With significant turbulent pumping the memory of the dynamo is severely degraded and thus long term prediction of the solar cycle is not possible; only a short term prediction of the next cycle peak may be possible based on observational data assimilation at the previous cycle minimum.

We review some of the currently used techniques to detect stellar magnetic fields on cool stars. Emphasis is put on spectropolarimetry with high-resolution spectrographs and its related data de-noising techniques and multi-line inverse modeling. Detections and results from Zeeman splittings and broadenings are briefly mentioned. We discuss some of our most recent Zeeman Doppler Imaging (ZDI) results and present a comparison of ZDI maps of the K-type WTTS V410 Tauri and the planet-hosting F8 star HD 179949 with results from other groups.

Observing high-energy gamma-rays from Active Galactic Nuclei (AGN) offers a unique potential to probe extremely tiny values of the intergalactic magnetic field (IGMF), a long standing question of astrophysics, astroparticle physics and cosmology. Very high energy (VHE) photons from blazars propagating along the line of sight interact with the extragalactic background light (EBL) and produce e+e− pairs. Through inverse-Compton interaction, mainly on the cosmic microwave background (CMB), these pairs generate secondary GeV-TeV components accompanying the primary VHE signal. Such secondary components would be detected in the gamma-ray range as delayed “pair echos” for very weak IGMF (B < 10−16G), while they should result in a spatially extended gamma-ray emission around the source for higher IGMF values (B > 10−16G). Coordinated observations with space (i.e. Fermi) and ground-based gamma-ray instruments, such as the present Cherenkov experiments H.E.S.S., MAGIC and VERITAS, the future Cherenkov Telescope Array (CTA) Observatory, and the wide-field detectors such as HAWC and LHAASO, should allow to analyze and finally detect such echos, extended emission or pair halos, and to further characterize the IGMF.

Most of the exoplanet science is dependent on the stellar knowledge. One of them that has to be understood is the magnetic activity when we search for planets with radial velocity or photometry measurements. The main shape of stellar activity and spots properties have to be understood, for example, to choose the best targets to search for low-mass planets in the habitable zone or to derive the accurate parameters of a planetary system. With that aim, we show in this presentation how these studies lead to give clues on spots latitudes and on the long term variation of stellar activity. The properties of magnetic activity on the low rotators solar-type stars are not easily reachable by other techniques (spectropolarimetry or Doppler imaging) and these studies should be used to constrain theories of stellar dynamo.

The quantum mechanical calculations for the A6Σ+ − X6Σ+ system of the CrH molecule were done in order to obtain its energy level structure and transition strenghts both in the absence and in the presence of a magnetic field. Employing this results and solving a set of the radiative transfer equations, we calculated the Stokes profiles for the entire 0-0 band for different magnetic field strengths and orientations. We show that the CrH lines produce a considerable polarization signal (up to 20%) at 0.5 - 10 kG. Furthermore, the polarization signal shows a significant asymmetry (broad-band polarization) that arises from the Paschen-Back effect in the individual CrH lines. An example of the signal, as it can be observed, is provided.