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The magnetic fields in the inner parts of some spiral galaxies are understood quite well. Their generation is connected with the dynamo mechanism that is based on the joint action of turbulent diffusion and the α-effect. Usually the galactic dynamo is described with the so-called no-z approximation which takes into account that the galaxy disc is quite thin, with the implication that some spatial derivatives may be replaced by algebraic expressions. Some galaxies have outer rings that are situated at some distance from the galactic centre. The magnetic field can be described there also using the no-z model. As the thickness of such objects is comparable with their width, it is necessary to take into account the z-dependence of the field. We have studied the magnetic field evolution using the no-z approximation and torus dynamo model for the torus with rectangular cross-section in the axisymmetric case. [ABSTRACT FROM AUTHOR]

The project DRESDYN (DREsden Sodium facility for DYNamo and thermohydraulic studies) conducted at Helmholtz–Zentrum Dresden–Rossendorf (HZDR) provides a new platform for a variety of liquid sodium experiments devoted to problems of geo- and astrophysical magnetohydrodynamics. The most ambitious experiment within this project is a precession-driven dynamo experiment that currently is under construction. It consists of a cylinder filled with liquid sodium that simultaneously rotates around two axes. The experiment is motivated by the idea of a precession-driven flow as a complementary energy source for the geodynamo or the ancient lunar dynamo. In the present study, we address numerical and experimental examinations in order to identify parameter regions where the onset of magnetic field excitation will be most probable. Both approaches show that in the strongly nonlinear regime the flow is essentially composed of the directly forced primary Kelvin mode and higher modes in terms of standing inertial waves that arise from nonlinear self-interactions. A peculiarity is the resonance-like emergence of an axisymmetric mode that represents a double roll structure in the meridional plane, which, however, only occurs in a very limited range of the precession ratio. This axisymmetric mode turns out to be beneficial for dynamo action, and kinematic simulations of the magnetic field evolution induced by the time-averaged flow exhibit magnetic field excitation at critical magnetic Reynolds numbers around , which is well within the range of the planned liquid sodium experiment. [ABSTRACT FROM AUTHOR]

Magnetic fields of planets, stars and galaxies are generated by self-excitation in moving electrically conducting fluids. Once produced, magnetic fields can play an active role in cosmic structure formation by destabilising rotational flows that would be otherwise hydrodynamically stable. For a long time, both hydromagnetic dynamo action as well as magnetically triggered flow instabilities had been the subject of purely theoretical research. Meanwhile, however, the dynamo effect has been observed in large-scale liquid sodium experiments in Riga, Karlsruhe and Cadarache. In this paper, we summarise the results of liquid metal experiments devoted to the dynamo effect and various magnetic instabilities such as the helical and the azimuthal magnetorotational instability and the Tayler instability. We discuss in detail our plans for a precession-driven dynamo experiment and a large-scale Tayler–Couette experiment using liquid sodium, and on the prospects to observe magnetically triggered instabilities of flows with positive shear. [ABSTRACT FROM AUTHOR]

The initial magnetic field of previous magnetorotational instability (MRI) simulations has always included a significant system-scale component, even if stochastic. However, it is of conceptual and practical interest to assess whether the MRI can grow when the initial field is turbulent. The ubiquitous presence of turbulent or random flows in astrophysical plasmas generically leads to a small-scale dynamo (SSD), which would provide initial seed turbulent velocity and magnetic fields in the plasma that becomes an accretion disc. Can the MRI grow from these more realistic initial conditions? To address this, we supply a standard shearing box with isotropically forced SSD generated magnetic and velocity fields as initial conditions and remove the forcing. We find that if the initially supplied fields are too weak or too incoherent, they decay from the initial turbulent cascade faster than they can grow via the MRI. When the initially supplied fields are sufficient to allow MRI growth and sustenance, the saturated stresses, large-scale fields and power spectra match those of the standard zero net flux MRI simulation with an initial large-scale vertical field. [ABSTRACT FROM AUTHOR]

Magnetic dynamo action caused by themagnetorotational instability is studied in the shearingbox approximation with no imposed net magnetic flux. Consistent with recent studies, the dynamo action is found to be sensitive to the aspect ratio of the box: it is much easier to obtain in tall boxes (stretched in the direction normal to the disc plane) than in long boxes (stretched in the radial direction). Our direct numerical simulations indicate that the dynamo is possible in both cases, given a large enough magnetic Reynolds number. To explain the relatively larger effort required to obtain the dynamo action in a long box, we propose that the turbulent eddies caused by the instability most efficiently fold and mix the magnetic field lines in the radial direction. As a result, in the long box the scale of the generated strong azimuthal (stream-wise directed) magnetic field is always comparable to the scale of the turbulent eddies. In contrast, in the tall box the azimuthal magnetic flux spreads in the vertical direction over a distance exceeding the scale of the turbulent eddies. As a result, different vertical sections of the tall box are permeated by large-scale non-zero azimuthal magnetic fluxes, facilitating the instability. In agreement with this picture, the cases when the dynamo is efficient are characterized by a strong intermittency of the local azimuthal magnetic fluxes. [ABSTRACT FROM AUTHOR]

We present an effectively global analytical asymptotic galactic dynamo solution for the regular magnetic field of an axisymmetric thin disc in the saturated state. This solution is constructed by combining two well-known types of local galactic dynamo solution, parametrized by the disc radius. Namely, the critical (zero growth) solution obtained by treating the dynamo equation as a perturbed diffusion equation is normalized using a non-linear solution that makes use of the ‘no-z’ approximation and the dynamical α-quenching non-linearity. This overall solution is found to be reasonably accurate when compared with detailed numerical solutions. It is thus potentially useful as a tool for predicting observational signatures of magnetic fields of galaxies. In particular, such solutions could be painted on to galaxies in cosmological simulations to enable the construction of synthetic polarized synchrotron and Faraday rotation measure data sets. Further, we explore the properties of our numerical solutions, and their dependence on certain parameter values. We illustrate and assess the degree to which numerical solutions based on various levels of approximation, common in the dynamo literature, agree with one another. [ABSTRACT FROM AUTHOR]

We investigate the dynamics of solar activity using a nonlinear one-dimensional dynamo model and a phenomenological equation for the evolution ofWolf numbers. This system of equations is solved numerically. We take into account the algebraic and dynamic nonlinearities of the alpha effect. The dynamic nonlinearity is related to the evolution of a small-scale magnetic helicity, and it leads to a complicated behaviour of solar activity. The evolution equation for the Wolf number is based on a mechanism of formation of magnetic spots as a result of the negative effective magnetic pressure instability (NEMPI). This phenomenon was predicted 25 yr ago and has been investigated intensively in recent years through direct numerical simulations and mean-field simulations. The evolution equation for the Wolf number includes the production and decay of sunspots. Comparison between the results of numerical simulations and observational data of Wolf numbers shows a 70 per cent correlation over all intervals of observation (about 270 yr). We determine the dependence of the maximum value of the Wolf number versus the period of the cycle and the asymmetry of the solar cycles versus the amplitude of the cycle. These dependences are in good agreement with observations. [ABSTRACT FROM AUTHOR]

Recent data on superflares on Sun-like stars and radiocarbon data on solar activity in the past are both indicative of transient epochs of unusually high magnetic activity. We propose an explanation for the grand activity maxima in the framework of a solar dynamo model with fluctuating parameters. Solar-type dynamos are oscillatory because of the combination of the solar-type differential rotation with positive (in the Northern hemisphere) alpha-effect. An artificial reversal of the sign in the alpha-effect changes the dynamo to a steady regime with hundreds of times larger magnetic energy compared to the amplitude of the cyclic dynamo. Sufficiently large and durable fluctuations reversing the sign of the alpha-effect during the growth phase of a magnetic cycle can, therefore, cause a transient change to a steady dynamo with considerably increased magnetic energy. This qualitative scenario for grand activity maxima is supported by computations of the dynamo model with a fluctuating alpha-effect. The computed statistics of several thousand magnetic cycles gives examples of cycles with very high magnetic energy. Our preliminary estimations, however, suggest that the probability of solar superflares is extremely low. [ABSTRACT FROM AUTHOR]

Context. Numerical modelling of convection driven dynamos in the Boussinesq approximation revealed fundamental characteristics of the dynamo-generated magnetic fields and the fluid flow. Because these results were obtained for an incompressible fluid of constant density, their validity for gas planets and stars remains to be assessed. A common approach is to take some density stratification into account with the so-called anelastic approximation. Aims. The validity of previous results obtained in the Boussinesq approximation is tested for anelastic models. We point out and explain specific differences between both types of models, in particular, with respect to the field geometry and the field strength, but we also compare scaling laws for the velocity amplitude, the magnetic dissipation time, and the convective heat flux. Methods. Our investigation is based on a systematic parameter study of spherical dynamo models in the anelastic approximation. We make use of a recently developed numerical solver and provide results for the test cases of the anelastic dynamo benchmark. Results. The dichotomy of dipolar and multipolar dynamos identified in Boussinesq simulations is also present in our sample of anelastic models. Dipolar models require that the typical length scale of convection is an order of magnitude larger than the Rossby radius. However, the distinction between both classes of models is somewhat less explicit than in previous studies. This is mainly due to two reasons: we found a number of models with a considerable equatorial dipole contribution and an intermediate overall dipole field strength. Furthermore, a large density stratification may hamper the generation of dipole dominated magnetic fields. Previously proposed scaling laws, such as those for the field strength, are similarly applicable to anelastic models. It is not clear, however, if this consistency necessarily implies similar dynamo processes in both settings. [ABSTRACT FROM AUTHOR]

Context. The large-scale magnetic field in the Sun varies with a period of approximately 22 years, although the amplitude of the cycle is subject to long-term modulation with recurrent phases of significantly reduced magnetic activity. It is believed that a hydromagnetic dynamo is responsible for producing this large-scale field, although this dynamo process is not well understood. Aims. Within the framework of mean-field dynamo theory, our aim is to investigate how competing mechanisms for poloidal field regeneration (namely a time-delayed Babcock-Leighton surface α-effect and an interface-type α-effect), can lead to the modulation of magnetic activity in a deep-seated solar dynamo model. Methods. We solve the standard αΩ dynamo equations in one spatial dimension, including source terms corresponding to both of the competing α-effects in the evolution equation for the poloidal field. This system is solved using two different methods. In addition to solving the one-dimensional partial differential equations directly, using numerical techniques, we also use a local approximation to reduce the governing equations to a set of coupled ordinary differential equations (ODEs), which are studied using a combination of analytical and numerical methods. Results. In the ODE model, it is straightforward to find parameters such that a series of bifurcations can be identified as the time delay is increased, with the dynamo transitioning from periodic states to chaotic states via multiply periodic solutions. Similar transitions can be observed in the full model, with the chaotically modulated solutions exhibiting solar-like behaviour. Conclusions. Competing α-effects could explain the observed modulation in the solar cycle. [ABSTRACT FROM AUTHOR]

Aims. The Sun shows strong variability in its magnetic activity, from Grand minima to Grand maxima, but the nature of the variability is not fully understood, mostly because of the insufficient length of the directly observed solar activity records and of uncertainties related to long-term reconstructions. Here we present a new adjustment-free reconstruction of solar activity over three millennia and study its different modes. Methods. We present a new adjustment-free, physical reconstruction of solar activity over the past three millennia, using the latest verified carbon cycle, 14C production, and archeomagnetic field models. This great improvement allowed us to study different modes of solar activity at an unprecedented level of details. Results. The distribution of solar activity is clearly bi-modal, implying the existence of distinct modes of activity. The main regular activity mode corresponds to moderate activity that varies in a relatively narrow band between sunspot numbers 20 and 67. The existence of a separate Grand minimum mode with reduced solar activity, which cannot be explained by random fluctuations of the regular mode, is confirmed at a high confidence level. The possible existence of a separate Grand maximum mode is also suggested, but the statistics is too low to reach a confident conclusion. Conclusions. The Sun is shown to operate in distinct modes - a main general mode, a Grand minimum mode corresponding to an inactive Sun, and a possible Grand maximum mode corresponding to an unusually active Sun. These results provide important constraints for both dynamo models of Sun-like stars and investigations of possible solar influence on Earth's climate. [ABSTRACT FROM AUTHOR]

Context. Star-forming dwarf galaxies can be seen as the local proxies of the high-redshift building blocks of more massive galaxies according to the current paradigm of the hierarchical galaxy formation. They are low-mass objects, and therefore their rotation speed is very low. Several galaxies are observed to show quite strong magnetic fields. These cases of strong ordered magnetic fields seem to correlate with a high, but not extremely high, star formation rate. Aims. We investigate whether these magnetic fields could be generated by the cosmic-ray-driven dynamo. The environment of a dwarf galaxy is unfavourable for the large-scale dynamo action because of the very slow rotation that is required to create the regular component of the magnetic field. Methods. We built a 3D global model of a dwarf galaxy that consists of two gravitational components: the stars and the dark-matter halo described by the purely phenomenological profile proposed previously. We solved a system of magnetohydrodynamic equations that include an additional cosmic-ray component described by the fluid approximation. Results. We found that the cosmic-ray-driven dynamo can amplify the magnetic field with an exponential growth rate. The e-folding time is correlated with the initial rotation speed. The final mean value of the azimuthal flux for our models is on the order of few μG and the system reaches its equipartition level. The results indicate that the cosmic-ray-driven dynamo is a process that can explain the magnetic fields in dwarf galaxies. [ABSTRACT FROM AUTHOR]

Context. Based on the rapidly increasing all-sky data of Faraday rotation measures and polarised synchrotron radiation, the Milky Way's magnetic field can now be modelled with an unprecedented level of detail and complexity. Aims. We aim to complement this phenomenological approach with a physically motivated, quantitative dynamo model - a model that moreover allows for the evolution of the system as a whole, instead of just solving the induction equation for a fixed static disc. Methods. Building on the framework of mean-field magnetohydrodynamics and extending it to the realm of a hybrid evolution, we performed three-dimensional global simulations of the Galactic disc. To eliminate free parameters, closure coefficients embodying the mean-field dynamo were calibrated against resolved local simulations of supernova-driven interstellar turbulence. Results. The emerging dynamo solutions comprise a mixture of the dominant axisymmetric S0 mode with even parity, and a subdominant A0 mode with odd parity. Notably, this superposition of modes creates a strong localised vertical field on one side of the Galactic disc. Moreover, we found significant radial pitch angles that decay with radius, which can be explained by flaring of the disc. In accordance with previous work, magnetic instabilities appear to be restricted to the calmer outer Galactic disc. Their main effect is to create strong fields at large radii such that the radial scale length of the magnetic field increases from 4 kpc (for a mean-field dynamo alone) to about 10 kpc in the hybrid models - the latter being in much better agreement with observations. Conclusions. There remain aspects (e.g., spiral arms, X-shaped halo fields, fluctuating fields) that are not captured by the current model and that will require further development towards a fully dynamical evolution. Nevertheless, we demonstrate that a hybrid modelling of the Galactic dynamo is feasible and can serve as a foundation for future efforts. [ABSTRACT FROM AUTHOR]

We investigate the saturation level of hydromagnetic turbulence driven by the magnetorotational instability in the case of vanishing net flux. Motivated by a recent paper of Bodo et al., we here focus on the case of a non-isothermal equation of state with constant thermal diffusivity. The central aim of the paper is to complement the previous result with closure parameters for mean-field dynamo models, and to test the hypothesis that the dynamo is affected by the mode of heat transport. We perform computer simulations of local shearing-box models of stratified accretion disks with approximate treatment of radiative heat transport, which is modeled via thermal conduction. We study the effect of varying the (constant) thermal diffusivity, and apply different vertical boundary conditions (BCs). In the case of impenetrable vertical boundaries, we confirm the transition from mainly conductive to mainly convective vertical heat transport below a critical thermal diffusivity. This transition is however much less dramatic when more natural outflow BCs are applied. Similarly, the enhancement of magnetic activity in this case is less pronounced. Nevertheless, heating via turbulent dissipation determines the thermodynamic structure of accretion disks and clearly affects the properties of the related dynamo. This effect, however, may have been overestimated in previous work, and a careful study of the role played by boundaries will be required. [ABSTRACT FROM AUTHOR]

Aims. We use observations of solar activity to constrain parameters relating to the α effect in stochastic nonlinear dynamo models. Methods. This is achieved through performing a comprehensive statistical comparison by computing probability distribution functions (PDFs) of solar activity from observations and from our simulation of α - Ω mean field dynamo model. The observational data that are used are the time history of solar activity inferred for C14 data in the past 11 000 years on a long time scale and direct observations of the sun spot numbers obtained in recent years 1795-1995 on a short time scale. Monte Carlo simulations are performed on these data to obtain probability distribution functions (PDFs) of the solar activity on both long and short time scales. These PDFs are then compared with predicted PDFs from numerical simulation of our α - Ω dynamo model, where α is assumed to have both mean α0 and fluctuating α' parts. Results. By varying the correlation time τα of fluctuating α', the ratio of the amplitude of the fluctuating to mean alpha αR = √α'2≺/α20 (where angular brackets ≺ ≻ denote ensemble average), and the ratio of poloidal to toroidal magnetic fields, we show that the results from our stochastic dynamo model can match the PDFs of solar activity when τα ϵ [22, 44] years with αR ϵ [0.21, 0.24]. [ABSTRACT FROM AUTHOR]

The induction equation of magnetohydrodynamics (MHD) is mathematically equivalent to a system of integral equations for the magnetic field in the bulk of the fluid and for the electric potential at its boundary. We summarize the recent developments concerning the numerical implementation of this scheme and its applications to various forward and inverse problems in dynamo theory and applied MHD. [ABSTRACT FROM PUBLISHER]

Context. Observations of rapidly rotating M dwarfs show a broad variety of large-scale magnetic fields encompassing dipoledominated and multipolar geometries. In dynamo models, the relative importance of inertia in the force balance, which is quantified by the local Rossby number, is known to have a strong impact on the magnetic field geometry. Aims. We aim to assess the relevance of the local Rossby number in controlling the large-scale magnetic field geometry of M dwarfs. Methods. We have explored the similarities between anelastic dynamo models in spherical shells and observations of activeM-dwarfs, focusing on field geometries derived from spectropolarimetric studies. To do so, we constructed observation-based quantities aimed to reflect the diagnostic parameters employed in numerical models. Results. The transition between dipole-dominated and multipolar large-scale fields in early to mid M dwarfs is tentatively attributed to a Rossby number threshold. We interpret late M dwarfs magnetism to result from a dynamo bistability occurring at low Rossby number. By analogy with numerical models, we expect different amplitudes of differential rotation on the two dynamo branches. [ABSTRACT FROM AUTHOR]

The paper presents a study of a solar dynamo model operating in the bulk of the convection zone with the toroidal magnetic field flux concentrated in the subsurface rotational shear layer. We explore how this type of dynamo may depend on spatial variations of turbulent parameters and on the differential rotation near the surface. The mean-field dynamo model takes into account the evolution of magnetic helicity and describes its nonlinear feedback on the generation of large-scale magnetic field by the α-effect. We compare the magnetic cycle characteristics predicted by the model, including the cycle asymmetry (associated with the growth and decay times) and the duration--amplitude relation (Waldmeier's effects), with the observed sunspot cycle properties. We show that the model qualitatively reproduces the basic properties of the solar cycles. [ABSTRACT FROM AUTHOR]

Abstract: This review provides an introduction to the generation and evolution of the Sun’s magnetic field, summarising both observational evidence and theoretical models. The eleven year solar cycle, which is well known from a variety of observed quantities, strongly supports the idea of a large-scale solar dynamo. Current theoretical ideas on the location and mechanism of this dynamo are presented. The solar cycle influences the behaviour of the global coronal magnetic field and it is the eruptions of this field that can impact on the Earth’s environment. These global coronal variations can be modelled to a surprising degree of accuracy. Recent high resolution observations of the Sun’s magnetic field in quiet regions, away from sunspots, show that there is a continual evolution of a small-scale magnetic field, presumably produced by small-scale dynamo action in the solar interior. Sunspots, a natural consequence of the large-scale dynamo, emerge, evolve and disperse over a period of several days. Numerical simulations can help to determine the physical processes governing the emergence of sunspots. We discuss the interaction of these emerging fields with the pre-existing coronal field, resulting in a variety of dynamic phenomena. [Copyright &y& Elsevier]

Abstract: The convective instability in a rapidly rotating, self-graviting sphere sets up in the form of equatorially symmetric, non-axisymmetric columnar vortices aligned with the rotation axis, carrying heat away in the cylindrical radial direction. In this study, we present numerical simulations of thermal convection and dynamo action driven by internal heating (intended to model a planetary core subject to uniform secular cooling) in a rotating sphere where, from the classical columnar convection regime, we find a spontaneous transition towards an unexpected and previously unobserved flow regime in which an equatorially antisymmetric, axisymmetric (EAA) mode strongly influences the flow. This EAA mode carries heat away along the rotation axis and is the nonlinear manifestation of the first linearly unstable axisymmetric mode. When the amplitude of the EAA mode reaches high enough values, we obtain hemispherical dynamos with one single hemisphere bearing more than 75% of the total magnetic energy at the surface of the rotating sphere. We perform the linear analysis of the involved convective modes and the nonlinear study of this hydrodynamic transition, with and without dynamo action, to obtain scaling laws for the regime boundaries. As secular cooling in a full sphere (i.e. without inner core) is a configuration which has probably been widespread in the early solar system in planetary cores, including the core of Mars, we discuss the possible implications of our results for the past martian dynamo. [Copyright &y& Elsevier]

It is shown that the saturated α-effect taken from the non-linear dynamo equations for the thin disc can still produce exponentially growing magnetic field in the case when this field does not feed back on the α. For negative dynamo number (stationary regime) stability is defined by the structure of the spectra of the linear problem for the positive dynamo numbers. The stability condition for the oscillatory solution (positive dynamo number) is also obtained and related to the phase shift of the original magnetic field, which produced saturated α and magnetic field in the kinematic regime. The results can be used to explain the similar effect observed in shell model simulations as well as in 3D dynamo models in the plane layer and sphere. [ABSTRACT FROM AUTHOR]

Numerical dynamo models are increasingly successful in modeling many features of the geomagnetic field. Moreover, they have proven to be a useful tool for understanding how the observations connect to the dynamo mechanism. More recently, dynamo simulations have also ventured to explain the surprising diversity of planetary fields found in our solar system. Here, we describe the underlying model equations, concentrating on the Boussinesq approximations, briefly discuss the numerical methods, and give an overview of existing model variations. We explain how the solutions depend on the model parameters and introduce the primary dynamo regimes. Of particular interest is the dependence on the Ekman number which is many orders of magnitude too large in the models for numerical reasons. We show that a minor change in the solution seems to happen at $\mbox {E}=3\mbox {$\times 10^{-6}$}$ whose significance, however, needs to be explored in the future. We also review three topics that have been a focus of recent research: field reversal mechanisms, torsional oscillations, and the influence of Earth’s thermal mantle structure on the dynamo. Finally we discuss the possibility of tidally or precession driven planetary dynamos. [ABSTRACT FROM AUTHOR]

Abstract: A recent dynamo model for Mercury assumes that the upper part of the planet''s fluid core is thermally stably stratified because the temperature gradient at the core–mantle boundary is subadiabatic. Vigorous convection driven by a superadiabatic temperature gradient at the boundary of a growing solid inner core and by the associated release of light constituents takes place in a deep sub-layer and powers a dynamo. These models have been successful at explaining the observed weak global magnetic field at Mercury''s surface. They have been based on the concept of codensity, which combines thermal and compositional sources of buoyancy into a single variable by assuming the same diffusivity for both components. Actual diffusivities in planetary cores differ by a large factor. To overcome the limitation of the codensity model, we solve two separate transport equations with different diffusivities in a double diffusive dynamo model for Mercury. When temperature and composition contribute comparable amounts to the buoyancy force, we find significant differences to the codensity model. In the double diffusive case convection penetrates the upper layer with a net stable density stratification in the form of finger convection. Compared to the codensity model, this enhances the poloidal magnetic field in the nominally stable layer and outside the core, where it becomes too strong compared to observation. Intense azimuthal flow in the stable layer generates a strong axisymmetric toroidal field. We find in double diffusive models a surface magnetic field of the observed strength when compositional buoyancy plays an inferior role for driving the dynamo, which is the case when the sulphur concentration in Mercury''s core is only a fraction of a percent. [Copyright &y& Elsevier]

Photospheric ephemeral regions (EPRs) cover the Sun like a magnetic carpet. From this, we update the Babcock – Leighton solar dynamo. Rather than sunspot fields appearing in the photosphere de novo from eruptions originating in the deep interior, we consider that sunspots form directly in the photosphere by a rapid accumulation of like-sign field from EPRs. This would only occur during special circumstances: locations and times when the temperature structure is highly superadiabatic and contains a large subsurface horizontal magnetic field (only present in the Sun’s lower latitudes). When these conditions are met, superadiabatic percolation occurs, wherein an inflow and downflow of gas scours the surface of EPRs to form active regions. When these conditions are not met, magnetic elements undergo normal percolation, wherein magnetic elements move about the photosphere in Brownian-type motions. Cellular automata (CA) models are developed that allow these processes to be calculated and thereby both small-scale and large-scale models of magnetic motions can be obtained. The small-scale model is compared with active region development and Hinode observations. The large-scale CA model offers a solar dynamo, which suggests that fields from decaying bipolar magnetic regions (BMRs) drift on the photosphere driven by subsurface magnetic forces. These models are related to observations and are shown to support Waldmeier’s findings of an inverse relationship between solar cycle length and cycle size. Evidence for significant amounts of deep magnetic activity could disprove the model presented here, but recent helioseismic observations of “butterfly patterns” at depth are likely just a reflection of surface activity. Their existence seems to support the contention made here that the field and flow separate, allowing cool, relatively field-free downdrafts to descend with little field into the nether worlds of the solar interior. There they heat by compression to form a hot solar-type Santa Ana wind deep below active regions. [ABSTRACT FROM AUTHOR]

Abstract: The conventional magnetic induction equation that governs hydromagnetic dynamo action is transformed into an equivalent integral equation system. An advantage of this approach is that the computational domain is restricted to the region occupied by the electrically conducting fluid and to its boundary. This integral equation approach is first employed to simulate kinematic dynamos excited by Beltrami-like flows in a finite cylinder. The impact of externally added layers around the cylinder on the onset of dynamo actions is investigated. Then it is applied to simulate dynamo experiments within cylindrical geometry including the “von Kármán sodium” (VKS) experiment and the Riga dynamo experiment. A modified version of this approach is utilized to investigate magnetic induction effects under the influence of externally applied magnetic fields which is also important to measure the proximity of a given dynamo facility to the self-excitation threshold. [Copyright &y& Elsevier]

The existence of a dynamo effect in a simplified magnetohydrodynamic model of turbulence is considered when the magnetic Prandtl number approaches zero or infinity. The magnetic field is interacting with an incompressible Kraichnan-Kazantsev model velocity field which incorporates also a viscous cutoff scale. An approximate system of equations in the different scaling ranges can be formulated and solved, so that the solution tends to the exact one when the viscous and magnetic-diffusive cutoffs approach zero. In this approximation we are able to determine analytically the conditions for the existence of a dynamo effect and give an estimate of the dynamo growth rate. Among other things we show that in the large magnetic Prandtl number case the dynamo effect is always present. Our analytical estimates are in good agreement with previous numerical studies of the Kraichnan-Kazantsev dynamo by Vincenzi (J. Stat. Phys. 106:1073–1091, ). [ABSTRACT FROM AUTHOR]

Abstract: The Solar Magnetic Field Telescope (SMFT) at the Huairou Solar Observing Station of the National Astronomical Observatory has been obtaining photospheric vector magnetograms on a daily basis for more than 20years. In this paper we first introduce our magnetograph and our data reduction routine. Then we focus on what we can learn from these vector magnetic field measurements about the magnetic non-potentiality of active regions. Derived physical quantities, such as shear angle, α value and current helicity, are good indicators of magnetic helicity. By studying values and evolutions of these physical quantities, we get a glimpse of the dynamo process in the solar interior. By examining the evolution of these quantities we can also learn what are the favorable conditions for coronal eruptions such as flares and coronal mass ejections. [Copyright &y& Elsevier]

The present article considers dynamo action in flows driven by Ekman and Taylor–Couette instabilities. The system comprises a rotating, horizontal plane layer of electrically conducting fluid. The top of the layer is at rest, while the base has a given velocity that drives a net shear across the layer. The fluid flow in the system is parameterised by a Reynolds number Re, the square root of the Taylor number t, and the angle???between the rotation vector and the vertical. When the rotation vector has a vertical component,???? p/2, then in the limit of large t, the shear takes the form of an thin Ekman layer localised at the bottom boundary. This may be subject to a hydrodynamic Ekman instability which for moderate Re generates steady cat's eyes in a co-moving frame. The flow gives dynamo action, amplifying magnetic fields in the form of sheets concentrated on hyperbolic points and their unstable manifolds. At greater Re, the cat's eyes become three-dimensional, and time-dependent amplifying fields with a more irregular structure. In nonlinear regimes the magnetic field and fluid flow show a relaxation oscillation for moderate Re, and for higher values, oscillatory fluid flows sustain tubes of magnetic field. When the rotation vector is entirely horizontal, ??=p /2, the shear driven is uniform across the layer. This can become subject to a primary Taylor–Couette instability driving a cellular flow, and with a further increase of Re, there is a secondary bifurcation to steady, wavy rolls. This flow supports a dynamo and its properties are studied in kinematic and nonlinear regimes. [ABSTRACT FROM AUTHOR]

The growth of magnetic field is considered in the stretch–fold–shear map in the limit of weak diffusion. Numerical results are given for insulating, perfectly conducting and periodic boundary conditions. The resulting eigenvalue branches and magnetic fields are related to eigenvalue branches for perfect dynamo action, obtained for zero diffusion using a complex variable formulation. The effect of diffusion on these perfect dynamo modes depends on their structure, growth rate and the diffusive boundary conditions employed. In some cases, the effect of diffusion is a small perturbation, giving a correction going to zero in the limit of weak diffusion, with a scaling exponent given analytically. In other cases weak diffusion can entirely destroy a perfect dynamo branch. Diffusive boundary layers can also generate entirely new branches. These different cases are elucidated, and within the framework of the asymptotic approximations used (which do not constitute a rigorous proof), it is seen that for all three boundary conditions employed, the stretch–fold–shear map is a fast dynamo. [ABSTRACT FROM AUTHOR]

In this article we address the problem of magnetic field generation and front propagation in turbulent electrically conducting fluids, involving the velocity with finite correlations times and small magnetic diffusivity. We suggest an integro-differential dynamo equation which involves the non-local terms for both the dynamo source α -term and turbulent transport of the mean magnetic field. We derive a set of formulas which allows us to determine the rate of magnetic front propagation in galaxies valid for arbitrary memory kernels. We illustrate the general results through the use of the exponential correlation functions for memory kernels and 'no-z' approximation. We find that the memory effects have strong influence on for both the growth rate and propagation speed. We perform numerical simulations of exterior front speed, and find that the transport memory essentially decreases the propagation rate. [ABSTRACT FROM AUTHOR]