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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]

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]

ABSTRACT We develop and subsequently explore the solution space of a simple flux transport dynamo model that incorporates a time-dependent large-scale meridional circulation. Based on recent observations, we prescribed an analytical form for the amplitude of this circulation and study its impact in the evolution of the magnetic field. We find that cyclic variations in the amplitude and frequency of the meridional flow affect the strength of the solar cycle. Variations in the amplitude of the fluctuations influence the shape of the solar cycle but are only relevant to the cycle's strength variations when they occur at a frequency different from or out of phase of the solar cycle's. [ABSTRACT FROM AUTHOR]

ABSTRACT The transfer of magnetic chirality in solar active regions is related to the emerging magnetic flux ropes generated in the subatmosphere. This analysis has been presented based on the calculation of the injection of magnetic helicity at the solar surface. As the long-term evolution of the accumulated magnetic helicity is followed, it is found that the transfer of reversal magnetic helicity of active regions is a complex process, and is not monotonic with the same sign. It is found that the dominant contribution of helicity occurs mainly in the fast-developing stage of active regions. By considering the hemispheric trends of magnetic helicity, it is proposed that the reversal helicity in solar active regions has two possible causes: local generation in the convection zone, and trans-equatorial processes in the subatmosphere. In addition to the mirror-symmetrical reverse of twisted magnetic field in the convection zone, the possibility of a trans-equatorial process is discussed in this paper. [ABSTRACT FROM AUTHOR]

ABSTRACT Observations of magnetism in very low mass stars recently made important progress, revealing characteristics that are now to be understood in the framework of dynamo theory. In parallel, there is growing evidence that dynamo processes in these stars share many similarities with planetary dynamos. We investigate the extent to which the weak-field versus strong-field bistability predicted for the geodynamo can apply to recent observations of two groups of very low mass fully-convective stars sharing similar stellar parameters but generating radically different types of magnetic fields. Our analysis is based on previously published spectropolarimetric and spectroscopic data. We argue that these can be interpreted in the framework of weak- and strong-field dynamos. [ABSTRACT FROM AUTHOR]

Recent numerical and analytical work has identified a possible new source of mean-field dynamo action, caused by fluctuations in the α-effect interacting with a large-scale shear. This process gives rise to a new source term in the averaged induction equation. Essentially the same term arises from the shear-current effect. This paper investigates the consequences of the new term in a two-dimensional solar dynamo model, in spherical geometry, with a realistic large-scale shear. In general, it is found that the new source term leads to an increase in the dynamo cycle period, although the details of this depend crucially upon the spatial variation of the fluctuations in the α-effect (or the shear-current term). Steady magnetic fields are generated when the new term plays a dominant role in the dynamo process. [ABSTRACT FROM AUTHOR]

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]

Using a one-dimensional -dynamo model appropriate to galaxies, we study the possibility of dynamo action driven by a stochastic α-effect and shear. To determine the field evolution, one needs to examine a large number of different realizations of the stochastic component of α. The net growth or decay of the field depends not only on the dynamo parameters but also on the particular realization, the correlation time of the stochastic α compared to turbulent diffusion time-scale and the time over which the system is evolved. For dynamos where both a coherent and fluctuating α are present, the stochasticity of α can help alleviate catastrophic dynamo quenching, even in the absence of helicity fluxes. One can obtain final field strengths up to a fraction ∼0.01 of the equipartition field for dynamo numbers , while fields comparable to require much larger degree of α-fluctuations or shear. This type of dynamo may be particularly useful for amplifying fields in the central regions of disc galaxies. [ABSTRACT FROM AUTHOR]

Using direct simulations, weakly non-linear theory and non-linear mean-field theory, it is shown that the quenched velocity field of a saturated non-linear dynamo can itself act as a kinematic dynamo. The flow is driven by a forcing function that would produce a Roberts flow in the absence of a magnetic field. This result confirms an analogous finding by Cattaneo & Tobias for the more complicated case of turbulent convection, suggesting that this may be a common property of non-linear dynamos; see also the talk given online at the Kavli Institute for Theoretical Physics ( ). It is argued that this property can be used to test non-linear mean-field dynamo theories. [ABSTRACT FROM AUTHOR]

The generation of a magnetic field in numerical simulations of the geodynamo is an intrinsically 3-D and time-dependent phenomenon. The concept of magnetic field lines and the frozen-flux approximation can provide insight into such systems, but a suitable visualization method is required. This paper presents results obtained using the Dynamical Magnetic Field line Imaging (DMFI) technique, which is a representation of magnetic field lines accounting for their local magnetic energy, together with an algorithm for the time evolution of their anchor points. The DMFI illustrations are consistent with previously published dynamo mechanisms, and allow further investigation of spatially and temporally complex systems. We highlight three types of magnetic structures: (i) magnetic cyclones and (ii) magnetic anticyclones are expelled by, but corotate with axial flow vortices; (iii) magnetic upwellings are amplified by stretching and advection within flow upwellings, and show structural similarity with helical plumes found in rotating hydrodynamic experiments. While magnetic anticyclones are responsible for the regeneration of a stable axial dipole, here we show that excursions and reversals of the dipole axis are caused by the emergence of magnetic upwellings, which amplify and transport a generally multipolar magnetic field from the inner to the outer boundary of the models. Geomagnetic observations suggest the presence of magnetic structures similar to those found in our models; thus, we discuss how our results may pertain to Earth's core dynamo processes. In order to make DMFI a standard tool for numerical dynamo studies, a public software package is available upon request to the authors (supplementary material is available at: ). [ABSTRACT FROM AUTHOR]

Using numerical simulations at moderate magnetic Reynolds numbers up to 220, it is shown that in the kinematic regime, isotropic helical turbulence leads to an α-effect and a turbulent diffusivity whose values are independent of the magnetic Reynolds number, Rm, provided Rm exceeds unity. These turbulent coefficients are also consistent with expectations from the first-order smoothing approximation. For small values of Rm, α and turbulent diffusivity are proportional to Rm. Over finite time-intervals, meaningful values of α and turbulent diffusivity can be obtained even when there is small-scale dynamo action that produces strong magnetic fluctuations. This suggests that the fields generated by the small-scale dynamo do not make a correlated contribution to the mean electromotive force. [ABSTRACT FROM AUTHOR]

We consider a conventional stellar -dynamo with dynamo generators localized in two spherical shells separated by a passive layer. The signs of the α-effect as well as rotational shear in the dynamo active layers can be chosen to give dynamo waves that propagate in opposite directions (poleward and equatorward) if the layers are considered separately in the framework of the Parker migratory dynamo. In a sequence of numerical experiments we show that the variety of dynamo-generated magnetic configurations in the system under discussion is quite rich. We identify the possibility of almost independent dynamo waves existing in the two layers as well as enslavement of one layer by the other, and of activity waves generated by a joint action of the two layers. We suggest some qualitative explanations of the behaviour and discuss also the limited nature of these explanations. This variety of phenomena suggests previously underexploited freedoms to understand how predictions of dynamo theory may accommodate the observed solar and stellar activity phenomenology. [ABSTRACT FROM AUTHOR]

More and more observations are showing a relatively weak, but persistent, non-axisymmetric magnetic field co-existing with the dominant axisymmetric field on the Sun. Its existence indicates that the non-axisymmetric magnetic field plays an important role in the origin of solar activity. A linear non-axisymmetric dynamo model is derived to explore the characteristics of the axisymmetric and the first non-axisymmetric modes and to provide a theoretical basis with which to explain the ‘active longitude’, ‘flip-flop’ and other non-axisymmetric phenomena. The model consists of an updated solar internal differential rotation, a turbulent diffusivity varying with depth, and an α-effect working at the tachocline in a rotating spherical system. The difference between the and the models and the conditions that favour the non-axisymmetric modes under solar-like parameters are also presented. [ABSTRACT FROM AUTHOR]

We present a simple semi-analytical model of non-linear, mean field galactic dynamos and use it to study the effects of various magnetic helicity fluxes. The dynamo equations are reduced using the ‘no- z’ approximation to a non-linear system of ordinary differential equations in time; we demonstrate that the model reproduces accurately earlier results, including those where non-linear behaviour is driven by a magnetic helicity flux. We discuss the implications and interplay of two types of magnetic helicity flux, one produced by advection (e.g. due to the galactic fountain or wind) and the other, arising from anisotropy of turbulence as suggested by Vishniac & Cho. We argue that the latter is significant if the galactic differential rotation is strong enough: in our model, for in terms of the corresponding turbulent magnetic Reynolds number. We confirm that the intensity of gas outflow from the galactic disc optimal for the dynamo action is close to that expected for normal spiral galaxies. The steady-state strength of the large-scale magnetic field supported by the helicity advection is still weaker than that corresponding to equipartition with the turbulent energy. However, the Vishniac–Cho helicity flux can boost magnetic field further to achieve energy equipartition with turbulence. For stronger outflows that may occur in starburst galaxies, the Vishniac–Cho flux can be essential for the dynamo action. However, this mechanism requires a large-scale magnetic field of at least to be launched, so that it has to be preceded by a conventional dynamo assisted by the advection of magnetic helicity by the fountain or wind. [ABSTRACT FROM AUTHOR]

The backreaction of the Lorentz force on the α-effect is studied in the limit of small magnetic and fluid Reynolds numbers, using the first-order smoothing approximation (FOSA) to solve both the induction and momentum equations. Both steady and time-dependent forcings are considered. In the low Reynolds number limit, the velocity and magnetic fields can be expressed explicitly in terms of the forcing function. The non-linear α-effect is then shown to be expressible in several equivalent forms in agreement with formalisms that are used in various closure schemes. On one hand, one can express α completely in terms of the helical properties of the velocity field as in traditional FOSA, or, alternatively, as the sum of two terms, a so-called kinetic α-effect and an oppositely signed term proportional to the helical part of the small-scale magnetic field. These results hold for both steady and time-dependent forcing at arbitrary strength of the mean field. In addition, the τ-approximation is considered in the limit of small fluid and magnetic Reynolds numbers. In this limit, the τ closure term is absent and the viscous and resistive terms must be fully included. The underlying equations are then identical to those used under FOSA, but they reveal interesting differences between the steady and time-dependent forcing. For steady forcing, the correlation between the forcing function and the small-scale magnetic field turns out to contribute in a crucial manner to determine the net α-effect. However for delta-correlated time-dependent forcing, this force–field correlation vanishes, enabling one to write α exactly as the sum of kinetic and magnetic α-effects, similar to what one obtains also in the large Reynolds number regime in the τ-approximation closure hypothesis. In the limit of strong imposed fields, B0, we find for delta-correlated forcing, in contrast to the well-known behaviour for the case of a steady forcing. The analysis presented here is also shown to be in agreement with numerical simulations of steady as well as random helical flows. [ABSTRACT FROM AUTHOR]

We test the quality of a new core flow imaging method that incorporates constraints on flow helicity, using synthetic magnetic secular variation data from 3-D self-consistent numerical dynamo models. Comparison with the dynamo model flows reveals that our imaging method delineates most of the main large-scale flow features, both in pattern and magnitude. The dynamo model flows are characterized by high-latitude vortices, some equatorial symmetry, columnar convection and a significant amount of flow along radial magnetic field contours. Our inversion method correctly images these aspects of the flows. The correlation coefficient between the dynamo velocity and the imaged velocity exceeds 0.5 in cases with large-scale flow and magnetic field pattern, but degrades substantially in more complex cases when the scale of the secular variation is small. The magnitude of the imaged velocity depends on the a priori-assumed ratio of tangential divergence to radial vorticity k, in some resemblance to the damping parameter in spectral methods, although with our method the misfit is insensitive to k-values. Including tangential magnetic diffusion in core flow inversion improves the quality of the imaged velocity pattern. The largest artefacts in the imaged velocities are due to unmodelled radial magnetic diffusion and truncation of the input magnetic field. [ABSTRACT FROM AUTHOR]

In an attempt to determine the outer scale of turbulence driven by localized sources, such as supernova explosions in the interstellar medium, we consider a forcing function given by the gradient of Gaussian profiles localized at random positions. Different coherence times of the forcing function are considered. In order to isolate the effects specific to the nature of the forcing function, we consider the case of a polytropic equation of state and restrict ourselves to forcing amplitudes such that the flow remains subsonic. When the coherence time is short, the outer scale agrees with the half-width of the Gaussian. Longer coherence times can cause extra power at large scales, but this would not yield power-law behaviour at scales larger than that of the expansion waves. At scales smaller than the scale of the expansion waves the spectrum is close to power law with a spectral exponent of −2. The resulting flow is virtually free of vorticity. Viscous driving of vorticity turns out to be weak and self-amplification through the non-linear term is found to be insignificant. No evidence for small-scale dynamo action is found in cases where the magnetic induction equation is solved simultaneously with the other equations. [ABSTRACT FROM AUTHOR]

The term ‘dynamo’ means different things to the laboratory fusion plasma and astrophysical plasma communities. To alleviate the resulting confusion and to facilitate interdisciplinary progress, we pinpoint conceptual differences and similarities between laboratory plasma dynamos and astrophysical dynamos. We can divide dynamos into three types: 1. magnetically dominated helical dynamos which sustain a large-scale magnetic field against resistive decay and drive the magnetic geometry towards the lowest energy state, 2. flow-driven helical dynamos which amplify or sustain large-scale magnetic fields in an otherwise turbulent flow and 3. flow-driven non-helical dynamos which amplify fields on scales at or below the driving turbulence. We discuss how all three types occur in astrophysics whereas plasma confinement device dynamos are of the first type. Type 3 dynamos require no magnetic or kinetic helicity of any kind. Focusing on Types 1 and 2 dynamos, we show how different limits of a unified set of equations for magnetic helicity evolution reveal both types. We explicitly describe a steady-state example of a Type 1 dynamo, and three examples of Type 2 dynamos: (i) closed volume and time dependent; (ii) steady state with open boundaries; (iii) time dependent with open boundaries. [ABSTRACT FROM AUTHOR]

The Archontis dynamo was the first stationary dynamo discovered which saturates with almost equal magnetic and kinetic energies in the limit of large Reynolds numbers. In this paper we present two further examples, one based on a series of numerical calculations and the other on the analytic rotor dynamos of Herzenberg. The forcing and flow in these new examples lack some of the symmetries of the Archontis dynamo are therefore more generic. The saturation mechanism is thus not a unique property of the Archontis dynamo. For the numerical solutions, we also have investigated the structure and stability of the flow and field near the stagnation points and those streamlines which enter and leave them. These structures play an important part in the operation of the dynamo mechanism, and the way they interact with one another is mirrored in the analytic example based on the Herzenberg rotors. [ABSTRACT FROM AUTHOR]

We present a novel application of a finite-volume technique to the numerical simulation of thermal convection within a rapidly rotating spherical shell. The performance of the method is extensively tested against a known standard solution at moderate Ekman number. Models at lower Ekman number demonstrate the potential of the method in a parameter range more appropriate to the flow in the molten metallic core of planetary interiors. In addition we present results for the magnetohydrodynamic dynamo problem. In order to avoid the need to solve for the magnetic field in the exterior, we use an approximate magnetic boundary condition. Compared with the geophysically relevant case of insulating boundaries, it is shown that the qualitative structures of the flow and the magnetic field are similar. However, a more quantitative comparison indicates that mean flow velocity and mean magnetic field strength are affected by the boundary conditions by about 20 per cent. [ABSTRACT FROM AUTHOR]

Focuses on the development of a four-scale helical dynamo theory for helical magnetic dynamo spectra. Dominance of the forcing scale; Completion by the end of the kinematic growth regime of the large-scale field; Implication for fractionally helical turbulence.

Fausto Cattaneo and David W Hughes delve beneath the surface of the Sun with numerical models of turbulent convection. Although magnetic dynamo action is traditionally associated with rotation, fast dynamo theory shows that chaotic flows, even without rotation, can act as efficient small-scale dynamos. Indeed, numerical simulations suggest that granular and supergranular convection may generate locally a substantial part of the field in the quiet photosphere. [ABSTRACT FROM AUTHOR]

We analyse the role of a fluctuating α-effect in αΩ dynamo models, and show that there is a mechanism for magnetic field generation, valid at large-scale separation, deriving from the interaction of mean shear and a fluctuating α-effect. We show that this effect can act as a dynamo even in the absence of a mean α-effect, and that the time-scale for dynamo waves is strongly affected by the presence of fluctuations. [ABSTRACT FROM AUTHOR]