With a non local shell model of magnetohydrodynamic turbulence we investigate numerically the turbulent dynamo action for low and high magnetic Prandtl numbers ($Pm$). The results obtained in the kinematic regime and along the way to dynamo saturation are understood in terms of a phenomenological approach based on the local ($Pm\ll 1$) or non local ($Pm\gg 1$) nature of the energy transfers. In both cases the magnetic energy grows at small scale and saturates as an inverse `` cascade ''.
Mean field dynamos may explain the origin of large scale magnetic fields of galaxies, but controversy arises over the extent of dynamo quenching by the growing field. Here we explain how apparently conflicting results may be mutually consistent, by showing the role of magnetic helicity conservation and boundary terms usually neglected. We estimate the associated magnetic energy flowing out of the Galaxy but emphasize that the mechanism of field escape needs to be addressed.
We present statistically robust observational evidence which imposes new limits on dynamo saturation in young solar-type stars. These are inferred from the increasing amplitude of the V-band optical flux with rotation, caused by the filling of the disc with surface spots in a non-axisymmetric pattern. Assuming spot coverage acts as a tracer of the total magnetic surface flux we find that the magnetic activity saturates at a level at least 6 -- 10 times greater than that inferred from chromospheric and transition line indicators. We suggest that these new limits imply a minimum rotation for sat…
A relativistic collisionless shock propagating into an unmagnetized medium leaves behind a strong large-scale magnetic field. This seems to follow from two assumptions: (i) GRB afterglows are explained by synchrotron emission of a relativistic shock, (ii) magnetic field can't exist on microscopic scales only, it would decay by phase space mixing. Assumption (i) is generally accepted because of an apparent success of the shock synchrotron phenomenological model of GRB afterglow. Assumption (ii) is confirmed in this work by a low-dimensional numerical simulation. One may hypothesize that relativ…
In this paper we discuss a dynamic flux-transport dynamo model that includes the feedback of the induced magnetic field on differential rotation and meridional flow. We consider two different approaches for the feedback: meanfield Lorentz force and quenching of transport coefficients such as turbulent viscosity and heat conductivity. We find that even strong feedback on the meridional flow does not change the character of the flux-transport dynamo significantly; however it leads to a significant reduction of differential rotation. To a large degree independent from the dynamo parameters, the s…
After the dynamo experiment in November 1999 had shown magnetic field self-excitation in a spiraling liquid metal flow, in a second series of experiments emphasis was placed on the magnetic field saturation regime as the next principal step in the dynamo process. The dependence of the strength of the magnetic field on the rotation rate is studied. Various features of the saturated magnetic field are outlined and possible saturation mechanisms are discussed.
In the context of astrophysical dynamos we illustrate that the no-cosines flow, with zero mean helicity, can drive fast dynamo action and study the dynamo's mode of operation during both the linear and non-linear saturation regime: It turns out that in addition to a high growth rate in the linear regime, the dynamo saturates at a level significantly higher than normal turbulent dynamos, namely at exact equipartition when the magnetic Prandtl number is on the order of unity. Visualization of the magnetic and velocity fields at saturation will help us to understand some of the aspects of the non…
The generation of large-scale magnetic fields is generically accompanied by the more rapid growth of small-scale fields. The growing Lorentz force due to these fields back reacts on the turbulence to saturate the mean-field and small-scale dynamos. For the mean-field dynamo, in a quasi-linear treatment of this saturation, it is generally thought that, while the alpha-effect gets renormalised and suppressed by non-linear effects, the turbulent diffusion is left unchanged. We show here that this is not true and the effect of the Lorentz forces, is also to generate additional non-linear hyperdiff…
We supplement the mean field dynamo growth equation with the total magnetic helicity evolution equation. This provides an explicitly time dependent model for alpha quenching in dynamo theory. For dynamos without shear, this approach accounts for the observed large scale field growth and saturation in numerical simulations. After a significant kinematic phase, the dynamo is resistively quenched, i.e. the saturation time depends on the microscopic resistivity. This is independent of whether or not the turbulent diffusivity is resistively quenched. We find that the approach is also successful for…
Dynamo action is investigated in simulations of locally isotropic and homogeneous turbulence in a slab between open boundaries. It is found that a `pseudo-vacuum' boundary condition (where the field is vertical) leads to strong helicity fluxes which significantly reduce the amplitude of the resulting large scale field. On the other hand, if there is a conducting halo outside the dynamo-active region the large scale field amplitude can reach larger values, but the time scale after which this field is reached increases linearly with the magnetic Reynolds number. In both cases most of the helicit…
The theory of large scale dynamos is reviewed with particular emphasis on the magnetic helicity constraint in the presence of closed and open boundaries. In the presence of closed or periodic boundaries, helical dynamos respond to the helicity constraint by developing small scale separation in the kinematic regime, and by showing long time scales in the nonlinear regime where the scale separation has grown to the maximum possible value. A resistively limited evolution towards saturation is also found at intermediate scales before the largest scale of the system is reached. Larger aspect ratios…
We study the effects of vertical outflows on mean-field dynamos in disks. These outflows could be due to thermal winds or magnetic buoyancy. We analyse numerical solutions of the nonlinear mean-field dynamo equations using a two-dimensional finite-difference model. Contrary to expectations, a modest vertical velocity can enhance dynamo action. This can lead to super-exponential growth of the magnetic field and to higher magnetic energies at saturation in the nonlinear regime.
The growth and saturation of magnetic field in conducting turbulent media with large magnetic Prandtl numbers are investigated. This regime is very common in low-density hot astrophysical plasmas. During the early (kinematic) stage, weak magnetic fluctuations grow exponentially and concentrate at the resistive scale, which lies far below the hydrodynamic viscous scale. The evolution becomes nonlinear when the magnetic energy is comparable to the kinetic energy of the viscous-scale eddies. A physical picture of the ensuing nonlinear evolution of the MHD dynamo is proposed. Phenomenological cons…
The current understanding of astrophysical magnetic fields is reviewed, focusing on their generation and maintenance by turbulence. In the astrophysical context this generation is usually explained by a self-excited dynamo, which involves flows that can amplify a weak 'seed' magnetic field exponentially fast. Particular emphasis is placed on the nonlinear saturation of the dynamo. Analytic and numerical results are discussed both for small scale dynamos, which are completely isotropic, and for large scale dynamos, where some form of parity breaking is crucial. Central to the discussion of larg…
We study a simple model for the solar dynamo in the framework of the Parker migratory dynamo, with a nonlinear dynamo saturation mechanism based on magnetic helicity conservation arguments. We find a parameter range in which the model demonstrates a cyclic behaviour with properties similar to that of Parker dynamo with the simplest form of algebraic alpha-quenching. We compare the nonlinear current helicity evolution in this model with data for the current helicity evolution obtained during 10 years of observations at the Huairou Solar Station of China. On one hand, our simulated data demonstr…
Magnetic helicity effects are discussed in laboratory and astrophysical settings. First, dynamo action in Taylor-Green flows is discussed for different boundary conditions. However, because of the lack of scale separation with respect to the container, no large scale field is being produced and there is no resistively slow saturation phase as otherwise expected. Second, the build-up of a large scale field is demonstrated in a simulation where a localized magnetic eddy produces field on a larger scale if the eddy possesses a swirl. Such a set-up might be realizable experimentally through coils.…
We report an extensive numerical study of the small-scale turbulent dynamo at large magnetic Prandtl numbers Pm. A Pm scan is given for the model case of low-Reynolds-number turbulence. We concentrate on three topics: magnetic-energy spectra and saturation levels, the structure of the field lines, and the field-strength distribution. The main results are (1) the folded structure (direction reversals at the resistive scale, field lines curved at the scale of the flow) persists from the kinematic to the nonlinear regime; (2) the field distribution is self-similar and appears to be lognormal duri…
We present results from numerical simulations of nonlinear MHD dynamo action produced by three-dimensional flows that become turbulent for high values of the fluid Reynolds number. The magnitude of the forcing function driving the flow is allowed to evolve with time in such way as to maintain an approximately constant velocity amplitude (and average kinetic energy) when the flow becomes hydrodynamically unstable. It is found that the saturation level of the dynamo increases with the fluid Reynolds number (at constant magnetic Prandtl number), and that the average growth rate approaches an asym…
The effect of shear on the growth of large scale magnetic fields in helical turbulence is investigated. The resulting large-scale magnetic field is also helical and continues to evolve, after saturation of the small scale field, on a slow resistive time scale. This is a consequence of magnetic helicity conservation. Because of shear, the time scale needed to reach an equipartition-strength large scale field is shortened proportionally to the ratio of the resulting toroidal to poloidal large scale fields.
(Abriged) The magnetorotational instability (MRI) is believed to be an efficient way to transport angular momentum in accretion discs. It has also been suggested as a way to amplify magnetic fields in discs, the instability acting as a nonlinear dynamo. Recent numerical work has shown that a large-scale magnetic field, which is predominantly azimuthal, can be sustained by motions driven by the MRI of this same field. Following this idea, we present an analytical calculation of the MRI in the presence of an azimuthal field with a non-trivial vertical structure. We find that the mean radial EMF …
Context: Observations indicate that the `quiet' solar photosphere outside active regions contains considerable amounts of magnetic energy and magnetic flux, with mixed polarity on small scales. The origin of this flux is unclear. Aims: We test whether local dynamo action of the near-surface convection (granulation) can generate a significant contribution to the observed magnetic flux. Methods: We have carried out MHD simulations of solar surface convection, including the effects of strong stratification, compressibility, partial ionization, radiative transfer, as well as an open lower boundary…
We formulate a solvable model that describes generation and saturation of mean magnetic field in a dynamo with kinetic helicity, in the limit of large magnetic Prandtl number. This model is based on the assumption that the stochastic part of the velocity field is Gaussian and white in time (the Kazantsev-Kraichnan ensemble), while the regular part describing the back reaction of the magnetic field is chosen from balancing the viscous and Lorentz stresses in the MHD Navier-Stokes equation. The model provides an analytical explanation for previously obtained numerical results.
The origin of cosmic magnetism is an issue of fundamental importance in astrophysics. We review here some of the ideas of how large scale magnetic fields in the universe, particularly in galaxies and galaxy clusters could arise. The popular paradigm involves the generation of a seed magnetic field followed by turbulent dynamo amplification of the seed field. We first outline various seed field generation mechanisms including Biermann batteries. These in general give a field much smaller than the observed field and so they require further amplification by dynamo action. The basic idea behind fl…
Our attention focuses on the stochastic dynamo equation with non-normal operator that give an insight into the role of stochastics and non-normality in the galactic magnetic field generation. The main point of this Letter is a discussion of the generation of a large-scale magnetic field that cannot be explained by traditional linear eigenvalue analysis. We present a simple stochastic model for the thin-disk axisymmetric $αΩ$ dynamo involving three factors: (a) the non-normality generated by differential rotation, (b) the nonlinearity reflecting how the magnetic field affects the turbulent dyna…
The self-excitation of magnetic field by a spiral Couette flow between two coaxial cylinders is considered. We solve numerically the fully nonlinear, three-dimensional MHD equations for magnetic Prandtl numbers Pm (ratio of kinematic viscosity to magnetic diffusivity) between 0.14 and 10 and kinematic and magnetic Reynolds numbers up to about 2000. In the initial stage of exponential field growth (kinematic dynamo regime), we find that the dynamo switches from one distinct regime to another as the radial width δr_B$ of the magnetic field distribution becomes smaller than the separation of the …
Dynamo action owing to helically forced turbulence and large-scale shear is studied using direct numerical simulations. The resulting magnetic field displays propagating wave-like behavior. This behavior can be modelled in terms of an αΩdynamo. In most cases super-equipartition fields are generated. By varying the fraction of helicity of the turbulence the regeneration of poloidal fields via the helicity effect (corresponding to the α-effect) is regulated. The saturation level of the magnetic field in the numerical models is consistent with a linear dependence on the ratio of the fractional he…
Magnetic field strengths inferred for relativistic outflows including gamma-ray bursts (GRB) and active galactic nuclei (AGN) are larger than naively expected by orders of magnitude. We present three-dimensional relativistic magnetohydrodynamics (MHD) simulations demonstrating amplification and saturation of magnetic field by a macroscopic turbulent dynamo triggered by the Kelvin-Helmholtz shear instability. We find rapid growth of electromagnetic energy due to the stretching and folding of field lines in the turbulent velocity field resulting from non-linear development of the instability. Us…
We develop a new nonlinear mean field dynamo theory that couples field growth to the time evolution of the magnetic helicity and the turbulent electromotive force, $\emfb$. We show that the difference between kinetic and current helicities emerges naturally as the growth driver when the time derivative of $\emfb$ is coupled into the theory. The solutions predict significant field growth in a kinematic phase and a saturation rate/strength that is magnetic Reynolds number dependent/independent in agreement with numerical simulations. The amplitude of early time oscillations provides a diagnostic…
The magnetic helicity has paramount significance in nonlinear saturation of galactic dynamo. We argue that the magnetic helicity conservation is violated at the lepton stage in the evolution of early Universe. As a result, a cosmological magnetic field which can be a seed for the galactic dynamo obtains from the beginning a substantial magnetic helicity which has to be taken into account in the magnetic helicity balance at the later stage of galactic dynamo.
It is shown that a dynamo can operate in an Active Galactic Nuclei accretion disk due to the Keplerian shear and due to the helical motions of expanding and twisting plumes of plasma heated by many star passages through the disk. Each plume rotates a fraction of the toroidal flux into poloidal flux, always in the same direction, through a finite angle, and proportional to its diameter. The predicted growth rate of poloidal magnetic flux, based upon two analytic approaches and numerical simulations, leads to a rapid exponentiation of a seed field, \sim 0.1 to \sim 0.01 per Keplerian period of t…
Observational and theoretical investigations provide evidence for non-uniform spot and magnetic flux distributions on rapidly rotating stars, which have a significant impact on their angular momentum loss rate through magnetised winds. Supplementing the formalism of MacGregor & Brenner (1991) with a latitude-dependent magnetised wind model, we analyse the effect of analytically prescribed surface distributions of open magnetic flux with different shapes and degrees of non-uniformity on the rotational evolution of a solar-like star. The angular momentum redistribution inside the star is treated…
We use three-dimensional direct numerical simulations of the helically forced magnetohydrodynamic equations in spherical shell segments in order to study the effects of changes in the geometrical shape and size of the domain on the growth and saturation of large-scale magnetic fields. We inject kinetic energy along with kinetic helicity in spherical domains via helical forcing using Chandrasekhar-Kendall functions. We take perfect conductor boundary conditions for the magnetic field to ensure that no magnetic helicity escapes the domain boundaries. We find dynamo action giving rise to magnetic…
In numerical studies of turbulence, hyperviscosity is often used as a tool to extend the inertial subrange and to reduce the dissipative subrange. By analogy, hyperdiffusivity (or hyperresistivity) is sometimes used in magnetohydrodynamics. The underlying assumption is that only the small scales are affected by this manipulation. In the present paper, possible side effects on the evolution of the large scale magnetic field are investigated. It is found that for turbulent flows with helicity, hyperdiffusivity causes the dynamo-generated magnetic field to saturate at a higher level than normal d…
We present magnetic flux measurements in seven rapidly rotating M dwarfs. Our sample stars have X-ray and H-alpha emission indicative of saturated emission, i.e., emission at a high level independent of rotation rate. Our measurements are made using near-infrared FeH molecular spectra observed with HIRES at Keck. Because of their large convective overturn times, the rotation velocity of M stars with small Rossby numbers is relatively slow and does not hamper the measurement of Zeeman splitting. The Rossby numbers of our sample stars are as small as 0.01. All our sample stars exhibit magnetic f…
A numerical model of isotropic homogeneous turbulence with helical forcing is investigated. The resulting flow, which is essentially the prototype of the alpha^2 dynamo of mean-field dynamo theory, produces strong dynamo action with an additional large scale field on the scale of the box (at wavenumber k=1; forcing is at k=5). This large scale field is nearly force-free and exceeds the equipartition value. As the magnetic Reynolds number R_m increases, the saturation field strength and the growth rate of the dynamo increase. However, the time it takes to built up the large scale field from equ…
We consider the problem of incompressible, forced, nonhelical, homogeneous and isotropic MHD turbulence with no mean magnetic field and large magnetic Prandtl number. This type of MHD turbulence is the end state of the turbulent dynamo, which generates folded fields with small-scale direction reversals. We propose a model in which saturation is achieved as a result of the velocity statistics becoming anisotropic with respect to the local direction of the magnetic folds. The model combines the effects of weakened stretching and quasi-two-dimensional mixing and produces magnetic-energy spectra i…
