Generation Of Large-scale Magnetic Fields Research Articles

Turbulent Processes and Mean-Field Dynamo

Mean-field dynamo theory has important applications in solar physics and galactic magnetism. We discuss some of the many turbulence effects relevant to the generation of large-scale magnetic fields in the solar convection zone. The mean-field description is then used to illustrate the physics of the alpha effect, turbulent pumping, turbulent magnetic diffusivity, and other effects on a modern solar dynamo model. We also discuss how turbulence transport coefficients are derived from local simulations of convection and then used in mean-field models.

Non-locality of the turbulent electromotive force

ABSTRACT The generation of large-scale magnetic fields ($\overline{\boldsymbol {B}}$) in astrophysical systems is driven by the mean turbulent electromotive force ($\overline{\rm{\boldsymbol {\cal E}} {}}$), the cross-correlation between local fluctuations of velocity and magnetic fields. This can depend non-locally on $\overline{\boldsymbol {B}}$ through a convolution kernel Kij. In a new approach to find Kij, we directly fit the time-series data of $\overline{\rm{\boldsymbol {\cal E}} {}}$ versus $\overline{\boldsymbol {B}}$ from a galactic dynamo simulation using singular value decomposition. We calculate the usual turbulent transport coefficients as moments of Kij, and show the importance of including non-locality over eddy length-scales to fully capture their amplitudes and that higher order corrections to the standard transport coefficients are small in this case.

Helical turbulent nonlinear dynamo at large magnetic Reynolds numbers

To investigate large-scale magnetic field generation in highly conducting magnetohydrodynamic (MHD) regimes typical of rotating astrophysical systems, we conduct high-resolution MHD simulations in the dynamical regime of large magnetic Reynolds numbers, of turbulence with an inhomogeneous kinetic helicity distribution. We obtain a nonlinear helical dynamo solution, characterized by a weak large-scale magnetic wave slowly propagating over saturated small-scale MHD turbulence, bypassing the catastrophic resistive quenching problem of homogeneous helical dynamos by developing turbulent fluxes of magnetic helicity through the system equator. Hints of fast-reconnection plasmoids are found.

Mean field dynamo action in shearing flows – II. Fluctuating kinetic helicity with zero mean

ABSTRACT Here we explore the role of temporal fluctuations in kinetic helicity on the generation of large-scale magnetic fields in the presence of a background linear shear flow. Key techniques involved here are same as in our earlier work, where we have used the renovating flow based model with shearing waves. Both the velocity and the helicity fields are treated as stochastic variables with finite correlation times, τ and τh, respectively. Growing solutions are obtained when τh > τ, even when this time-scale separation, characterized by m = τh/τ, remains below the threshold for causing the turbulent diffusion to turn negative. In regimes when turbulent diffusion remains positive, and τ is of the order of eddy turnover time T, the axisymmetric modes display non-monotonic behaviour with shear rate S: both, the growth rate γ and the wavenumber k* corresponding to the fastest growing mode, first increase, reach a maximum and then decrease with |S|, with k* being always smaller than eddy-wavenumber, thus boosting growth of magnetic fields at large length-scales. The cycle period Pcyc of growing dynamo wave is inversely proportional to |S| at small shear, exactly similar to the fixed kinetic helicity case of our earlier work. This dependence becomes shallower at larger shear. Interestingly enough, various curves corresponding to different choices of m collapse on top of each other in a plot of mPcyc with |S|.

Large-scale magnetic field saturation and the Elsasser number in rotating spherical dynamo models

ABSTRACT Numerical simulations are used to investigate large-scale (mean) magnetic field generation in rotating spherical dynamos. Beyond a certain threshold, we find that the magnitude of the mean magnetic field becomes nearly independent of the system rotation rate and buoyancy forcing. The analysis suggests that this saturation arises from the Malkus-Proctor mechanism in which a Coriolis-Lorentz force balance is achieved in the zonal component of the mean momentum equation. When based on the large-scale magnetic field, the Elsasser number is near unity in the saturated regime. The results show that the large and small magnetic field saturate via distinct mechanisms in rapidly rotating dynamos, and that only the axisymmetric component of the magnetic field appears to follow an Elsasser number scaling.

Renormalization group analysis of the turbulent hydromagnetic dynamo: Effect of anisotropy

The turbulent hydromagnetic dynamo is a process of magnetic field generation by chaotic flow of an electrically conducting fluid (plasma, liquid iron etc.). It is responsible for generation of large-scale magnetic fields of astrophysical objects such as planets, stars, accretion discs, galaxies, galaxy clusters etc. In particular, the dynamical process of induction of large-scale fields is strongly nonlinear and the effect of the Lorentz force is crucial. The aim of the analysis presented here is to provide analytic expressions for the large-scale electromotive force (EMF) in the limit of rapid rotation, with inclusion of both types of nonlinearities - the effect of the Lorentz force (hitherto scarcely considered) and the nonlinear evolution of turbulent fluctuations. The renormalization group technique is applied to extract the final expression for the mean EMF from the full nonlinear dynamical equations (Navier-Stokes, induction equation) and the mean-field equations are studied in order to demonstrate amplification and saturation of the mean magnetic field in two simplifying limits, that is the limit of a thin disc and a limit of a narrow spherical gap.

Renormalization Group Analysis of the Turbulent Hydromagnetic Dynamo: The Effect of Nonstationarity

Abstract The turbulent hydromagnetic dynamo is a process of magnetic field generation by chaotic flow of an electrically conducting fluid (plasma, liquid iron, etc.). It is responsible for generation of large-scale magnetic fields of astrophysical objects such as planets, stars, accretion disks, galaxies, galaxy clusters, etc. In particular, the dynamical process of induction of large-scale fields by highly conducting plasma has been very difficult to understand, as very low resistivity is not capable of creating a phase shift between magnetic and kinetic components of waves, making their interaction ineffective for generation of a large-scale electromotive force (EMF). The aim of the analysis presented here is to demonstrate that when the typically invoked statistical stationarity of turbulence is relaxed, large-scale magnetic fields can be very effectively generated by low-resistivity plasma. The renormalization group technique is applied to extract the final expression for the mean EMF from the fully nonlinear dynamical equations (Navier–Stokes, induction equation), and the mean field equations are solved for a force-free mode. Nonstationarity is shown to strongly enhance the process of large-scale EMF generation via wave interactions, and the dynamo effect induced by nonstationarity is proved to be effective. The results are also used to demonstrate the influence of magnetic fields and nonstationarity on energy and helicity spectra of turbulent flows.

Small-Scale Analysis of Hydrodynamical Helicity Suppression in the Mean-Field Dynamo-Model

We compare the classical mean-field dynamo model proposed by Steenbeck, Krause, and Radler to describe the generation of large-scale magnetic fields and the Kazantsev model that describes the small-scale dynamo in an unbounded homogeneous and isotropic flow. We consider the subcritical regime of small magnetic Reynolds numbers whereby there is no rapid generation. The same regime can also be understood as a process in which the small-scale generation is stopped due to its intrinsic mechanisms. Within both approaches we examine what distinguishes the spectra of the linear and nonlinear processes under the suppression of hydrodynamic (kinetic) helicity or, in other words, compare the alpha-quenchings. We check whether averaging the induction equation over scales larger than the velocity field correlation length leads to the loss of any features in the spectrum near the dissipative scale. We study the various types of dynamo stabilization using which seems more justified physically than the standard alpha-quenching, but more difficult within large-scale models containing limited information about the random velocity field. In particular, we compare the integral suppression whereby the total energy is conserved and the spectral suppression that suggests the conservation of energy and helicity in each spectral shell without assuming their redistribution over the spectrum.

Magnetic helicity and prospects for its observation in the interstellar medium

Magnetic helicity is one of the integrals of nonviscous flows in magnetohydrodynamics that determines the number of linkages of magnetic field lines in a medium. It is among a number of helicities that characterize the degree of mirror asymmetry of velocity and magnetic fields. The helicities play a crucial role in driving the generation of large-scale magnetic fields in stars and spiral galaxies. Until recently, measurements of various helicities were based on astronomical observations of the Sun’s active regions, but not in the Sun’s deep layers where the solar dynamo is operative. Galaxies are transparent to some extent and are therefore very attractive in this sense for observing the helicity of its magnetic field. Theoretical advances and the first successful attempts at such observations are reviewed.

Generation of large-scale magnetic fields due to fluctuating in shearing systems

We explore the growth of large-scale magnetic fields in a shear flow, due to helicity fluctuations with a finite correlation time, through a study of the Kraichnan–Moffatt model of zero-mean stochastic fluctuations of the$\unicode[STIX]{x1D6FC}$parameter of dynamo theory. We derive a linear integro-differential equation for the evolution of the large-scale magnetic field, using the first-order smoothing approximation and the Galilean invariance of the$\unicode[STIX]{x1D6FC}$-statistics. This enables construction of a model that is non-perturbative in the shearing rate$S$and the$\unicode[STIX]{x1D6FC}$-correlation time$\unicode[STIX]{x1D70F}_{\unicode[STIX]{x1D6FC}}$. After a brief review of the salient features of the exactly solvable white-noise limit, we consider the case of small but non-zero$\unicode[STIX]{x1D70F}_{\unicode[STIX]{x1D6FC}}$. When the large-scale magnetic field varies slowly, the evolution is governed by a partial differential equation. We present modal solutions and conditions for the exponential growth rate of the large-scale magnetic field, whose drivers are the Kraichnan diffusivity, Moffatt drift, shear and a non-zero correlation time. Of particular interest is dynamo action when the$\unicode[STIX]{x1D6FC}$-fluctuations are weak; i.e. when the Kraichnan diffusivity is positive. We show that in the absence of Moffatt drift, shear does not give rise to growing solutions. But shear and Moffatt drift acting together can drive large-scale dynamo action with growth rate$\unicode[STIX]{x1D6FE}\propto |S|$.

Does Nonaxisymmetric Dynamo Operate in the Sun?

Abstract We explore effects of random nonaxisymmetric perturbations of kinetic helicity (the α effect) and diffusive decay of bipolar magnetic regions on generation and evolution of large-scale nonaxisymmetric magnetic fields on the Sun. Using a reduced 2D nonlinear mean-field dynamo model and assuming that bipolar regions emerge due to magnetic buoyancy in situ of the large-scale dynamo action, we show that fluctuations of the α effect can maintain the nonaxisymmetric magnetic fields through a solar-type α 2Ω dynamo process. It is found that diffusive decay of bipolar active regions is likely to be the primary source of nonaxisymmetric magnetic fields observed on the Sun. Our results show that nonaxisymmetric dynamo models with stochastic perturbations of the α effect can explain periods of extremely high activity (“super-cycle” events) as well as periods of deep decline of magnetic activity. We compare the models with synoptic observations of solar magnetic fields for the last four activity cycles and discuss implications of our results for interpretation of observations of stellar magnetic activity.

Magnetic field generation by pointwise zero-helicity three-dimensional steady flow of an incompressible electrically conducting fluid.

We introduce six families of three-dimensional space-periodic steady solenoidal flows, whose kinetic helicity density is zero at any point. Four families are analytically defined. Flows in four families have zero helicity spectrum. Sample flows from five families are used to demonstrate numerically that neither zero kinetic helicity density nor zero helicity spectrum prohibit generation of large-scale magnetic field by the two most prominent dynamo mechanisms: the magnetic α-effect and negative eddy diffusivity. Our computations also attest that such flows often generate small-scale field for sufficiently small magnetic molecular diffusivity. These findings indicate that kinetic helicity and helicity spectrum are not the quantities controlling the dynamo properties of a flow regardless of whether scale separation is present or not.

Analysis of mean and fluctuating helicity measured by TomoPIV in swirling jet

Important role of helicity was theoretically predicted for the generation of large-scale magnetic fields and atmospheric vortices. Helicity can lead to a reduction of turbulent dissipation in the atmosphere or in a specific constrained flow, e.g. in pipe. We use the TomoPIV data (42 cube of grid points, resolution 0.84 mm) to measure 3D velocity field of turbulent swirling flows. We study spatial distribution of the mean and fluctuating components of energy and helicity. We find that helical turbulence excitation and decay along stream of the jet strongly depend on the inflow swirl. We observe spatial separation of turbulent flow with different sign of helicity while integrated values are conserves. It is shown that large scale swirling flow induces helicity at the small scales. Our results bring valuable materials for benchmark the modern numerical simulations with turbulent closure technique.

Analysis of mean and fluctuating helicity measured by TomoPIV in swirling jet

Important role of helicity was theoretically predicted for the generation of large-scale magnetic fields and atmospheric vortices. Helicity can lead to a reduction of turbulent dissipation in the atmosphere or in a specific constrained flow, e.g. in pipe. We use the TomoPIV data (42 cube of grid points, resolution 0.84 mm) to measure 3D velocity field of turbulent swirling flows. We study spatial distribution of the mean and fluctuating components of energy and helicity. We find that helical turbulence excitation and decay along stream of the jet strongly depend on the inflow swirl. We observe spatial separation of turbulent flow with different sign of helicity while integrated values are conserves. It is shown that large scale swirling flow induces helicity at the small scales. Our results bring valuable materials for benchmark the modern numerical simulations with turbulent closure technique.

Large-scale magnetic fields, non-Gaussianity, and gravitational waves from inflation

We explore the generation of large-scale magnetic fields in the so-called moduli inflation. The hypercharge electromagnetic fields couple to not only a scalar field but also a pseudoscalar one, so that the conformal invariance of the hypercharge electromagnetic fields can be broken. We explicitly analyze the strength of the magnetic fields on the Hubble horizon scale at the present time, the local non-Gaussianity of the curvature perturbations originating from the massive gauge fields, and the tensor-to-scalar ratio of the density perturbations. As a consequence, we find that the local non-Gaussianity and the tensor-to-scalar ratio are compatible with the recent Planck results.

Kinematic dynamo in a tetrahedron composed of helical Fourier modes

It is generally believed that helicity can play a significant role in turbulent systems, e.g. supporting the generation of large-scale magnetic fields, but its exact contribution is not clearly understood. For example there are well-known examples of large scale dynamos produced by a flow which is pointwise non-helical. In any case a break of mirror symmetry seems to be always at the heart of the dynamo mechanism. A fruitful framework to analyze such processes is the use of helical mode decomposition. In pure hydrodynamics such framework has proved its availability in study of the processes responsible for helicity cascades. It has also been used in the analysis of MHD helical mode interactions. The present work deals with the kinematic dynamo problem, solving the induction equation within the framework of helical Fourier modes decomposition. We show that the simplest modes configuration leading to an unstable solution has the form of a tetrahedron. Then the dynamo is produced by only two scales flow. We find necessary conditions for such dynamo action, not certainly related to flow helicity. The results help to understand generic dynamo flows like the one studied by G.O. Roberts (1972).

TURBULENT DYNAMO IN A CONDUCTING FLUID AND A PARTIALLY IONIZED GAS

ABSTRACT By following the Kazantsev theory and taking into account both microscopic and turbulent diffusion of magnetic fields, we develop a unified treatment of the kinematic and nonlinear stages of a turbulent dynamo process, and we study the dynamo process for a full range of magnetic Prandtl number P m and ionization fractions. We find a striking similarity between the dependence of dynamo behavior on P m in a conducting fluid and (a function of ionization fraction) in a partially ionized gas. In a weakly ionized medium, the kinematic stage is largely extended, including not only exponential growth but a new regime of dynamo characterized by a linear-in-time growth of magnetic field strength, and the resulting magnetic energy is much higher than the kinetic energy carried by viscous-scale eddies. Unlike the kinematic stage, the subsequent nonlinear stage is unaffected by microscopic diffusion processes and has a universal linear-in-time growth of magnetic energy with the growth rate as a constant fraction 3/38 of the turbulent energy transfer rate, showing good agreement with earlier numerical results. Applying the analysis to the first stars and galaxies, we find that the kinematic stage is able to generate a field strength only an order of magnitude smaller than the final saturation value. But the generation of large-scale magnetic fields can only be accounted for by the relatively inefficient nonlinear stage and requires longer time than the free-fall time. It suggests that magnetic fields may not have played a dynamically important role during the formation of the first stars.

On the connections between solar and stellar dynamo models

AbstractWe here discuss the various dynamo models which have been designed to explain the generation and evolution of large-scale magnetic fields in stars. We focus on the models that have been applied to the Sun and can be tested for other solar-type stars now that modern observational techniques provide us with detailed stellar magnetic field observations. Mean-field flux-transport dynamo models have been developed for decades to explain the solar cycle and applications to more rapidly-rotating stars are discussed. Tremendous recent progress has been made on 3D global convective dynamo models. They do not however for now produce regular flux emergence that could be responsible for surface active regions and questions about the role of these active regions in the dynamo mechanism are still difficult to address with such models. We finally discuss 3D kinematic dynamo models which could constitute a promising combined approach, in which data assimilation could be applied.

Helicity and celestial magnetism

This informal article discusses the central role of magnetic and kinetic helicity in relation to the evolution of magnetic fields in geophysical and astrophysical contexts. It is argued that the very existence of magnetic fields of the intensity and scale observed is attributable in large part to the chirality of the background turbulence or random-wave field of flow, the simplest measure of this chirality being non-vanishing helicity. Such flows are responsible for the generation of large-scale magnetic fields which themselves exhibit magnetic helicity. In the geophysical context, the turbulence has a ‘magnetostrophic’ character in which the force balance is primarily that between buoyancy forces, Coriolis forces and Lorentz forces associated with the dynamo-generated magnetic field; the dominant nonlinearity here arises from the convective transport of buoyant elements erupting from the ‘mushy zone’ at the inner core boundary. At the opposite extreme, in a highly conducting low-density plasma, the near-invariance of magnetic field topology (and of associated helicity) presents the challenging problem of ‘magnetic relaxation under topological constraints’, of central importance both in astrophysical contexts and in controlled-fusion plasma dynamics. These problems are reviewed and open issues, particularly concerning saturation mechanisms, are reconsidered.

DEPENDENCE OF STELLAR MAGNETIC ACTIVITY CYCLES ON ROTATIONAL PERIOD IN A NONLINEAR SOLAR-TYPE DYNAMO

ABSTRACT We study the turbulent generation of large-scale magnetic fields using nonlinear dynamo models for solar-type stars in the range of rotational periods from 14 to 30 days. Our models take into account nonlinear effects of dynamical quenching of magnetic helicity, and escape of magnetic field from the dynamo region due to magnetic buoyancy. The results show that the observed correlation between the period of rotation and the duration of activity cycles can be explained in the framework of a distributed dynamo model with a dynamical magnetic feedback acting on the turbulent generation from either magnetic buoyancy or magnetic helicity. We discuss implications of our findings for the understanding of dynamo processes operating in solar-like stars.