Mean-field Dynamo Research Articles

Magnetic field and kinetic helicity evolution in simulations of interacting disk galaxies

Context. There are indications that the magnetic field evolution in galaxies is influenced by tidal interactions and mergers between galaxies. Aims. We carried out a parameter study of interacting disk galaxies with impact parameters ranging from central collisions to weakly interacting scenarios. The orientations of the disks were also varied. In particular, we investigated how magnetic field amplification depends on these parameters. Methods. We used magnetohydrodynamics for gas disks in combination with live dark-matter halos in adaptive mesh refinement simulations. The disks were initialized using a setup for isolated disks in hydrostatic equilibrium. Since we focused on the impact of tidal forces on magnetic field evolution, adiabatic physics was applied. Small-scale filtering of the velocity and magnetic field allowed us to estimate the turbulent electromotive force (EMF) and kinetic helicity. Results. Time series of the average magnetic field in central and outer disk regions show pronounced peaks during close encounters and mergers. This agrees with observed magnetic fields at different interaction stages. The central field strength exceeds 10 μG (corresponding to an amplification factor of 2–3) for small impact parameters. As the disks are increasingly disrupted and turbulence is produced by tidal forces, the small-scale EMF reaches a significant fraction of the total EMF. The small-scale kinetic helicity is initially antisymmetric across the disk plane. Though its evolution is sensitive to both the impact parameter and inclinations of the rotation axes with respect to the relative motion of the disks, antisymmetry is generally broken through interactions and the merger remnant loses most of the initial helicity. The EMF and the magnetic field also decay rapidly after coalescence. Conclusions. The strong amplification during close encounters of the interacting galaxies is mostly driven by helical flows and a mean-field dynamo. The small-scale dynamo contributes significantly in post-interaction phases. However, the amplification of the magnetic field cannot be sustained.

MRI turbulence in vertically stratified accretion discs at large magnetic Prandtl numbers

ABSTRACT The discovery of the first binary neutron star merger, GW170817, has spawned a plethora of global numerical relativity simulations. These simulations are often ideal (with dissipation determined by the grid) and/or axisymmetric (invoking ad hoc mean-field dynamos). However, binary neutron star mergers (similar to X-ray binaries and active galactic nuclei inner discs) are characterized by large magnetic Prandtl numbers, $\rm Pm$, (the ratio of viscosity to resistivity). $\rm Pm$ is a key parameter determining dynamo action and dissipation but it is ill-defined (and likely of order unity) in ideal simulations. To bridge this gap, we investigate the magnetorotational instability (MRI) and associated dynamo at large magnetic Prandtl numbers using fully compressible, three-dimensional, vertically stratified, isothermal simulations of a local patch of a disc. We find that, within the bulk of the disc (z ≲ 2H, where H is the scale-height), the turbulent intensity (parametrized by the stress-to-thermal-pressure ratio α), and the saturated magnetic field energy density, Emag, produced by the MRI dynamo, both scale as a power with Pm at moderate Pm (4 ≲ Pm ≲ 32): Emag ∼ Pm0.74 and α ∼ Pm0.71, respectively. At larger Pm (≳ 32), we find deviations from power-law scaling and the onset of a plateau. Compared to our recent unstratified study, this scaling with Pm becomes weaker further away from the disc mid-plane, where the Parker instability dominates. We perform a thorough spectral analysis to understand the underlying dynamics of small-scale MRI-driven turbulence in the mid-plane and of large-scale Parker-unstable structures in the atmosphere.

Budget equations and astrophysical non-linear mean-field dynamos

ABSTRACTSolar, stellar and galactic large-scale magnetic fields are originated due to a combined action of non-uniform (differential) rotation and helical motions of plasma via mean-field dynamos. Usually, non-linear mean-field dynamo theories take into account algebraic and dynamic quenching of alpha effect and algebraic quenching of turbulent magnetic diffusivity. However, the theories of the algebraic quenching do not take into account the effect of modification of the source of turbulence by the growing large-scale magnetic field. This phenomenon is due to the dissipation of the strong large-scale magnetic field resulting in an increase of the total turbulent energy. This effect has been studied using the budget equation for the total turbulent energy (which takes into account the feedback of the generated large-scale magnetic field on the background turbulence) for (i) a forced turbulence, (ii) a shear-produced turbulence, and (iii) a convective turbulence. As the result of this effect, a non-linear dynamo number decreases with increase of the large-scale magnetic field, so that that the mean-field αΩ, α2, and α2Ω dynamo instabilities are always saturated by the strong large-scale magnetic field.

Toroidal Magnetic Flux Budget in Mean-field Dynamo Model of Solar Cycles 23 and 24

We study the toroidal magnetic flux budget of the axisymmetric part of a data-driven 3D mean-field dynamo model of Solar Cycles 23 and 24. The model simulates the global solar dynamo that includes the effects of the formation and evolution of bipolar magnetic regions (BMRs) emerging on the solar surface. By applying Stokes’s theorem to the dynamo induction equation, we show that the hemispheric magnitude of the net axisymmetric toroidal magnetic field generation rate in the bulk of the convection zone can only partially be estimated from the surface parameters of the differential rotation and the axisymmetric radial magnetic field. The contribution of the radial integral along the equator, which is mostly due to the rotational radial shear at the bottom of the convection zone, has the same magnitude and is nearly in phase with the effect of the surface latitudinal differential rotation. Also, the toroidal field generation rate estimate strongly depends on the latitudinal profile of the surface radial magnetic field near the poles. This profile in our dynamo models significantly deviates from the polar magnetic field distribution observed during the minima of Solar Cycles 22, 23, and 24. The cause of this discrepancy requires further observational and theoretical studies. Comparing the 2D axisymmetric and the 3D nonaxisymmetric dynamo models, we find an increase in the toroidal field generation rate in the 3D model due to the surface effects of BMRs, resulting in an increase in the axisymmetric poloidal magnetic field magnitude.

Modeling reversals of galactic magnetic fields at large distances from centers of milky-way-like galaxies using computations on GPUs

Nowadays it is strongly believed that in a large number of spiral galaxies there are regular magnetic fields. Their existence is proved by measurements of the Faraday rotation of polarization plane of electromagnetic waves which are received on modern radio telescopes. The theoretical description of magnetic fields generation is connected with the mean field dynamo mechanism. It is based on joint action of the ?-effect and differential rotation. At the first stage of evolution, magnetic fields enlarge exponentially with the growth rate described by the largest eigenvalue of the corresponding differential operator. If the field becomes comparable with the equipartition value, the nonlinear terms become more important, and they are connected with saturation of the field growth. The non-linear system of equations has several stationary points, and some of them are stable. According to the contrast structures theory for a quite small turbulent viscosity and some initial conditions, in different regions there will be magnetic fields of opposite directions, and they will be divided by narrow transition layers. Such features, for example, characterize the magnetic field of the Milky Way. Most of the existing works describe reversals for quite moderate distances from the galaxy center. However, it was shown previously that the magnetic field can principally be generated also in outer parts of galaxies, which are situated at distances of more than 10 kpc from the rotation axis. It is interesting to describe the appearance of reversals in such parts of galaxies. In this work we have studied the dynamo action in outer parts of the Milky-Way-like galaxies. It is shown that it is possible to generate opposite magnetic fields there. We have used random initial conditions to obtain spatial reversals. Because of a large volume of computations, they were carried out by using graphics processing units (GPUs).

Impact of a mean field dynamo on neutron star mergers leading to magnetar remnants

Impact of a mean field dynamo on neutron star mergers leading to magnetar remnants

Unified treatment of mean-field dynamo and angular-momentum transport in magnetorotational instability-driven turbulence.

Magnetorotational instability-driven (MRI-driven) turbulence and dynamo phenomena are analyzed using direct statistical simulations. Our approach begins by developing a unified mean-field model that combines the traditionally decoupled problems of the large-scale dynamo and angular momentum transport in accretion disks. The model consists of a hierarchical set of equations, capturing up to the second-order correlators, while a statistical closure approximation is employed to model the three-point correlators. We highlight the web of interactions that connect different components of stress tensors-Maxwell, Reynolds, and Faraday-through shear, rotation, correlators associated with mean fields, and nonlinear terms. We determine the dominant interactions crucial for the development and sustenance of MRI turbulence. Our general mean-field model for the MRI-driven system allows for a self-consistent construction of the electromotive force, inclusive of inhomogeneities and anisotropies. Within the realm of large-scale magnetic field dynamo, we identify two key mechanisms-the rotation-shear-current effect and the rotation-shear-vorticity effect-that are responsible for generating the radial and vertical magnetic fields, respectively. We provide the explicit (nonperturbative) form of the transport coefficients associated with each of these dynamo effects. Notably, both of these mechanisms rely on the intrinsic presence of large-scale vorticity dynamo within MRI turbulence.

Mean-field dynamo due to spatio-temporal fluctuations of the turbulent kinetic energy

In systems where the standard $\alpha$ effect is inoperative, one often explains the existence of mean magnetic fields by invoking the ‘incoherent $\alpha$ effect’, which appeals to fluctuations of the mean kinetic helicity at a mesoscale. Most previous studies, while considering fluctuations in the mean kinetic helicity, treated the mean turbulent kinetic energy at the mesoscale as a constant, despite the fact that both these quantities involve second-order velocity correlations. The mean turbulent kinetic energy affects the mean magnetic field through both turbulent diffusion and turbulent diamagnetism. In this work, we use a double-averaging procedure to analytically show that fluctuations of the mean turbulent kinetic energy at the mesoscale (giving rise to $\eta$ -fluctuations at the mesoscale, where the scalar $\eta$ is the turbulent diffusivity) can lead to the growth of a large-scale magnetic field even when the kinetic helicity is zero pointwise. Constraints on the operation of such a dynamo are expressed in terms of dynamo numbers that depend on the correlation length, correlation time and strength of these fluctuations. In the white-noise limit, we find that these fluctuations reduce the overall turbulent diffusion, while also contributing a drift term which does not affect the growth of the field. We also study the effects of non-zero correlation time and anisotropy. Turbulent diamagnetism, which arises due to inhomogeneities in the turbulent kinetic energy, leads to growing mean-field solutions even when the $\eta$ -fluctuations are statistically isotropic.

Magnetic fields of low-mass main sequences stars: non-linear dynamo theory and mean-field numerical simulations

ABSTRACT Our theoretical and numerical analysis have suggested that for low-mass main sequences stars (of the spectral classes from M5 to G0) rotating much faster than the Sun, the generated large-scale magnetic field is caused by the mean-field α2Ω dynamo, whereby the α2 dynamo is modified by a weak differential rotation. Even for a weak differential rotation, the behaviour of the magnetic activity is changed drastically from aperiodic regime to non-linear oscillations and appearance of a chaotic behaviour with increase of the differential rotation. Periods of the magnetic cycles decrease with increase of the differential rotation, and they vary from tens to thousand years. This long-term behaviour of the magnetic cycles may be related to the characteristic time of the evolution of the magnetic helicity density of the small-scale field. The performed analysis is based on the mean-field simulations (MFS) of the α2Ω and α2 dynamos and a developed non-linear theory of α2 dynamo. The applied MFS model was calibrated using turbulent parameters typical for the solar convective zone.

Steady states of the Parker instability: the effects of rotation

ABSTRACT We model the Parker instability in vertically stratified isothermal gas using non-ideal MHD three-dimensional simulations. Rotation, especially differential, more strongly and diversely affects the nonlinear state than the linear stage (where we confirm the most important conclusions of analytical models), and stronger than any linear analyses predict. Steady-state magnetic fields are stronger and cosmic ray energy density is higher than in comparable non-rotating systems. Transient gas outflows induced by the nonlinear instability persist longer, of order 2 Gyr, with rotation. Stratification combined with (differential) rotation drives helical flows, leading to mean-field dynamo. Consequently, the nonlinear state becomes oscillatory (while both the linear instability and the dynamo are non-oscillatory). The horizontal magnetic field near the mid-plane reverses its direction propagating to higher altitudes as the reversed field spreads buoyantly. The spatial pattern of the large-scale magnetic field may explain the alternating magnetic field directions in the halo of the edge-on galaxy NGC 4631. Our model is unique in producing a large-scale magnetic structure similar to such observation. Furthermore, our simulations show that the mean kinetic helicity of the magnetically driven flows has the sign opposite to that in the conventional non-magnetic flows. This has profound consequences for the nature of the dynamo action and large-scale magnetic field structure in the coronae of spiral galaxies that remain to be systematically explored and understood. We show that the energy density of cosmic rays and magnetic field strength are not correlated at scales of order 1 kiloparsec.

Numerical dependencies of the galactic dynamo in isolated galaxies with SPH

Simulating and evolving magnetic fields within global galaxy simulations provides a large tangled web of numerical complexity due to the vast amount of physical processes involved. Understanding the numerical dependencies that act on the galactic dynamo is a crucial step in determining what resolution and conditions are required to properly capture the magnetic fields observed in galaxies. Here, we present an extensive study on the numerical dependencies of the galactic dynamo in isolated spiral galaxies using smoothed particle magnetohydrodynamics. We performed 53 isolated spiral galaxy simulations with different initial setups, feedback, resolution, Jeans floor, and dissipation parameters. The results show a strong mean-field dynamo occurring in the spiral-arm region of the disk, likely produced by the classical alpha-omega dynamo or the recently described gravitational instability dynamo. The inclusion of feedback is seen to work in both a destructive and positive fashion for the amplification process. Destructive interference for the amplification occurs due to the breakdown of filament structure in the disk, the increase of turbulent diffusion, and the ejection of magnetic flux from the central plane to the circumgalactic medium. The positive effect of feedback is the increase in vertical motions and the turbulent fountain flows that develop, showing a high dependence on the small-scale vertical structure and the numerical dissipation within the galaxy. Galaxies with an effective dynamo saturate their magnetic energy density at levels between 10 and 30% of the thermal energy density. The density-averaged numerical Prandtl number is found to be below unity throughout the galaxy for all our simulations, with an increasing value with radius. Assuming a turbulent injection length of 1 kpc, the numerical magnetic Reynolds number is within the range of Remag = 10 − 400, indicating that some regions are below the levels required for the small-scale dynamo (Remag, crit = 30 − 2700) to be active.

Effects of Emerging Bipolar Magnetic Regions in Mean-field Dynamo Model of Solar Cycles 23 and 24

We model the physical parameters of Solar Cycles 23 and 24 using a nonlinear dynamical mean-field dynamo model that includes the formation and evolution of bipolar magnetic regions (BMRs). The Parker-type dynamo model consists of a complete MHD system in the mean-field formulation: the 3D magnetic induction equation, and 2D momentum and energy equations in the anelastic approximation. The initialization of BMRs is modeled in the framework of Parker’s magnetic buoyancy instability. It defines the depths of BMR injections, which are typically located at the edge of the global dynamo waves. The distribution with longitude and latitude and the size of the initial BMR perturbations are taken from the NOAA database of active regions. The modeling results are compared with various observed characteristics of the solar cycles. Only the BMR perturbations located in the upper half of the convection zone lead to magnetic active regions on the solar surface. While the BMRs initialized in the lower part of the convection zone do not emerge on the surface, they still affect the global dynamo process. Our results show that BMRs can play a substantial role in the dynamo processes and affect the strength of the solar cycles. However, the data driven model shows that the BMR’s effect alone cannot explain the weak Cycle 24. This weak cycle and the prolonged preceding minimum of magnetic activity were probably caused by a decrease of the turbulent helicity in the bulk of the convection zone during the decaying phase of Cycle 23.

Spatio-temporal non-localities in a solar-like mean-field dynamo

ABSTRACT The scale separation approximation, which is in the base of the solar mean-field dynamo models, can be hardly justified both by observations and theoretical applications to astrophysical dynamos. The general expression for the mean turbulent electromotive force can be written in integral form with convolution of the turbulent effects and mean magnetic field variations over scales of the turbulent flows and global scales of the mean-field dynamo. Following results of direct numerical simulations (DNS), which had been reported earlier, we take the Lorentzian form of the integral convolution kernels as an experimental fact. It allows us to approximate the governing equation for the mean electromotive force by the reaction–diffusion type equation. Solution of the eigenvalue problem reveals a few curious properties of the dynamo model with the non-local mean electromotive force. We find a decrease of the critical dynamo instability threshold, and an increase the dynamo periods of the unstable modes, as reported in earlier studies. Simultaneously, the non-local model shows substantially lower growth rate of the unstable dynamo modes in proximity of the critical threshold than the model which employs the scale separation approximation. We verify these findings using the non-linear solar dynamo model. For the supercritical regime, when the α-effect magnitude is about twice of the instability threshold, the model shows the Parker’s dynamo wave solutions with the wave propagating from the mid-latitude at the bottom of the convection zone towards the solar equator at the surface.

Simulating the magnetorotational instability on a moving mesh with the shearing box approximation

ABSTRACT The magnetorotational instability (MRI) is an important process in sufficiently ionized accretion discs, as it can create turbulence that acts as an effective viscosity, mediating angular momentum transport. Due to its local nature, it is often analysed in the shearing box approximation with Eulerian methods, which otherwise would suffer from large advection errors in global disc simulations. In this work, we report on an extensive study that applies the quasi-Lagrangian, moving-mesh code arepo, combined with the Dedner cleaning scheme to control deviations from $\nabla \cdot \boldsymbol B=0$, to the problem of magnetized flows in shearing boxes. We find that we can resolve the analytical linear growth rate of the MRI with mean background magnetic field well. In the zero net flux case, there is a threshold value for the strength of the divergence cleaning above which the turbulence eventually dies out, and in contrast to previous Eulerian simulations, the strength of the MRI does not decrease with increasing resolution. In boxes with larger vertical aspect ratio we find a mean-field dynamo, as well as an active shear current effect that can sustain MRI turbulence for at least 200 orbits. In stratified simulations, we obtain an active αω dynamo and the characteristic butterfly diagram. Our results compare well with previous results obtained with static grid codes such as athena. We thus conclude that arepo represents an attractive approach for global disc simulations due to its quasi-Lagrangian nature, and for shearing box simulations with large density variations due to its continuously adaptive resolution.

Jets from Accretion Disk Dynamos: Consistent Quenching Modes for Dynamo and Resistivity

Astrophysical jets are launched from strongly magnetized systems that host an accretion disk surrounding a central object. The origin of the magnetic field, which is a key component of the launching process, is still an open question. Here we address the question of how the magnetic field required for jet launching is generated and maintained by a dynamo process. By carrying out nonideal MHD simulations (PLUTO code), we investigate how the feedback of the generated magnetic field on the mean-field dynamo affects the disk and jet properties. We find that a stronger quenching of the dynamo leads to a saturation of the magnetic field at a lower disk magnetization. Nevertheless, we find that, while applying different dynamo feedback models, the overall jet properties remain unaffected. We then investigate a feedback model that encompasses a quenching of the magnetic diffusivity. Our modeling considers a more consistent approach for mean-field dynamo modeling simulations, as the magnetic quenching of turbulence should be considered for both a turbulent dynamo and turbulent magnetic diffusivity. We find that, after the magnetic field is saturated, the Blandford–Payne mechanism can work efficiently, leading to more collimated jets, which move, however, with slower speed. We find strong intermittent periods of flaring and knot ejection for low Coriolis numbers. In particular, flux ropes are built up and advected toward the inner disk thereby cutting off the inner disk wind, leading to magnetic field reversals, reconnection and, the emergence of intermittent flares.

Electromagnetic Counterparts of Binary-neutron-star Mergers Leading to a Strongly Magnetized Long-lived Remnant Neutron Star

We explore the electromagnetic counterparts that will associate with binary-neutron-star mergers for the case that remnant massive neutron stars survive for ≳0.5 s after the merger. For this study, we employ the outflow profiles obtained by long-term general-relativistic neutrino-radiation magnetohydrodynamics simulations with a mean-field dynamo effect. We show that a synchrotron afterglow with high luminosity can be associated with the merger event if the magnetic fields of the remnant neutron stars are significantly amplified by the dynamo effect. We also perform a radiative transfer calculation for kilonovae and find that, for the highly amplified magnetic field cases, the kilonovae can be bright in the early epoch (t ≤ 0.5 d), while it shows the optical emission which rapidly declines in a few days and the very bright near-infrared emission which lasts for ∼10 days. All these features have not been found in GW170817, indicating that the merger remnant neutron star formed in GW170817 might have collapsed to a black hole within several hundreds milliseconds or magnetic-field amplification might be a minor effect.

Mean fields and fluctuations in compressible magnetohydrodynamic flows

We apply Gaussian smoothing to obtain mean magnetic field, density, velocity, and magnetic and kinetic energy densities from our numerical model of the interstellar medium, based on three-dimensional magnetohydrodynamic equations in a shearing box in size. The interstellar medium is highly compressible, as the turbulence is transonic or supersonic; it is thus an excellent context in which to explore the use of smoothing to represent physical variables in a compressible medium in terms of their mean and fluctuating parts. Unlike alternative averaging procedures, such as horizontal averaging, Gaussian smoothing retains the three-dimensional structure of the mean fields. Although Gaussian smoothing does not obey the Reynolds rules of averaging, physically meaningful and mathematically sound central statistical moments are defined as suggested by Germano [Turbulence – The filtering approach. J. Fluid Mech. 1992, 238, 325–336]. We discuss methods to identify an optimal smoothing scale ℓ and the effects of this choice on the results. From spectral analysis of the magnetic, density and velocity fields, we find a suitable smoothing length for all three fields, of . Such a smoothing scale is likely to be sensitive to the choice of simulation parameters; this may be considered in future work, but here we just explore the methodology. We discuss the properties of third-order statistical moments in fluctuations of kinetic energy density in compressible flows, and suggest their physical interpretation. The mean magnetic field, amplified by a mean-field dynamo, significantly alters the distribution of kinetic energy in space and between scales, reducing the magnitude of kinetic energy at intermediate scales. This intermediate-scale kinetic energy is a useful diagnostic of the importance of SN-driven outflows.

General Relativistic Magnetohydrodynamics Mean-Field Dynamos

Large-scale, ordered magnetic fields in several astrophysical sources are supposed to be originated, and maintained against dissipation, by the combined amplifying action of rotation and small-scale turbulence. For instance, in the solar interior, the so-called α−Ω mean-field dynamo is known to be responsible for the observed 22-years magnetic cycle. Similar mechanisms could operate in more extreme environments, like proto neutron stars and accretion disks around black holes, for which the physical modelling needs to be translated from the regime of magnetohydrodynamics (MHD) and Newtonian gravity to that of a plasma in a general relativistic curved spacetime (GRMHD). Here we review the theory behind the mean field dynamo in GRMHD, the strategies for the implementation of the relevant equations in numerical conservative schemes, and we show the most important applications to the mentioned astrophysical compact objects obtained by our group in Florence. We also present novel results, such as three-dimensional GRMHD simulations of accretion disks with dynamo and the application of our dynamo model to a super massive neutron star, remnant of a binary neutron star merger as obtained from full numerical relativity simulations.

Dynamo instabilities in plasmas with inhomogeneous chiral chemical potential

We study the dynamics of magnetic fields in chiral magnetohydrodynamics, which takes into account the effects of an additional electric current related to the chiral magnetic effect in high-energy plasmas. We perform direct numerical simulations, considering weak seed magnetic fields and inhomogeneities of the chiral chemical potential ${\ensuremath{\mu}}_{5}$ with a zero mean. We demonstrate that a small-scale chiral dynamo can occur in such plasmas if fluctuations of ${\ensuremath{\mu}}_{5}$ are correlated on length scales that are much larger than the scale on which the dynamo growth rate reaches its maximum. Magnetic fluctuations grow by many orders of magnitude due to the small-scale chiral dynamo instability. Once the nonlinear backreaction of the generated magnetic field on fluctuations of ${\ensuremath{\mu}}_{5}$ sets in, the ratio of these scales decreases and the dynamo saturates. When magnetic fluctuations grow sufficiently to drive turbulence via the Lorentz force before reaching maximum field strength, an additional mean-field dynamo phase is identified. The mean magnetic field grows on a scale that is larger than the integral scale of turbulence after the amplification of the fluctuating component saturates. The growth rate of the mean magnetic field is caused by a magnetic $\ensuremath{\alpha}$ effect that is proportional to the current helicity. With the onset of turbulence, the power spectrum of ${\ensuremath{\mu}}_{5}$ develops a universal ${k}^{\ensuremath{-}1}$ scaling independently of its initial shape, while the magnetic energy spectrum approaches a ${k}^{\ensuremath{-}3}$ scaling.

Production of a Chiral Magnetic Anomaly with Emerging Turbulence and Mean-Field Dynamo Action.

In relativistic magnetized plasmas, asymmetry in the number densities of left- and right-handed fermions, i.e., a nonzero chiral chemical potential μ_{5}, leads to an electric current along the magnetic field. This causes a chiral dynamo instability for a uniform μ_{5}, but our simulations reveal a dynamo even for fluctuating μ_{5} with zero mean. It produces magnetically dominated turbulence and generates mean magnetic fields via the magnetic α effect. Eventually, a universal scale-invariant k^{-1} spectrum of μ_{5} and a k^{-3} magnetic spectrum are formed independently of the initial condition.