Observations in polarized emission reveal the existence of large-scale coherent magnetic fields in a wide range of spiral galaxies. Radio-polarization data show that these fields are strongly inclined towards the radial direction, with pitch angles up to $35\degr$ and thus cannot be explained by differential rotation alone. Global dynamo models describe the generation of the radial magnetic field from the underlying turbulence via the so called $α$-effect. However, these global models still rely on crude assumptions about the small-scale turbulence. To overcome these restrictions we perform fully dynamical MHD simulations of interstellar turbulence driven by supernova explosions. From our simulations we extract profiles of the contributing diagonal elements of the dynamo $α$-tensor as functions of galactic height. We also measure the coefficients describing vertical pumping and find that the ratio $\hatγ$ between these two effects has been overestimated in earlier analytical work, where dynamo action seemed impossible. In contradiction to these models based on isolated remnants we always find the pumping to be directed inward. In addition we observe that $\hatγ$ depends on whether clustering in terms of super-bubbles is taken into account. Finally, we apply a test field method to derive a quantitative measure of the turbulent magnetic diffusivity which we determine to be ~ 2 kpc kms.
We revisit the possible turbulent sources of the solar dynamo. Studying axisymmetric mean-field dynamo models, we find that the large-scale poloidal magnetic field could be generated not only by the famous alpha effect, but also by the Omega x J and shear-current effects. The inclusion of these additional turbulent sources alleviates several of the known problems of solar mean-field dynamo models.
We are concerned with large scale magnetic field dynamo generation and propagation of magnetic fronts in turbulent electrically conducting fluids. An effective equation for the large scale magnetic field is developed here that takes into account the finite correlation times of the turbulent flow. This equation involves the memory integrals corresponding to the dynamo source term describing the alpha-effect and turbulent transport of magnetic field. We find that the memory effects can drastically change the dynamo growth rate, in particular, non-local turbulent transport might increase the grow…
The paper deals with a simple spherical mean-field dynamo model of $α^2$-type in the case of high electrical conductivity. A spherically symmetric distribution of turbulent motions is assumed inside a spherical fluid body surrounded by free space, and some complete form of the corresponding mean electromotive force is taken into account. For a turbulence lacking reflectional symmetry finite growth rates of magnetic fields prove to be possible even in the limit of perfect conductivity, that is, the model corresponds to a fast dynamo. In accordance with the theorem by Bondi and Gold the dynamo-g…
The prevailing theory for the origin of cosmic magnetic fields is that they have been amplified to their present values by the turbulent dynamo inductive action in the protogalactic and galactic medium. Up to now, in calculation of the turbulent dynamo, it has been customary to assume that there is no the back reaction of the magnetic field on the turbulence, as long as the magnetic energy is less than the turbulent kinetic energy. This assumption leads to the kinematic dynamo theory. However, the applicability of the kinematic dynamo theory to protogalaxies is rather limited. The reason is th…
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 ''.
The prevailing theory for the origin of cosmic magnetic fields is that they have been amplified to their present values by the turbulent dynamo inductive action in the protogalactic and galactic medium. Up to now, in calculation of the turbulent dynamo, it has been customary to assume that there is no back reaction of the magnetic field on the turbulence, as long as the magnetic energy is less than the turbulent kinetic energy. This assumption leads to the kinematic dynamo theory. However, the applicability of this theory to protogalaxies is rather limited. The reason is that in protogalaxies …
Using a periodic box calculation it is shown that, owing to helicity conservation, a large scale field can only develop on a resistive timescale. This behaviour can be reproduced by a mean-field dynamo with alpha and eta_t quenchings that are equally strong and `catastrophic'.
Large scale dynamos produce small scale current helicity as a waste product that quenches the large scale dynamo process (alpha effect). This quenching can be catastrophic (i.e.intensify with magnetic Reynolds number) unless one has fluxes of small scale magnetic (or current) helicity out of the system. We derive the form of helicity fluxes in turbulent dynamos, taking also into account the nonlinear effects of Lorentz forces due to fluctuating fields. We confirm the form of an earlier derived magnetic helicity flux term, and also show that it is not renormalized by the small scale magnetic fi…
The existence of large-scale dynamos in rigidly rotating turbulent convection without shear is studied using three-dimensional numerical simulations of penetrative rotating compressible convection. We demonstrate that rotating convection in a Cartesian domain can drive a large-scale dynamo even in the absence of shear. The large-scale field contains a significant fraction of the total field in the saturated state. The simulation results are compared with one-dimensional mean-field dynamo models where turbulent transport coefficients, as determined using the test field method, are used. The rea…
The turbulent pumping effect corresponds to the transport of magnetic flux due to the presence of density and turbulence gradients in convectively unstable layers. In the induction equation it appears as an advective term and for this reason it is expected to be important in the solar and stellar dynamo processes. In this work, we have explored the effects of the turbulent pumping in a flux-dominated Babcock-Leighton solar dynamo model with a solar-like rotation law. The results reveal the importance of the pumping mechanism for solving current limitations in mean field dynamo modeling such as…
Analytical solution of first order torsion $α$-effect in twisted magnetic flux tubes representing a flux tube dynamo in Riemannian space is presented. Toroidal and poloidal component of the magnetic field decays as $r^{-1}$, while grow exponentially in time. The rate of speed of the helical dynamo depends upon the value of Frenet curvature of the tube. The $α$ factor possesses a fundamental contribution from constant torsion tube approximation. It is also assumed that the curvature of the magnetic axis of the tube is constant. Though $α$-effect dynamo equations are rather more complex in Riema…
Planetary and stellar dynamos likely result from turbulent motions in magnetofluids with kinematic viscosities that are small compared to their magnetic diffusivities. Laboratory experiments are in progress to produce similar dynamos in liquid metals. This work reviews recent computations of thresholds in critical magnetic Reynolds number above which dynamo amplification can be expected for mechanically-forced turbulence (helical and non-helical, short wavelength and long wavelength) as a function of the magnetic Prandtl number $P_M$. New results for helical forcing are discussed, for which a …
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…
Large-scale magnetic fields in galaxies are thought to be generated by a turbulent dynamo. However the same turbulence also leads to a small-scale dynamo which generates magnetic noise at a more rapid rate. The efficiency of the large-scale dynamo depends on how this noise saturates. We examine this issue taking into account ambipolar drift, which obtains in a galaxy with significant neutral gas. We argue that, (1) the small-scale dynamo generated field does not fill the volume, but is concentrated into intermittent rope like structures. The flux ropes are curved on the turbulent eddy scales. …
We present and analyze a simplified stochastic $αΩ-$dynamo model which is designed to assess the influence of additive and multiplicative noises, non-normality of dynamo equation, and nonlinearity of the $α-$% effect and turbulent diffusivity, on the generation of a large-scale magnetic field in the subcritical case. Our model incorporates random fluctuations in the $α-$parameter and additive noise arising from the small-scale fluctuations of magnetic and turbulent velocity fields. We show that the noise effects along with non-normality can lead to the stochastic amplification of the magnetic …
Small scale turbulent dynamo action in compressible transonic turbulence is discussed. It is shown that the critical value of the magnetic Reynolds number displays a bimodal behavior and changes from a typical value of 35 for small Mach numbers to about 80 for larger Mach numbers. The transition between the two regimes is relatively sharp. The direct simulations are then compared with simulations where shocks are captured using a shock viscosity that becomes large at locations where there are shocks. In the presence of shear it is shown that large scale dynamo action is possible.
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…
Using recent results on the operation of turbulent dynamos, we show that a turbulent dynamo can amplify a large scale magnetic field in the envelopes of asymptotic giant branch (AGB) stars. We propose that a slow rotation of the AGB envelope can fix the symmetry axis, leading to the formation of an axisymmetric magnetic field structure. Unlike solar-type alpha-omega dynamos, the rotation has only a small role in amplifying the toroidal component of the magnetic field. The large-scale magnetic field is strong enough for the formation of magnetic cool spots on the AGB stellar surface. The spots …
We simulate the evolution of an initially weak magnetic field in forced turbulence for a range of Prandtl numbers. The field grows exponentially with the Kulsrud-Anderson $k^{3/2}$ spectrum until the magnetic energy approaches the viscous-scale kinetic energy, where the magnetic forces then backreact on the velocity. Further growth proceeds more slowly until a saturated state is reached where the magnetic and kinetic energies are equal, and where the magnetic energy exists primarily at the resistive scale. We discuss the structure of this turbulence and the extrapolation of the results to astr…
It is shown that the turbulent dynamo $α$-effect converts magnetic helicity from the turbulent field to the mean field when the turbulence is electromagnetic while the magnetic helicity of the mean-field is transported across space when the turbulence is electrostatic or due to the electron diamagnetic effect. In all cases, however, the dynamo effect strictly conserves the total helicity except for resistive effects and a small battery effect. Implications for astrophysical situations, especially for the solar dynamo, are discussed.
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…
Several lines of evidence suggest that protogalactic and galactic environments manage to grow magnetic field very rapidly. This makes the theoretical problem of achieving rapid growth of magnetic fields in such environments difficult. Following Balsara, Benjamin and Cox (2001), we show that a multiphase ISM that is dominated by realistic energy inputs via supernova explosions will naturally become a strongly turbulent medium with large positive and negative values of the fluid helicity. The resultant interstellar turbulence seems to have some of the essential characteristics of a fast dynamo. …
Turbulence with a large magnetic Reyonolds number, generically leads to rapidly growing magnetic noise over and above any mean field. We revisit the dynamics of this fluctuating field, in homogeneous, isotropic, helical turbulence. Assuming the turbulence to be Markovian, we first rederive, in a fairly transparent manner, the equation for the mean field, and corrected Fokker-Plank type equations for the magnetic correlations. In these equations, we also incorporate the effects of ambipolar drift which would obtain if the turbulent medium has a significant neutral component. We apply these equa…
We study an example of instability in presence of a multiplicative noise, namely the spontaneous generation of a magnetic field in a turbulent medium. This so-called turbulent dynamo problem remains challenging, experimentally and theoretically. In this field, the prevailing theory is the Mean-Field Dynamo (Krause and Rädler, 1980) where the dynamo effect is monitored by the mean magnetic field (other possible choices would be the energy, flux,...). In recent years, it has been shown on stochastic oscillators that this type of approach could be misleading. In this paper, we develop a stochasti…
The evolution of magnetic fields is studied using simulations of forced helical turbulence with strong imposed shear. After some initial exponential growth, the magnetic field develops a large scale travelling wave pattern. The resulting field structure possesses magnetic helicity, which is conserved in a periodic box by the ideal MHD equations and can hence only change on a resistive time scale. This constrains strongly the growth time of the large scale magnetic field, but less strongly the length of the cycle period. Comparing with the case without shear, the time scale for large scale fiel…
The nonlinear coefficients defining the mean electromotive force (i.e., the nonlinear turbulent magnetic diffusion, the nonlinear effective velocity, the nonlinear kappa-tensor, etc.) are calculated for an anisotropic turbulence. A particular case of an anisotropic background turbulence (i.e., the turbulence with zero mean magnetic field) with one preferential direction is considered. It is shown that the toroidal and poloidal magnetic fields have different nonlinear turbulent magnetic diffusion coefficients. It is demonstrated that even for a homogeneous turbulence there is a nonlinear effect…
The emergence of a large scale magnetic field from randomly forced isotropic strongly helical flows is discussed in terms of the inverse cascade of magnetic helicity and the alpha-effect. In simulations of such flows the maximum field strength exceeds the equipartition field strength for large scale separation. However, helicity conservation controls the speed at which this final state is reached. In the presence of open boundaries magnetic helicity fluxes out of the domain are possible. This reduces the timescales of the field growth, but it also tends to reduce the maximum attainable field s…
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…
A plane-shear flow in a fluid with forced turbulence is considered. If the fluid is electrically-conducting then a mean electromotive force (EMF) results even without basic rotation and the magnetic diffusivity becomes a highly anisotropic tensor. It is checked whether in this case self-excitation of a large-scale magnetic field is possible (so-called WxJ-dynamo) and the answer is NO. The calculations reveal the cross-stream components of the EMF perpendicular to the mean current having the wrong signs, at least for small magnetic Prandtl numbers. After our results numerical simulations with m…
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…
The turbulent magnetic diffusivity tensor is determined in the presence of rotation or shear. The question is addressed whether dynamo action from the shear-current effect can explain large-scale magnetic field generation found in simulations with shear. For this purpose a set of evolution equations for the response to imposed test fields is solved with turbulent and mean motions calculated from the momentum and continuity equations. The corresponding results for the electromotive force are used to calculate turbulent transport coefficients. The diagonal components of the turbulent magnetic di…
An effect of sheared large-scale motions on a mean electromotive force in a nonrotating turbulent flow of a conducting fluid is studied. It is demonstrated that in a homogeneous divergence-free turbulent flow the alpha-effect does not exist, however a mean magnetic field can be generated even in a nonrotating turbulence with an imposed mean velocity shear due to a new ''shear-current" effect. A contribution to the electromotive force related with the symmetric parts of the gradient tensor of the mean magnetic field (the kappa-effect) is found in a nonrotating turbulent flows with a mean shear.…
We have extended our previous mean-field galactic dynamo model which included algebraic and dynamic alpha nonlinearities (Kleeorin et al., A&A, v. 387, 453, 2002), to include also a quenching of turbulent diffusivity. We readily obtain equilibrium states for the large-scale magnetic field in the local disc dynamo model, and these fields have strengths that are comparable to the equipartition field strength. We find that the algebraic nonlinearity alone (i.e. quenching of both the alpha effect and turbulent magnetic diffusion) cannot saturate the growth of the mean magnetic field; only the comb…
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…
We add the $α-$ effect in the dynamo driven accretion disk model proposed by Tout & Pringle (1992), i.e., a dynamo model depends on the physical processes such as Parker instability, Balbus-Hawley instability, magnetic field reconnection and $α-ω$ mean field dynamo as well. The $α-$ effect in the dynamo mechanism is determined by the strength of turbulence of the accretion flow. When the turbulent Mach number $M_t$ is less than 0.25, the solutions of the magnetic fields oscillate around their equilibrium values. The increase of the value of $M_t$ makes the amplitude of the oscillation smaller …
Magnetic field amplification in astrophysics ultimately requires an understanding of magnetohydrodynamic turbulence. Kinetic helicity has long been known to be important for large scale field growth in forced MHD turbulence, and has been recently demonstrated numerically to be asymptotically consistent with slow mean field dynamo action in a periodic box. Here we show numerically that the magnetic spectrum at and below the forcing scale is also strongly influenced by kinetic helicity. We identify a critical value, $f_{h,crit}$ above which the magnetic spectrum develops maxima at wavenumber $= …
Direct numerical simulations of turbulent Hall dynamos are presented. The evolution of an initially weak and small scale magnetic field in a system maintained in a stationary turbulent regime by a stirring force at a macroscopic scale is studied to explore the conditions for exponential growth of the magnetic energy. Scaling of the dynamo efficiency with the Reynolds numbers is studied, and the resulting total energy spectra are found to be compatible with a Kolmogorov type law. A faster growth of large scale magnetic fields is observed at intermediate intensities of the Hall effect.
We study numerically the dependence of the critical magnetic Reynolds number Rmc for the turbulent small-scale dynamo on the hydrodynamic Reynolds number Re. The turbulence is statistically homogeneous, isotropic, and mirror--symmetric. We are interested in the regime of low magnetic Prandtl number Pm=Rm/Re<1, which is relevant for stellar convective zones, protostellar disks, and laboratory liquid-metal experiments. The two asymptotic possibilities are Rmc->const as Re->infinity (a small-scale dynamo exists at low Pm) or Rmc/Re=Pmc->const as Re->infinity (no small-scale dynamo exists at low P…
The shear-current effect in a nonrotating homogeneous turbulent convection with a large-scale constant shear is studied. The large-scale velocity shear causes anisotropy of turbulent convection, which produces the mean electromotive force $\bec{\cal E}^{(W)} \propto {\bf W} {\bf \times} {\bf J}$ and the mean electric current along the original mean magnetic field, where ${\bf W}$ is the background mean vorticity due to the shear and ${\bf J}$ is the mean electric current. This results in a large-scale dynamo even in a nonrotating and nonhelical homogeneous sheared turbulent convection, whereby…
An unsolved problem in turbulent dynamo theory is the ``back reaction'' problem: to what degree does the mean magnetic field suppress the turbulent dynamo coefficients which are needed to drive its growth? The answer will ultimately derive from a combination of numerical and analytical studies. Here we show that analytic approaches to the dynamo and back reaction problems require one to separate turbulent quantities into two components: those influenced by the mean field (which are therefore anisotropic) and those independent of the mean field (and are therefore isotropic), no matter how weak …
The small-scale turbulent dynamo in the high Prandtl number regime is described in terms of the one-point Fourier space correlators. The second order correlator of this kind is the energy spectrum and it has been previously studied in detail. We examine the higher order k-space correlators which contain important information about the phases of the magnetic wavepackets and about the dominant structures of the magnetic turbulence which cause intermittency. In particular, the fourth-order correlators contain information about the mean-square phase difference between any two components of the mag…
A review of recent studies on a new mechanism of generation of large-scale magnetic field in a sheared turbulent plasma is presented. This mechanism is associated with the shear-current effect which is related to the W x J-term in the mean electromotive force. This effect causes the generation of the large-scale magnetic field even in a nonrotating and nonhelical homogeneous sheared turbulent convection whereby the alpha effect vanishes. It is found that turbulent convection promotes the shear-current dynamo instability, i.e., the heat flux causes positive contribution to the shear-current eff…
(abridged) Aims: Three-dimensional numerical simulations of penetrative compressible convection with uniform horizontal shear are used to study dynamo action and the generation of large-scale magnetic fields. Methods: We consider cases where the magnetic Reynolds number is either marginal or moderately supercritical with respect to small-scale dynamo action in the absence of shear and rotation. The effects of magnetic helicity fluxes are studied by comparing results for the magnetic field with open and closed boundaries. Results: Without shear no large-scale dynamos are found even if the ingre…
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…
Standard magnetohydrodynamic theories, such as the mean field dynamo theory, have been criticized when the back reaction of the magnetic field on turbulent motions is neglected. For the dynamo, this back reaction has been argued to suppress the turbulent motions required for optimal mean field production. Here it is suggested that if the magnetic field is spatially intermittent, for example residing in flux tubes, the back reaction on turbulent flows may be significantly reduced.
We construct a magnetic helicity conserving dynamo theory which incorporates a calculated magnetic helicity current. In this model the fluid helicity plays a small role in large scale magnetic field generation. Instead, the dynamo process is dominated by a new quantity, derived from asymmetries in the second derivative of the velocity correlation function, closely related to the `twist and fold' dynamo model. The turbulent damping term is, as expected, almost unchanged. Numerical simulations with a spatially constant fluid helicity and vanishing resistivity are not expected to generate large s…
The amplification of magnetic fields in a highly conducting fluid is studied numerically. During growth, the magnetic field is spatially intermittent: it does not uniformly fill the volume, but is concentrated in long thin folded structures. Contrary to a commonly held view, intermittency of the folded field does not increase indefinitely throughout the growth stage if diffusion is present. Instead, as we show, the probability-density function (PDF) of the field strength becomes self-similar. The normalized moments increase with magnetic Prandtl number in a powerlike fashion. We argue that the…
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…
