Intermittent magnetic field excitation by a turbulent flow of liquid sodium

The magnetic field measured in the Madison dynamo experiment shows intermittent periods of growth when an axial magnetic field is applied. The geometry of the intermittent field is consistent with the fastest-growing magnetic eigenmode predicted by kinematic dynamo theory using a laminar model of the mean flow. Though the eigenmodes of the mean flow are decaying, it is postulated that turbulent fluctuations of the velocity field change the flow geometry such that the eigenmode growth rate is temporarily positive. Therefore, it is expected that a characteristic of the onset of a turbulent dynamo is magnetic intermittency.     

Dynamo quenching due to shear flow

We provide a theory of dynamo (alpha effect) and momentum transport in three-dimensional magnetohydrodynamics. For the first time, we show that the alpha effect is reduced by the shear even in the absence of magnetic field. The alpha effect is further suppressed by magnetic fields well below equipartition (with the large-scale flow) with different scalings depending on the relative strength of shear and magnetic field. The turbulent viscosity is also found to be significantly reduced by shear and magnetic fields, with positive value. These results suggest a crucial effect of shear and magnetic field on dynamo quenching and momentum transport reduction, with important implications for laboratory and astrophysical plasmas, in particular, for the dynamics of the Sun.     

Magnetic dynamo action at low magnetic Prandtl numbers

Amplification of magnetic field due to kinematic turbulent dynamo action is studied in the regime of small magnetic Prandtl numbers. Such a regime is relevant for planets and stars interiors, as well as for liquid-metal laboratory experiments. A comprehensive analysis based on the Kazantsev-Kraichnan model is reported, which establishes the dynamo threshold and the dynamo growth rates for varying kinetic helicity of turbulent fluctuations. It is proposed that in contrast with the case of large magnetic Prandtl numbers, the kinematic dynamo action at small magnetic Prandtl numbers is significantly affected by kinetic helicity, and it can be made quite efficient with an appropriate choice of the helicity spectrum.     

Transition from large-scale to small-scale dynamo

The dynamo equations are solved numerically with a helical forcing corresponding to the Roberts flow. In the fully turbulent regime the flow behaves as a Roberts flow on long time scales, plus turbulent fluctuations at short time scales. The dynamo onset is controlled by the long time scales of the flow, in agreement with the former Karlsruhe experimental results. The dynamo mechanism is governed by a generalized α effect, which includes both the usual α effect and turbulent diffusion, plus all higher order effects. Beyond the onset we find that this generalized α effect scales as O(Rm(-1)), suggesting the takeover of small-scale dynamo action. This is confirmed by simulations in which dynamo occurs even if the large-scale field is artificially suppressed.     

Effect of electromagnetic boundary condition on dynamo actions

In this paper,based on the mean field dynamo theory,the influence of the electromagnetic boundary condition on the dynamo actions driven by the small scale turbulent flows in a cylindrical vessel is investigated by the integral equation approach.The numerical results show that the increase of the electrical conductivity or magnetic permeability of the walls of the cylindrical vessel can reduce the critical magnetic Reynolds number.Furthermore,the critical magnetic Reynolds number is more sensitive to the varying electrical conductivity of the end wall or magnetic permeability of the side wall.For the anisotropic dynamo which is the mean field model of the Karlsruhe experiment,when the relative electrical conductivity of the side wall or the relative magnetic permeability of the end wall is less than some critical value,the m=1(m is the azimuthal wave number)magnetic mode is the dominant mode,otherwise the m=0 mode predominates the excited magnetic field.Therefore,by changing the material of the walls of the cylindrical vessel,one can select the magnetic mode excited by the anisotropic dynamo.     

The Alpha Effect: The Connection between Cyclonic Events and Current Helicity

In a magnetized plasma, resistive diffusion of large-scale magnetic fields can be suppressed or even overcome by a turbulently generated electromotive force. For a plasma in which the turbulence is homogeneous and isotropic this EMF is characterized by the ensemble average = ?B0, where ?v and ?b represent the turbulent fields and B0 defines the large-scale field. Determination of the statistical properties of the turbulence that are required to generate a finite alpha effect, as it has become known, is one of the central subjects of dynamo theory. Parker has shown that helical velocity fluctuations possessing a net amount of kinetic helicity are capable of dynamo action. These "cyclonic events" produce electromagnetic fluctuations characterized by their own statistical properties. Within the context of "mean-field electrodynamics" we show that these fluctuations possess a net amount of current helicity, and find that a necessary condition for dynamo action is that the turbulent current helicity and the current helicity in the large-scale field be of opposite sign.     

Magnetic Field in a Screw Flow with Fluctuations

We consider the influence of fluctuations in a screw flow of a conducting liquid on the effect of magnetic field self-excitation; the solution of this problem is important for experimental realization of a turbulent dynamo. We propose a theoretical approach based on the solution of averaged equations obtained in the limit of a short correlation time. The applicability of this approach is confirmed by direct numerical simulation of the initial equations. We demonstrate the influence of the correlation of fluctuations on the dynamo effect threshold. It is shown that the solution of the mean-field equations differs from the solution based on direct numerical simulation for a finite correlation time. The advantages and disadvantages of the two approaches are estimates, as well as the importance of the discovered difference in the context of problems of magnetic field self-excitation. The influence of helicity and intermittency on the type of the solution is considered.     

Generation of a magnetic field by dynamo action in a turbulent flow of liquid sodium

We report the observation of dynamo action in the von Kármán sodium experiment, i.e., the generation of a magnetic field by a strongly turbulent swirling flow of liquid sodium. Both mean and fluctuating parts of the field are studied. The dynamo threshold corresponds to a magnetic Reynolds number R(m) approximately 30. A mean magnetic field of the order of 40 G is observed 30% above threshold at the flow lateral boundary. The rms fluctuations are larger than the corresponding mean value for two of the components. The scaling of the mean square magnetic field is compared to a prediction previously made for high Reynolds number flows.     

Numerical simulation of a turbulent magnetic dynamo

We present numerical simulations of a turbulent magnetic dynamo mimicking closely the Riga-dynamo experiment at Re approximately 3.5x10(6) and 15< or =Rem< or =20. The Reynolds-averaged Navier-Stokes equations for the fluid flow and turbulence field are solved simultaneously with the direct numerical solution of the magnetic field equations. The fully integrated two-way-coupled simulations reproduced all features of the magnetic self-excitation detected by the Riga experiment, with frequencies and amplitudes of the self-generated magnetic field in good agreement with the experimental records, and provided full insight into the unsteady magnetic and velocity fields and the mechanisms of the dynamo action.     

Dynamo Effect in the Kraichnan Magnetohydrodynamic Turbulence

The existence of a dynamo effect in a simplified magnetohydrodynamic model of turbulence is considered when the magnetic Prandtl number approaches zero or infinity. The magnetic field is interacting with an incompressible Kraichnan-Kazantsev model velocity field which incorporates also a viscous cutoff scale. An approximate system of equations in the different scaling ranges can be formulated and solved, so that the solution tends to the exact one when the viscous and magnetic-diffusive cutoffs approach zero. In this approximation we are able to determine analytically the conditions for the existence of a dynamo effect and give an estimate of the dynamo growth rate. Among other things we show that in the large magnetic Prandtl number case the dynamo effect is always present. Our analytical estimates are in good agreement with previous numerical studies of the Kraichnan-Kazantsev dynamo by Vincenzi (J. Stat. Phys. 106:1073–1091, 2002).     

Nonlinear current helicity fluxes in turbulent dynamos and alpha quenching

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 field, just like turbulent diffusion. Additional nonlinear fluxes are identified, which are driven by the anisotropic and antisymmetric parts of the magnetic correlations. These could provide further ways for turbulent dynamos to transport out small scale magnetic helicity, so as to avoid catastrophic quenching.     

漂移波湍流中“clumps”理论

本文基于Misguich和Balescu提出的轨道的随机处理发展了漂移波湍流中“clumps”的一种理论。指出clump效应不仅存在于非磁化湍性等离子体中也存在于磁化湍性等离子体中。它的存在使得实际横越磁场的扩散比Dupree理论预言的要小得多。导出了clumps寿命的一个明晰的表达式,它正比于横越磁场扩散的特征时间并对数地依赖于粒子的初始相对位置。 关键词：     

Magnetopause charging and transfer of momentum and energy into magnetosphere

The theory of charged current sheets is compared with plasma data of Prognoz-8, Interball-1, Polar, and Cluster satellites. The possibility of momentum and energy transfer into the magnetosphere, irrespective of magnetic field line reconnection, as a specific dynamo effect, is shown. This relates statistical properties of the turbulent boundary layers with the character of the transfer through thin boundaries.     

Mach number dependence of turbulent magnetic field amplification: solenoidal versus compressive flows

We study the growth rate and saturation level of the turbulent dynamo in magnetohydrodynamical simulations of turbulence, driven with solenoidal (divergence-free) or compressive (curl-free) forcing. For models with Mach numbers ranging from 0.02 to 20, we find significantly different magnetic field geometries, amplification rates, and saturation levels, decreasing strongly at the transition from subsonic to supersonic flows, due to the development of shocks. Both extreme types of turbulent forcing drive the dynamo, but solenoidal forcing is more efficient, because it produces more vorticity.     

Hyperdiffusion in nonlinear large- and small-scale turbulent dynamos

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 backreacts on the turbulence to saturate the mean-field and small-scale dynamos. For the mean-field dynamo, in a quasilinear treatment of this saturation, it is generally thought that, while the alpha effect gets renormalized and suppressed by nonlinear 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 nonlinear hyperdiffusion of the mean field. A combination of such nonlinear hyperdiffusion with diffusion at small scales also arises in a similar treatment of small-scale dynamos, and is crucial to understand its saturation.     

The Dynamo-Driven Magnetic Helicity Transport

In this paper, a new set of the evolution equations for the helicity of the mean magnetic field and the mean helicity of the fluctuating magnetic field is derived from the Maxwell equations and the generalized Ohm's law with the dynamo action. It is shown that there exist two kinds of the dynamo-driven magnetic helicity transport. One of them makes the mean magnetic field helicity transfer to the fluctuating magnetic field, yielding an anomalous loop voltage. The other makes the fluctuating magnetic field helicity transfer to the mean magnetic field, which provides a convincing evidence for the existence of the dynamo current. Therefore, the two kinds of the magnetic helicity transport describe the mutual conversion between the regular and irregular motions. The formulas of the loop voltage and the dynamo current are given. In particular, we give out the formula of the dynamo current-generated equilibrium magnetic field which provides a concrete mode of the magnetic field creation and maintenance in both astrophysical and laboratory (e.g., reversed-field pinch) plasmas.     

Impact of impellers on the axisymmetric magnetic mode in the VKS2 dynamo experiment

In the von Kármán Sodium 2 (VKS2) successful dynamo experiment of September 2006, the observed magnetic field showed a strong axisymmetric component, implying that nonaxisymmetric components of the flow field were acting. By modeling the induction effect of the spiraling flow between the blades of the impellers in a kinematic dynamo code, we find that the axisymmetric magnetic mode is excited. The control parameters are the magnetic Reynolds number of the mean flow, the coefficient measuring the induction effect alpha, and the type of boundary conditions. We show that using realistic values of alpha, the observed critical magnetic Reynolds number, Rm;{c} approximately 32, can be reached easily with ferromagnetic boundary conditions. We conjecture that the dynamo action achieved in this experiment may not be related to the turbulence in the bulk of the flow, but rather to the alpha effect induced by the impellers.     

New dynamical mean-field dynamo theory and closure approach

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, E. We show that the difference between kinetic and current helicities emerges naturally as the growth driver when the time derivative of E 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 for the closure.     

Clustering of polarity reversals of the geomagnetic field

Often in nature the temporal distribution of inhomogeneous stochastic point processes can be modeled as a realization of renewal Poisson processes with a variable rate. Here we investigate one of the classical examples, namely, the temporal distribution of polarity reversals of the geomagnetic field. In spite of the commonly used underlying hypothesis, we show that this process strongly departs from a Poisson statistics, the origin of this failure stemming from the presence of temporal clustering. We find that a Lévy statistics is able to reproduce paleomagnetic data, thus suggesting the presence of long-range correlations in the underlying dynamo process.     

Metric-torsion decay of non-adiabatic chiral helical magnetic fields against chiral dynamo action in bouncing cosmological models

Metric-torsion effects on chiral massless fermions are investigated in the realm of the adiabatic amplification of cosmological magnetic fields (CMFs) in a general relativistic framework and in the framework of Einstein–Cartan (EC) bouncing cosmologies. In GR the chiral effect is proportional to the Hubble factor and the solution of the dynamo equation leads to an adiabatic magnetic field, while in Einstein–Cartan bouncing cosmology we have non-adiabatic magnetic fields where the breaking of adiabaticity is given by a torsion term. Using a EWPT magnetic field of the order of \(B_{\text {seed}}\sim {10^{24}}\) G at 5 pc scale, we obtain a CMF in EC of the order of \(10^{-10}\) G, which is still able to seed a galactic dynamo which amplifies this field up to galactic magnetic fields of four orders of magnitude, which is a mild dynamo. In the case of massive chiral fermions it is shown that torsion actually attenuated the convective dynamo term in the dynamo equation obtained from the QED of an electron–positron pair \(e^{-}e^{+}\). Chiral effects on general relativity may lead to strong magnetic fields of the order of \(\sim {10^{18}}\) G at the early universe resulting from pure metric effects. Strong magnetic fields of the order of \(B_{\text {metric}-\text {torsion}}\sim {10^{8}}\) G may be obtained from very strong seed fields. At 1 Mpc scale of the present universe a galactic dynamo seed of the order of \(10^{-19}\) G is found. It is shown in this paper that chiral dynamo effects in the expanded universe can be obtained if one takes into account the speed of the cosmic plasma.