On the Nonlinear Nature of the Turbulent α-Effect

Cattaneo, Fausto; Hughes, David W.; Thelen, Jean-Claude

doi:10.1017/s1539299600014829

Cited by 21 publications

(29 citation statements)

References 8 publications

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“…This is exactly what was predicted theoretically [34,35,36,37]. When periodic boundary conditions are imposed, MHD simulations [38,42] can produce such turbulence, demonstrating slow and quenched dynamos [43]. Stationarity and homogeneity of a turbulence implies that there exist no preferential directions in time and space for the system to evolve.…”

Section: Stationary and Homogeneous Turbulence Versus Driven Systemssupporting

confidence: 75%

“…The concept of slow dynamo is closely related, if not identical, to the so-called back-reaction of mean magnetic field on the α-effect in the analytic MHD models [34,35,36,37], confirmed by MHD simulations [38]. A self-consistent constraint due to Lorentz force on the flow [39] applies on the kinematic dynamo effects,…”

Section: Back-reaction Of Mean Field On Dynamo Actionmentioning

confidence: 72%

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The Alpha Dynamo Effects in Laboratory Plasmas

Ji¹,

Prager²

2001

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A concise review of observations of the α dynamo effect in laboratory plasmas is given. Unlike many astrophysical systems, the laboratory pinch plasmas are driven magnetically. When the system is overdriven, the resultant instabilities cause magnetic and flow fields to fluctuate, and their correlation induces electromotive forces along the mean magnetic field. This α-effect drives mean parallel electric current, which, in turn, modifies the initial background mean magnetic structure towards the stable regime. This drive-andrelax cycle, or the so-called self-organization process, happens in magnetized plasmas in a time scale much shorter than resistive diffusion time, thus it is a fast and unquenched dynamo process. The observed α-effect redistributes magnetic helicity (a measure of twistedness and knottedness of magnetic field lines) but conserves its total value. It can be shown that fast and unquenched dynamos are natural consequences of a driven system where fluctuations are statistically either not stationary in time or not homogeneous in space, or both. Implications to astrophysical phenomena will be discussed.

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Section: Stationary and Homogeneous Turbulence Versus Driven Systemssupporting

confidence: 75%

Section: Back-reaction Of Mean Field On Dynamo Actionmentioning

confidence: 72%

The Alpha Dynamo Effects in Laboratory Plasmas

Ji¹,

Prager²

2001

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“…Here µ and · are respectively the small-scale velocity and magnetic fields, s ¹ ¦ c µ and¦ c · are the small-scale vorticity and current, and´is a typical correlation time for these turbulent motions. Attempts to measure this quantity in direct simulations using different methods can be found in Cattaneo and Hughes (1996), and Brandenburg (2001). In the absence of a mean flow , equation (9) predicts an exponential growth above a certain threshold if…”

Section: Kinematic Regimementioning

confidence: 99%

Direct numerical simulations of helical dynamo action: MHD and beyond

Gomez

Mininni

2004

Nonlin. Processes Geophys.

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Abstract. Magnetohydrodynamic dynamo action is often invoked to explain the existence of magnetic fields in several astronomical objects. In this work, we present direct numerical simulations of MHD helical dynamos, to study the exponential growth and saturation of magnetic fields. Simulations are made within the framework of incompressible flows and using periodic boundary conditions. The statistical properties of the flow are studied, and it is found that its helicity displays strong spatial fluctuations. Regions with large kinetic helicity are also strongly concentrated in space, forming elongated structures. In dynamo simulations using these flows, we found that the growth rate and the saturation level of magnetic energy and magnetic helicity reach an asymptotic value as the Reynolds number is increased. Finally, extensions of the MHD theory to include kinetic effects relevant in astrophysical environments are discussed.

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“…In this way we do not consider quenching effects, i.e. reductions of the coefficients defining the mean electromotive force with growing mean magnetic field, which are very important in view of the nonlinear behavior of dynamos and have been discussed in a number of papers (see, e.g., Gruzinov & Diamond 1994, Cattaneo & Hughes 1996, Seehafer 1996, Kulsrud 1999, Field et al 1999, Rogachevskii & Kleeorin 2001, Kleeorin et al 2002a, Blackman & Brandenburg 2002). Finally we use a τ -approximation in the equations describing the deviation of the cross-helicity tensor from that for zero magnetic field.…”

Section: Introductionmentioning

confidence: 99%

The mean electromotive force for MHD turbulence: The case of a weak mean magnetic field and slow rotation

Raedler¹,

Kleeorin²,

Rogachevskii³

2003

GGAF

113

159

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The mean electromotive force that occurs in the framework of mean-field magnetohydrodynamics is studied for cases in which magnetic field fluctuations are not only due to the action of velocity fluctuations on the mean magnetic field. The possibility of magnetic field fluctuations independent of a mean magnetic field, as they may occur as a consequence of a small-scale dynamo, is taken into account. Particular attention is payed to the effect of a mean rotation of the fluid on the mean electromotive force, although only small rotation rates are considered. Anisotropies of the turbulence due to gradients of its intensity or its helicity are admitted. The mean magnetic field is considered to be weak enough to exclude quenching effects. A τ -approximation is used in the equation describing the deviation of the cross-helicity tensor from that for zero mean magnetic field, which applies in the limit of large hydrodynamic Reynolds numbers.For the effects described by the mean electromotive force like α-effect, turbulent diffusion of magnetic fields etc. in addition to the contributions determined by the velocity fluctuations also those determined by the magnetic field fluctuations independent of the mean magnetic field are derived. Several old results are confirmed, partially under more general assumptions, and quite a few new ones are given. Provided the kinematic helicity and the current helicity of the fluctuations have the same signs the α-effect is always diminished by the magnetic fluctuations. In the absence of rotation these have, however, no influence on the turbulent diffusion. Besides the diamagnetic effect due to a gradient of the intensity of the velocity fluctuations there is a paramagnetic effect due to a gradient of the intensity of the magnetic fluctuations. In the absence of rotation these two effects compensate each other in the case of equipartition of the kinetic and magnetic energies of the fluctuations of the original turbulence, i.e. that with zero mean magnetic field, but the rotation makes the situation more complex. The Ω × J-effect works in the same way with velocity fluctuations and magnetic field fluctuations. A contribution to the electromotive force connected with the symmetric parts of the gradient tensor of the mean magnetic field, which does not occur in the absence of rotation, was found in the case of rotation, resulting from velocity or magnetic fluctuations.The implications of the results for the mean electromotive force for mean-field dynamo models are discussed with special emphasis to dynamos working without α-effect.The results for the coefficients defining the mean electromotive force which are determined by the velocity fluctuations in the case of vanishing mean motion agree formally with the results obtained in the kinematic approach, specified by second-order approximation and high-conductivity limit. However, their range of validity is clearly larger.

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On the Nonlinear Nature of the Turbulent α-Effect

Abstract: Galactic magnetic fields are, typically, modelled by meanfield dynamos involving the a-effect. Here we consider, very briefly, some of the issues involving the nonlinear dependence of a on the mean field.

Cited by 21 publications

References 8 publications

The Alpha Dynamo Effects in Laboratory Plasmas

The Alpha Dynamo Effects in Laboratory Plasmas

Direct numerical simulations of helical dynamo action: MHD and beyond

The mean electromotive force for MHD turbulence: The case of a weak mean magnetic field and slow rotation

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