On the mean-field theory of the Karlsruhe Dynamo Experiment

Rädler, K.-H.; Rheinhardt, M.; Apstein, E.; Fuchs, Helmut V.

doi:10.5194/npg-9-171-2002

Cited by 56 publications

(97 citation statements)

References 19 publications

(15 reference statements)

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“…The crucial induction effect of the fluid motion is then, with respect to the mean magnetic field, described as an anisotropic α-effect. The α-coefficient and related quantities have first been calculated for the Roberts flow [19,20,22,23,25]. In the calculations with the spin generator flow carried out so far, apart from the case of small flow rates, a simplifying but not strictly justified assumption was used.…”

Section: Introductionmentioning

confidence: 99%

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Contributions to the theory of a two-scale homogeneous dynamo experiment

Rädler

Brandenburg

2003

Phys. Rev. E

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The principle of the Karlsruhe dynamo experiment is closely related to that of the Roberts dynamo working with a simple fluid flow which is, with respect to proper Cartesian co-ordinates x, y and z, periodic in x and y and independent of z. A modified Roberts dynamo problem is considered with a flow more similar to that in the experimental device. Solutions are calculated numerically, and on this basis an estimate of the excitation condition of the experimental dynamo is given. The modified Roberts dynamo problem is also considered in the framework of the mean-field dynamo theory, in which the crucial induction effect of the fluid motion is an anisotropic α-effect. Numerical results are given for the dependence of the mean-field coefficients on the fluid flow rates. The excitation condition of the dynamo is also discussed within this framework. The behavior of the dynamo in the nonlinear regime, i.e. with backreaction of the magnetic field on the fluid flow, depends on the effect of the Lorentz force on the flow rates. The quantities determining this effect are calculated numerically. The results for the mean-field coefficients and the quantities describing the backreaction provide corrections to earlier results, which were obtained under simplifying assumptions.

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Section: Introductionmentioning

confidence: 99%

“…Both direct numerical solutions of the induction equation for the magnetic field [12,13,14,15,16,17,18] as well as meanfield theory and solutions of the corresponding equations [19,20,21,22,23,24] have been employed. We focus our attention here on this mean-field approach.…”

Section: Introductionmentioning

confidence: 99%

Contributions to the theory of a two-scale homogeneous dynamo experiment

Rädler

Brandenburg

2003

Phys. Rev. E

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“…Regarding the kinematic α effect, Childress (1979) found that in steady convection α decreases with increasing R m like R −1/2 m . This result is now understood to be a common feature of steady flows (Rädler et al 2002, Rädler & Brandenburg 2008, and is generally not shared by unsteady (e.g. turbulent) flows (Sur et al 2008).…”

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confidence: 97%

Advances in Theory and Simulations of Large-Scale Dynamos

Brandenburg

2009

Space Sci Rev

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Recent analytical and computational advances in the theory of large-scale dynamos are reviewed. The importance of the magnetic helicity constraint is apparent even without invoking mean-field theory. The tau approximation yields expressions that show how the magnetic helicity gets incorporated into mean-field theory. The test-field method allows an accurate numerical determination of turbulent transport coefficients in linear and nonlinear regimes. Finally, some critical views on the solar dynamo are being offered and targets for future research are highlighted.

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“…Only in the last days of the last century, in December 1999, after expensive preparations, two dynamos ran successfully with liquid sodium flows, one in Riga (Gailitis et al 2000) and one in Karlsruhe (Müller & Stieglitz 2000. The first one (Riga) is clearly different from a mean-field dynamo, but the second one (Karlsruhe) can be well understood as a meanfield dynamo of α 2 type (see Rädler et al 2002).…”

Section: Laboratory Experimentsmentioning

confidence: 99%

Mean‐field dynamos: The old concept and some recent developments

Rädler

2014

Astron Nachr

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This article elucidates the basic ideas of electrodynamics and magnetohydrodynamics of mean fields in turbulently moving conducting fluids. It is stressed that the connection of the mean electromotive force with the mean magnetic field and its first spatial derivatives is in general neither local nor instantaneous and that quite a few claims concerning pretended failures of the mean-field concept result from ignoring this aspect. In addition to the mean-field dynamo mechanisms of α 2 and αΩ type several others are considered. Much progress in mean-field electrodynamics and magnetohydrodynamics results from the test-field method for calculating the coefficients that determine the connection of the mean electromotive force with the mean magnetic field. As an important example the memory effect in homogeneous isotropic turbulence is explained. In magnetohydrodynamic turbulence there is the possibility of a mean electromotive force that is primarily independent of the mean magnetic field and labeled as Yoshizawa effect. Despite of many efforts there is so far no convincing comprehensive theory of α quenching, that is, the reduction of the α effect with growing mean magnetic field, and of the saturation of mean-field dynamos. Steps toward such a theory are explained. Finally, some remarks on laboratory experiments with dynamos are made.

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On the mean-field theory of the Karlsruhe Dynamo Experiment

Cited by 56 publications

References 19 publications

Contributions to the theory of a two-scale homogeneous dynamo experiment

Contributions to the theory of a two-scale homogeneous dynamo experiment

Advances in Theory and Simulations of Large-Scale Dynamos

Mean‐field dynamos: The old concept and some recent developments

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