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Axisymmetric dynamo action produced by differential rotation, with anisotropic electrical conductivity and anisotropic magnetic permeability

Published online by Cambridge University Press:  08 February 2021

Franck Plunian Open the ORCID record for Franck Plunian [Opens in a new window]  and
Thierry Alboussière Open the ORCID record for Thierry Alboussière [Opens in a new window]
Franck Plunian*
Affiliation:
Université Grenoble Alpes, Université Savoie Mont Blanc, CNRS, IRD, IFSTTAR, ISTerre, 38000Grenoble, France
Thierry Alboussière
Affiliation:
Univ. Lyon, Univ. Lyon 1, ENSL, CNRS, LGL-TPE, F-69622, Villeurbanne, France
*
†Email address for correspondence: [email protected]
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Abstract

The effect on dynamo action of an anisotropic electrical conductivity conjugated to an anisotropic magnetic permeability is considered. Not only is the dynamo fully axisymmetric, but it requires only a simple differential rotation, which twice challenges the well-established dynamo theory. Stability analysis is conducted entirely analytically, leading to an explicit expression of the dynamo threshold. The results show a competition between the anisotropy of electrical conductivity and that of magnetic permeability, the dynamo effect becoming impossible if the two anisotropies are identical. For isotropic electrical conductivity, Cowling's neutral point argument does imply the absence of an azimuthal component of current density, but does not prevent the dynamo effect as long as the magnetic permeability is anisotropic.

Keywords

plasma instabilities
Type
Research Article
Information
Journal of Plasma Physics , Volume 87 , Issue 1 , February 2021 , 905870110
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Copyright
Copyright © The Author(s), 2021. Published by Cambridge University Press

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References

REFERENCES

Alboussière, T., Cardin, P., Debray, F., La Rizza, P., Masson, J.-P., Plunian, F., Ribeiro, A. & Schmitt, D. 2011 Experimental evidence of Alfvén wave propagation in a gallium alloy. Phys. Fluids 23 (9), 096601.CrossRefGoogle Scholar
Alboussière, T., Drif, K. & Plunian, F. 2020 Dynamo action in sliding plates of anisotropic electrical conductivity. Phys. Rev. E 101, 033107.CrossRefGoogle ScholarPubMed
Avalos-Zuñiga, R. & Plunian, F. 2005 Influence of inner and outer walls electromagnetic properties on the onset of a stationary dynamo. Eur. Phys. J. B 47, 127–135.CrossRefGoogle Scholar
Avalos-Zuñiga, R., Plunian, F. & Gailitis, A. 2003 Influence of electromagnetic boundary conditions onto the onset of dynamo action in laboratory experiments. Phys. Rev. E 68, 066307.CrossRefGoogle ScholarPubMed
Braginskii, S. I. 1965 Transport processes in a plasma. Rev. Plasma Phys. 1, 205.Google Scholar
Brandenburg, A. 2018 Advances in mean-field dynamo theory and applications to astrophysical turbulence. J. Plasma Phys. 84 (4), 735840404.CrossRefGoogle Scholar
Busse, F. H. & Wicht, J. 1992 A simple dynamo caused by conductivity variations. Geophys. Astrophys. Fluid Dyn. 64 (1–4), 135–144.CrossRefGoogle Scholar
Cowling, T. G. 1934 The magnetic field of sunspots. Mon. Not. R. Astron. Soc. 94, 39–48.CrossRefGoogle Scholar
Deuss, A. 2014 Heterogeneity and anisotropy of earth's inner core. Annu. Rev. Earth Planet. Sci. 42 (1), 103–126.CrossRefGoogle Scholar
Gailitis, A., Lielausis, O., Platacis, E., Dement'ev, S., Cifersons, A., Gerbeth, G., Gundrum, T., Stefani, F., Christen, M. & Will, G. 2001 Magnetic field saturation in the Riga dynamo experiment. Phys. Rev. Lett. 86, 3024–3027.CrossRefGoogle ScholarPubMed
Kaiser, R., Schmitt, B. J. & Busse, F. H. 1994 On the invisible dynamo. Geophys. Astrophys. Fluid Dyn. 77 (1–4), 93–109.CrossRefGoogle Scholar
Kaiser, R. & Tilgner, A. 1999 On Vainshtein's dynamo conjecture. Proc. R. Soc. Lond. A 455 (1988), 3139–3162.CrossRefGoogle Scholar
Kaiser, R. & Tilgner, A. 2014 The axisymmetric antidynamo theorem revisited. SIAM J. Appl. Maths 74 (2), 571–597.CrossRefGoogle Scholar
Krause, F. & Rädler, K. H. 1980 Mean-field Magnetohydrodynamics and Dynamo Theory. Pergamon Press.Google Scholar
Kreuzahler, S., Ponty, Y., Plihon, N., Homann, H. & Grauer, R. 2017 Dynamo enhancement and mode selection triggered by high magnetic permeability. Phys. Rev. Lett. 119, 234501.CrossRefGoogle ScholarPubMed
Lortz, D. 1989 Axisymmetric dynamo solutions. Z. Naturforsch. 44a, 1041–1045.CrossRefGoogle Scholar
Lowes, F. J. & Wilkinson, I. 1963 Geomagnetic dynamo: a laboratory model. Nature 198, 1158–1160.CrossRefGoogle Scholar
Lowes, F. J. & Wilkinson, I. 1968 Geomagnetic dynamo: an improved laboratory model. Nature 219, 717–718.CrossRefGoogle Scholar
Miralles, S., Bonnefoy, N., Bourgoin, M., Odier, P., Pinton, J.-F., Plihon, N., Verhille, G., Boisson, J., Daviaud, F. & Dubrulle, B. 2013 Dynamo threshold detection in the Von Kármán sodium experiment. Phys. Rev. E 88, 013002.CrossRefGoogle ScholarPubMed
Monchaux, R., Berhanu, M., Bourgoin, M., Moulin, M., Odier, P., Pinton, J.-F., Volk, R., Fauve, S., Mordant, N., Pétrélis, F., et al. 2007 Generation of a magnetic field by dynamo action in a turbulent flow of liquid sodium. Phys. Rev. Lett. 98, 044502.CrossRefGoogle Scholar
Nore, C., Castanon Quiroz, D., Cappanera, L. & Guermond, J.-L. 2018 Numerical simulation of the von Kármán sodium dynamo experiment. J. Fluid Mech. 854, 164–195.CrossRefGoogle Scholar
Ohta, K., Nishihara, Y., Sato, Y., Hirose, K., Yagi, T., Kawaguchi, S. I., Hirao, N. & Ohishi, Y. 2018 An experimental examination of thermal conductivity anisotropy in hcp iron. Front. Earth Sci. 6, 176.CrossRefGoogle Scholar
Plunian, F. & Alboussière, T. 2020 Axisymmetric dynamo action is possible with anisotropic conductivity. Phys. Rev. Res. 2, 013321.CrossRefGoogle Scholar
Rincon, F. 2019 Dynamo theories. J. Plasma Phys. 85 (4), 205850401.CrossRefGoogle Scholar
Ruderman, M. S. & Ruzmaikin, A. A. 1984 Magnetic field generation in an anisotropically conducting fluid. Geophys. Astrophys. Fluid Dyn. 28 (1), 77–88.CrossRefGoogle Scholar
Schaeffer, N., Jault, D., Nataf, H.-C. & Fournier, A. 2017 Turbulent geodynamo simulations: a leap towards Earth's core. Geophys. J. Intl 211 (1), 1–29.CrossRefGoogle Scholar
Stieglitz, R. & Müller, U. 2001 Experimental demonstration of a homogeneous two-scale dynamo. Phys. Fluids 13 (3), 561–564.CrossRefGoogle Scholar
Tigrine, Z., Nataf, H.-C., Schaeffer, N., Cardin, P. & Plunian, F. 2019 Torsional Alfvén waves in a dipolar magnetic field: experiments and simulations. Geophys. J. Intl 219, S83–S100.CrossRefGoogle Scholar