Laboratory Experiments and Numerical Simulations on Magnetic Instabilities
Magnetic fields of planets, stars, and galaxies are generated by self-excitation in moving electrically conducting fluids. Once produced, magnetic fields can play an active role in cosmic structure formation by destabilizing rotational flows that would be otherwise hydrodynamically stable. For a long time, both hydromagnetic dynamo action and magnetically triggered flow instabilities had been the subject of purely theoretical research. Meanwhile, however, the dynamo effect has been observed in large-scale liquid sodium experiments in Riga, Karlsruhe, and Cadarache. In this chapter, we summarize the results of some smaller liquid metal experiments devoted to various magnetic instabilities, such as the helical and the azimuthal magnetorotational instability, the Tayler instability, and the different instabilities that appear in a magnetized spherical Couette flow. We conclude with an outlook on a large scale Tayler-Couette experiment using liquid sodium, and on the prospects to observe magnetically triggered instabilities of flows with positive shear.
This work was supported by Deutsche Forschungsgemeinschaft in the frame of the focus programme 1488 (PlanetMag). Intense collaboration with Rainer Hollerbach on the theory and numerics of the different instabilities is gratefully acknowledged. We thank Thomas Gundrum for his contributions in setting up and running the experiments, and Elliot Kaplan for his numerical and experimental work on the HEDGEHOG experiment. We are grateful to Johannes Wicht for the introduction into the MagIC code. F.S. likes to thank Oleg Kirillov for his efforts to establish a comprehensive WKB theory of the magnetically triggered instabilities, and George Mamatsashvili for his work on non-modal aspects of MRI.
- Adams, M.M., Stone, D.R., Zimmerman, D.S., Lathrop, D.P.: Liquid sodium models of the Earth’s core. Prog. Earth Planet. Sci. 29, 1–18 (2015).Google Scholar
- Charbonneau, P.: Dynamo models of the solar cycle. Liv. Rev. Sol. Phys. 7, 3 (2010)Google Scholar
- Lebreton, Y., Maeder, A.: Stellar evolution with turbulent diffusion mixing. VI - The solar model, surface Li-7, and He-3 abundances, solar neutrinos and oscillations. Astron. Astrophys. 175, 99 (1987)Google Scholar
- Mamatsashvili, G., Stefani, F.: Linking dissipation-induced instabilities with nonmodal growth: the case of helical magnetorotational instability. Phys. Rev. E 76, 016310 (2016)Google Scholar
- Seilmayer, M., Galindo, V., Gerbeth, G., Gundrum, T., Stefani, F., Gellert, M., Rüdiger, G., Schultz, M.: Experimental evidence for nonaxisymmetric magnetorotational instability in a rotating liquid metal exposed to an azimuthal magnetic field. Phys. Rev. Lett. 113, 024505 (2014)ADSCrossRefGoogle Scholar
- Sorriso-Valvo, L., Stefani, F., Carbone, V. Nigro, G., Lepreti, F., Vecchio, A. Veltri, P: A statistical analysis of polarity reversals of the geomagnetic field. Phys. Earth Planet. Inter. 164, 197–207 (2007)Google Scholar
- Starace, M., Weber, N., Seilmayer, M., Kasprzyk, C., Weier, T., Stefani, F., Eckert, S.: Ultrasound Doppler flow measurement in a liquid metal columns under the influence of a strong axial electric current. Magnetohydrodynamics 51, 249–256 (2015)Google Scholar
- Stefani, F., Eckert, S., Gerbeth, G., Giesecke, A., Gundrum, T., Steglich, C., Wustmann, B.: DRESDYN - a new facility for MHD experiments with liquid sodium. Magnetohydrodynamics 48, 103–113 (2012)Google Scholar
- Stefani, F., Albrecht, T., Gerbeth, G., Giesecke, A., Gundrum, T., Herault, J., Nore, C. Steglich, C.: Towards a precession driven dynamo experiment. Magnetohydrodynamics 51, 275–284 (2015)Google Scholar
- Weber, N., Galindo, V., Stefani, F., Weier, T.: Numerical simulation of the Tayler instability in liquid metals. 15, 043034 (2013)Google Scholar
- Zahn, J.P.: In: Goupil, M.-J., Zahn, J.-P. (eds.) Rotation and Mixing in Stellar Interiors. Lecture Notes of Physics, vol. 336, p. 141. Springer, New York (1990)Google Scholar