Dr. Gunter Gerbeth
Director Institute of Fluid Dynamics
Phone: +49 351 260 - 3480, 3484
Fax: +49 351 260 - 3440

Dr. Gerd Mutschke
Institute of Fluid Dynamics
Phone: +49 351 260 - 2480
Fax: +49 351 260 - 12480

Petra Vetter
Secretary Institute of Fluid Dynamics
Phone: +49 351 260 - 3480
Fax: 13480, 3440

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Project A2: Magnetic field dynamos and the magnetorotational instability

PI: Frank Stefani (HZDR)
Partners: HZDR, UG, UP, IPUL, CU, KIT

1. Scientific case for the project

1.1 Background

Magnetic fields of planets, stars, and galaxies are produced by the homogenous dynamo effect [1,6]. They play a key role in cosmic structure formation by enabling angular momentum transport in accretion disks around central objects, like protostars or black holes, by virtue of the magnetorotational instability (MRI) [2]. The related, but current-driven kink-type Tayler instability (TI) is at the root of an alternative model of stellar dynamos [3,7], and could also explain helical structures in cosmic jets. Interestingly, in the context of energy storage technology, the very same TI has to be considered as a size limiting effect for the envisioned large-scale liquid metal batteries [8]. A similar surprising link to energy technologies exists for the dynamo effect which is under discussion as a possible source of dangerous flow instabilities in fast breeder reactors which should definitely be avoided.
After decades of purely theoretical and numerical research, the last years have seen tremendous progress in the experimental study both of the homogeneous dynamo effect as well as of magnetically triggered flow instabilities [9-11]. Meanwhile, the hydromagnetic dynamo effect has been evidenced in three large scale liquid sodium experiments in Riga [12,13], Karlsruhe [14,15], and Cadarache [4]. The helical version of MRI, and the TI were studied recently in two liquid metal experiments at HZDR [16,17]. Further dynamo and/or MRI related experiments with liquid metals are pursued in Madison, Maryland, Socorro, Princeton, and Perm, with the 3 m spherical Couette experiment in Maryland being the most impressive one [5].

1.2 Most important goals of the planned work

The project will support, and later exploit, the experimental capabilities to become available in the framework of the DRESden Sodium facility for DYNamo and thermohydraulic studies (DRESDYN) in order to make further progress in the investigation of the origin and action of cosmic magnetic fields.
The most ambitious set-up of DRESDYN will be a large-scale precession experiment with liquid sodium (see Fig. 3). On one hand, the motivation for this experiment comes from the geo- and astrophysical question whether precessing cosmic bodies are capable of producing magnetic fields [18,19]. On the other hand, the set-up is also thought as a truly homogeneous experimental dynamo, without using internal blades or propellers.
The second liquid sodium experiment will be a Taylor-Couette set-up for the combined investigation of TI and of different versions of MRI (standard, helical, and azimuthal), and of the transitions between them [20]. While mainly focusing on the new DRESDYN installations at HZDR, the project will strongly rely on the vast dynamo experiences generated at the experiments at KIT and at IPUL, and it will support the upgrade of the latter with the prospect of identifying more interesting back-reaction effects [21]. At the same time the Riga dynamo will also be used for testing and calibrating magnetic field and velocity measuring sensors at high velocities, which is urgently needed for the later instrumentation of the DRESDYN experiments.

Fig. 3: Sketch of the planned precession driven dynamo experiment at HZDR
All these experimental activities will be accompanied by theoretical investigations of precession driven dynamos at UG and of MRI and TI at UP and CU.

2. Existing competencies and infrastructure

DRESDYN is a running project at HZDR with a budget of about 23 M€ for the new laboratory and the installation of the precession and MRI experiments. Its realization is foreseen for 2013 and 2014, thus first experiments will be in operation in 2015. The project will give support to the new DRESDYN experiments by means of numerical simulations and by analyzing experimental data from the necessary water pre-experiments and (later) from the real liquid sodium experiments. The Riga dynamo experiment, which has been working since 1999 [10,12,13], is still in operation and will be available for further experiments. The partner at UG has vast experience with the numerical simulation of the Karlsruhe experiment [15] and precession driven dynamos [18,19]. The group at UP has worked for many years on cosmic dynamos [1] and on magnetically driven instabilities [7]. The partner at CU has vast experience with the identification of convective and absolute instabilities, as they occur in connection with the helical version of MRI [22,23].

3. Resource planning and Budget Justification

A PhD student will work at HZDR with main focus on WP1 and WP3, with intense support from the PI and further members of the MHD department. The numerical simulations at UG and UP will be also conducted by PhD students. The theoretical studies at CU on the helical MRI will be supported in the framework of a work contract. There is no further support from the Alliance for the experiments at HZDR as they are financed in frame of DRESDYN.


[1] G. Rüdiger, R. Hollerbach, 2004, The Magnetic Universe – Geophysical and Astrophysical Dynamo Theory. Wiley-VCH, Weinheim.
[2] S.A. Balbus, J.F. Hawley, 1998, Instability, Turbulence, and Enhanced Transport in Accretion disks. Rev. Mod. Phys., Vol. 70, 1-53.
[3] H.C. Spruit, 2002, Dynamo Action by Differential Rotation in a Stably Stratified Stellar Interior. Astro. Astrophys., Vol. 381, 923-932.
[4] R. Monchaux et al., 2007, Generation of a Magnetic Field by Dynamo Action in a Turbulent Flow of Liquid Sodium. Phys. Rev. Lett., Vol. 98, 044502.
[5] D.P. Lathrop, C.B. Forest, 2011, Magnetic Dynamos in the Lab. Physics Today, Vol. 64, 40-45.
[6] J. Wicht, A. Tilgner, 2010, Theory and Modeling of Planetary Dynamos. Space Sci. Rev., Vol. 152, 501-542.
[7] R. Arlt, G. Rüdiger, 2011, Magnetic Fields of Ap Stars as a Result of the Tayler Instability. Astron. Nachr., Vol. 332, 70-76.
[8] F. Stefani, T. Weier, T. Gundrum, G. Gerbeth, 2011, How to circumvent the size limitation of liquid metal batteries due to the Tayler instability. Ener. Conv. Manag., Vol. 52, 2982-2986.
[9] A. Tilgner, 2002, Laboratory Dynamo Experiments and what we Learned from them. Astron. Nachr., Vol. 323, 407-410.
[10] A. Gailitis, O. Lielausis, E. Platacis, G. Gerbeth, F. Stefani, 2002, Colloquium: Laboratory Experiments on Hydromagnetic Dynamos. Rev. Mod. Phys., Vol. 74, 973-990.
[11] F. Stefani, A. Gailitis, G. Gerbeth, 2008, Magnetohydrodynamic Experiments on Cosmic Magnetic Fields. ZAMM, Vol. 88, 930-954.
[12] A. Gailitis, O. Lielausis, S. Dement’ev, E. Platacis, A. Cifersons, G. Gerbeth, T. Gundrum, F. Stefani, M. Christen, H. Hänel, G. Will, 2000, Detection of a Flow Induced Magnetic Field Eigenmode in the Riga dynamo facility. Phys. Rev. Lett., Vol. 84, 4365-4368.
[13] A. Gailitis, O. Lielausis, E. Platacis, S. Dement’ev, A. Cifersons, G. Gerbeth, T. Gundrum, F. Stefani, M. Christen, G. Will, 2001, Magnetic Field Saturation in the Riga Dynamo experiment. Phys. Rev. Lett., Vol. 86, 3024-3027.
[14] Stieglitz, U. Müller, 2001, Turbulence Experimental Demonstration of a Homogeneous Two-scale Dynamo. Phys. Fluids, Vol. 13, 561-564.
[15] A. Tilgner, 2002, Numerical Simulation of the Onset of Dynamo Action in an Experimental Two-Scale Dynamo. Phys. Fluids, Vol. 14, 4092-4094.
[16] F. Stefani, T. Gundrum, G. Gerbeth, G. Rüdiger, M. Schultz, J. Szklarski, R. Hollerbach, 2006, Experimental Evidence for Magnetorotational Instability in a Taylor-Couette Flow under the Influence of a Helical Magnetic Field. Phys. Rev. Lett., Vol. 97, 184502.
[17] M. Seilmayer, F. Stefani, T. Gundrum, T. Weier, G. Gerbeth, M. Gellert, G. Rüdiger, 2012, Experimental Evidence for Tayler Instability in a Liquid Metal Column. Phys. Rev. Lett., Vol. 108, 244501.
[18] A. Tilgner, 2005, Precession Driven Dynamos. Phys. Fluids, Vol. 17, 034104.
[19] A. Tilgner, 2007, Kinematic Dynamos with Precession Driven Flow in a Sphere. Geophys. Astrophys. Fluid Dyn., Vol. 101, 1-9.
[20] O.N. Kirillov, F. Stefani, 2010, Kinematic On the Relation of Standard and helical Magnetorotational Instability. Astrophys. J., Vol. 712, 52-68.
[21] F. Stefani, A. Gailitis, G. Gerbeth, 2011, Kinematic Energy Oscillations and a Possible Route to Chaos in a modified Riga Dynamo. Astron. Nachr., Vol. 332, 4-10.
[22] J. Priede, I. Grants, G. Gerbeth, 2007, Inductionless magnetorotational instability in a Taylor-Couette flow with a helical magnetic field. Phys. Rev. E, Vol. 75, 047303-4.
[23] J. Priede, G. Gerbeth, 2009, Absolute versus convective helical magnetorotational instability in a Taylor-Couette flow. Phys. Rev. E, Vol. 79, 046310.