Gunter Gerbeth

Detection of a flow induced magnetic field eigenmode in the riga dynamo facility

In a closed volume of molten sodium an intense single-vortex-like helical flow has been produced by an outside powered propeller. At a flow rate of 0.67 m(3)/s a slowly growing magnetic field eigenmode was detected. For a slightly lower flow, additional measurements showed a slow decay of this mode. The measured results correspond satisfactorily with numerical predictions for the growth rates and frequencies.

Magnetic Field Saturation in the Riga Dynamo Experiment

After the dynamo experiment in November 1999 [A. Gailitis et al., Phys. Rev. Lett. 84, 4365 (2000)] had shown magnetic field self-excitation in a spiraling liquid metal flow, in a second series of experiments emphasis was placed on the magnetic field saturation regime as the next principal step in the dynamo process. The dependence of the strength of the magnetic field on the rotation rate is studied. Various features of the saturated magnetic field are outlined and possible saturation mechanisms are discussed.

Experimental evidence for magnetorotational instability in a Taylor-Couette flow under the influence of a helical magnetic field.

A recent paper [R. Hollerbach and G. Rudiger, Phys. Rev. Lett. 95, 124501 (2005)] has shown that the threshold for the onset of the magnetorotational instability (MRI) in a Taylor-Couette flow is dramatically reduced if both axial and azimuthal magnetic fields are imposed. In agreement with this prediction, we present results of a Taylor-Couette experiment with the liquid metal alloy GaInSn, showing evidence for the existence of the MRI at Reynolds numbers of order 1000 and Hartmann numbers of order 10.

Contactless inductive flow tomography.

The three-dimensional velocity field of a propeller-driven liquid metal flow is reconstructed by a contactless inductive flow tomography. The underlying theory is presented within the framework of an integral equation system that governs the magnetic field distribution in a moving electrically conducting fluid. For small magnetic Reynolds numbers this integral equation system can be cast into a linear inverse problem for the determination of the velocity field from externally measured magnetic fields. A robust reconstruction of the large scale velocity field is already achieved by applying the external magnetic field alternately in two orthogonal directions and measuring the corresponding sets of induced magnetic fields. Kelvins theorem is exploited to regularize the resulting velocity field by using the kinetic energy of the flow as a regularizing functional. The results of this technique are shown to be in satisfactory agreement with ultrasonic measurements.

Asymmetric polarity reversals, bimodal field distribution, and coherence resonance in a spherically symmetric mean-field dynamo model.

Using a mean-field dynamo model with a spherically symmetric helical turbulence parameter alpha which is algebraically quenched and disturbed by additional noise, the basic features of geomagnetic polarity reversals are shown to be generic consequences of the dynamo action in the vicinity of exceptional points of the spectrum. This simple paradigmatic model yields long periods of constant polarity which are interrupted by self-accelerating field decays leading to asymmetric polarity reversals. It shows the recently discovered bimodal field distribution, and it gives a natural explanation of the correlation between polarity persistence time and field strength. The dependence of the persistence time on the noise shows typical features of coherence resonance.

Helical magnetorotational instability in a Taylor-Couette flow with strongly reduced Ekman pumping

The magnetorotational instability (MRI) is thought to play a key role in the formation of stars and black holes by sustaining the turbulence in hydrodynamically stable Keplerian accretion disks. In previous experiments the MRI was observed in a liquid metal Taylor-Couette flow at moderate Reynolds numbers by applying a helical magnetic field. The observation of this helical MRI (HMRI) was interfered with a significant Ekman pumping driven by solid end caps that confined the instability only to a part of the Taylor-Couette cell. This paper describes the observation of the HMRI in an improved Taylor-Couette setup with the Ekman pumping significantly reduced by using split end caps. The HMRI, which now spreads over the whole height of the cell, appears much sharper and in better agreement with numerical predictions. By analyzing various parameter dependencies we conclude that the observed HMRI represents a self-sustained global instability rather than a noise-sustained convective one.

Velocity Measurement Techniques for Liquid Metal Flows

Analysis and control of fluid flows, often subsidiary to industrial design issues,require measurements of the flow field. For classical transparent fluids such aswater or gas a variety of well-developed techniques (laser Doppler and parti-cle image velocimetry, Schlieren optics, interferometric techniques, etc.) havebeen established. In contrast, the situation regardingopaque liquids still lacksalmost any commercial availability. Metallic and semiconductor melts oftenpose additional problems of high temperature and chemical aggressiveness,rendering any reliable determination of the flow field a challenging task. Thisreview intends to summarise different approaches suitable for velocity mea-surements in liquid metal flows and to discuss perspectives, particularly inview of some recent developments (ultrasound, magnetic tomography).Focus-ing mainly on local velocity measurements, it is subsequently distinguishedbetween invasive and non-invasive methods, leaving entirely aside the acqui-sition of temperature, pressure, and concentration, for which [1] may serve asa comprehensive reference.

Buoyant melt flows under the influence of steady and rotating magnetic fields

Rotating magnetic fields are of growing interest for crystal growth technologies from the melt. For a few millitesla they provide a controlled motion within the melt, thus controlling the heat and mass transfer and the temperature fluctuations. This paper gives numerical results for the stability thresholds of rotating magnetic field and buoyancy driven melt convections, also by additionally superimposing a steady magnetic field. Some numerical results are given for a possible explanation of the surprising stabilizing action of the rotating magnetic field on a pre-given buoyant flow.

Riga dynamo experiment and its theoretical background

It is widely believed that almost all magnetic fields in a natural environment are the result of the dynamo process—the field generation in moving nearly homogeneous electro-conducting fluids. This dynamo process occurs in the depths of celestial bodies such as the Earth, most of the planets, the Sun, other stars, and even galaxies. The Riga dynamo experiment is not intended as a model of any particular celestial body. It aims at demonstrating the basic dynamo mechanism—that the intense motion in a large volume of a good electro-conducting liquid creates a magnetic field. In the present paper, the set-up and the main results of this experiment are presented, with some focus on the theoretical interpretation of the data.

Magnetohydrodynamic experiments on cosmic magnetic fields

It is widely known that cosmic magnetic fields, i.e. the fields of planets, stars, and galaxies, are produced by the hydromagnetic dynamo effect in moving electrically conducting fluids. It is less well known that cosmic magnetic fields play also an active role in cosmic structure formation by enabling outward transport of angular momentum in accretion disks via the magnetorotational instability (MRI). Considerable theoretical and computational progress has been made in understanding both processes. In addition to this, the last ten years have seen tremendous efforts in studying both effects in liquid metal experiments. In 1999, magnetic field self-excitation was observed in the large scale liquid sodium facilities in Riga and Karlsruhe. Recently, self-excitation was also obtained in the French “von Karman sodium” (VKS) experiment. An MRI-like mode was found on the background of a turbulent spherical Couette flow at the University of Maryland. Evidence for MRI as the first instability of an hydrodynamically stable flow was obtained in the “Potsdam Rossendorf Magnetic Instability Experiment” (PROMISE). In this review, the history of dynamo and MRI related experiments is delineated, and some directions of future work are discussed.