Ambivalent effects of added layers on steady kinematic dynamos in cylindrical geometry: application to the VKS experiment

The intention of the ''von Karman sodium'' (VKS) experiment is to study the hydromagnetic dynamo effect in a highly turbulent and unconstrained flow. Much effort has been devoted to the optimization of the mean flow and the lateral boundary conditions in order to minimize the critical magnetic Reynolds number and hence the necessary motor power. The main focus of this paper lies on the role of ''lid layers'', i.e. layers of liquid sodium between the impellers and the end walls of the cylinder. First, we study an analytical test flow to show that lid layers can have an ambivalent effect on the efficiency of the dynamo. The critical magnetic Reynolds number shows a flat minimum for a small lid layer thickness, but increases for thicker layers. For the actual VKS geometry it is shown that static lid layers yield a moderate increase of the critical magnetic Reynolds number by approximately 12 per cent. A more dramatic increase by 100 until 150 per cent can occur when some rotational flow is taken into account in those layers. Possible solutions of this problem are discussed for the real dynamo facility.Comment: 24 pages, 11 figures, minor changes, to appear in European Journal of Mechanics B/Fluid

Electromagnetic induction in non-uniform domains

Kinematic simulations of the induction equation are carried out for different setups suitable for the von-K\'arm\'an-Sodium (VKS) dynamo experiment. Material properties of the flow driving impellers are considered by means of high conducting and high permeability disks that are present in a cylindrical volume filled with a conducting fluid. Two entirely different numerical codes are mutually validated by showing quantitative agreement on Ohmic decay and kinematic dynamo problems using various configurations and physical parameters. Field geometry and growth rates are strongly modified by the material properties of the disks even if the high permeability/high conductivity material is localized within a quite thin region. In contrast the influence of external boundary conditions remains small. Utilizing a VKS like mean fluid flow and high permeability disks yields a reduction of the critical magnetic Reynolds number for the onset of dynamo action of the simplest non-axisymmetric field mode. However this decrease is not sufficient to become relevant in the VKS experiment. Furthermore, the reduction of Rm_c is essentially influenced by tiny changes in the flow configuration so that the result is not very robust against small modifications of setup and properties of turbulence

Cylindrical anisotropic α2\alpha^{2} dynamos

We explore the influence of geometry variations on the structure and the time-dependence of the magnetic field that is induced by kinematic $\alpha^{2}$ dynamos in a finite cylinder. The dynamo action is due to an anisotropic $\alpha$ effect which can be derived from an underlying columnar flow. The investigated geometry variations concern, in particular, the aspect ratio of height to radius of the cylinder, and the thickness of the annular space to which the columnar flow is restricted. Motivated by the quest for laboratory dynamos which exhibit Earth-like features, we start with modifications of the Karlsruhe dynamo facility. Its dynamo action is reasonably described by an $\alpha^{2}$ mechanism with anisotropic $\alpha$ tensor. We find a critical aspect ratio below which the dominant magnetic field structure changes from an equatorial dipole to an axial dipole. Similar results are found for $\alpha^{2}$ dynamos working in an annular space when a radial dependence of $\alpha$ is assumed. Finally, we study the effect of varying aspect ratios of dynamos with an $\alpha$ tensor depending both on radial and axial coordinates. In this case only dominant equatorial dipoles are found and most of the solutions are oscillatory, contrary to all previous cases where the resulting fields are steady.Comment: 15 pages, 8 figure

Towards a precession driven dynamo experiment

The most ambitious project within the DREsden Sodium facility for DYNamo and thermohydraulic studies (DRESDYN) at Helmholtz-Zentrum Dresden-Rossendorf (HZDR) is the set-up of a precession-driven dynamo experiment. After discussing the scientific background and some results of water pre-experiments and numerical predictions, we focus on the numerous structural and design problems of the machine. We also outline the progress of the building's construction, and the status of some other experiments that are planned in the framework of DRESDYN.Comment: 9 pages, 6 figures, submitted to Magnetohydrodynamic

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 discs. 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.Comment: 30 pages, 22 figures, submitted to PR

Spectral properties of oscillatory and non-oscillatory {\alpha}^2-dynamos

The eigenvalues and eigenfunctions of a linear {\alpha}^{2}-dynamo have been computed for different spatial distributions of an isotropic \alpha-effect. Oscillatory solutions are obtained when \alpha exhibits a sign change in the radial direction. The time-dependent solutions arise at so called exceptional points where two stationary modes merge and continue as an oscillatory eigenfunction with conjugate complex eigenvalues. The close proximity of oscillatory and non-oscillatory solutions may serve as the basic ingredient for reversal models that describe abrupt polarity switches of a dipole induced by noise. Whereas the presence of an inner core with different magnetic diffusivity has remarkable little impact on the character of the dominating dynamo eigenmodes, the introduction of equatorial symmetry breaking considerably changes the geometric character of the solutions. Around the dynamo threshold the leading modes correspond to hemispherical dynamos even when the symmetry breaking is small. This behavior can be explained by the approximate dipole-quadrupole degeneration for the unperturbed problem. More complicated scenarios may occur in case of more realistic anisotropies of \alpha- and \beta-effect or through non-linearities caused by the back-reaction of the magnetic field (magnetic quenching).Comment: 11 pages, 6 figures, accepted for publication in Geophys. Astrophys. Fluid Dy