A liquid metal experiment on the Tayler instability

Introduction Various magnetohydrodynamic instabilities with relevance to cosmic magnetic fields have been studied experimentally [1]. Dynamo action was observed in the large scale liquid sodium experiments in Riga, Karlsruhe and Cadarache. The helical version of the magnetorotational instability (MRI) was studied in Dresden-Rossendorf, and a further experiment in Princeton attempts to investigate the standard version of MRI. What is missing yet in the liquid metal laboratory is any evidence of the Tayler instability (TI) [2]. In the language of plasma physics, TI can be considered as the limiting case of the kink-instability in a current-carrying line-tied plasma (experimentally studied in [3]) when the safety factor of the Kruskal-Shafranov condition goes to zero. In the astrophysical context, the Tayler instability has been discussed as one possible ingredient of the solar dynamo mechanism (Tayler-Spruit dynamo [4]), and as a possible source of helical structures in galactic jets and outflows [5]. TI is also widely used as a mechanism to increase angular momentum transport in star evolution models [6] even if there is not yet observational evidence for its existence [7]. Also the mixing of chemicals inside a star will be influenced by TI [8]. Recent numerical predictions [9] have shown that the observation of the TI in columns of typical liquid metals will need electrical currents in the order of kA, depending on the conductivity, density and viscosity of the liquid that enter the definition of the Hartmann number. The lowest value appears for the case of a full column, while the presence of an inner radial boundary leads to an increase of the critical current. In this paper, we describe an experimental set-up for the investigation of the TI, we show first results, and we discuss the possible relevance of the TI for large-scale liquid metal batteries as they are presently under consideration as cheap means for the storage of renewable energies.