Experimental Evidence for a Transient Tayler Instability in a Cylindrical Liquid-Metal Column

In the current-driven, kink-type Tayler instability (TI) a sufficiently strong azimuthal magnetic field becomes unstable against nonaxisymmetric perturbations. The TI has been discussed as a possible ingredient of the solar dynamo mechanism and a source of the helical structures in cosmic jets. It is also considered as a size-limiting factor for liquid metal batteries. We report on a liquid metal TI experiment using a cylindrical column of the eutectic alloy GaInSn to which electrical currents of up to 8 kA are applied. We present results of external magnetic field measurements that indicate the transient occurrence of the TI in good agreement with numerical predictions. The interference of TI with the competing large-scale convection, resulting from Joule heating, is also discussed.

Figure 1

Experimental setup. Left: Scheme with liquid metal column and fluxgate sensors positioned along the vertical axis and the azimuth. Right: Photograph of the central part of the experiment.

Figure 2

Magnetic fields measured along the vertical axis, for $r_i=12.5\mathrm{mm}$ and $I=7\mathrm{kA}$. (a) Time dependence of $B_z$ at the 11 fluxgate sensors. (b) Power spectral density dependent on time and wavelength. Note the dominance of short wavelength signals in the initial phase, and the dominance of the long wavelength signal at later times. (c) Detailed time evolution of the PSD for four significant wavelengths, showing a transition to an exponential growth around $t\sim 150\mathrm{s}$, which is later stopped at $t\sim 280\mathrm{s}$. The dashed, tangent lines indicate the growth of the short wavelength modes.

Figure 3

Magnetic field data measured along the azimuth, for $r_i=12.5\mathrm{mm}$ and $I=7\mathrm{kA}$. (a) Time dependence of $B_z$ at the 4 fluxgate sensors. The $m=1$ character is clearly visible. (b) Squared magnetic field amplitude of the $m=1$ mode. The dot indicates the inflection point. (c) Angle of the $m=1$ mode.

Figure 4

(a) Measured growth rates (markers) and their numerical predictions (lines) for three different radii of the inner cylinder, dependent on the current. (b) Measured squared magnetic field strength (markers) of the $m=1$ mode, and their piecewise linear fits (lines). The maximum squared fields for $r_i=0$, 6, and 12.5 mm are 61.0, 543.3, and $1668.1\mu {\mathrm{T}}^2$, respectively.

Figure 5

Comparison of the determined critical currents with the numerical predictions for the $m=1$ mode. The numerical prediction for the $m=0$ (sausage) mode is indicated partly.