We analyse numerically a pinch-type instability in a semi-infinite planarlayer of inviscid conducting liquid bounded by solid walls and carrying auniform electric current. Our model is as simple as possible but still capturesthe salient features of the instability which otherwise may be obscured by thetechnical details of more comprehensive numerical models and laboratoryexperiments. Firstly, we show the instability in liquid metals, which arerelatively poor conductors, differs significantly from theastrophysically-relevant Tayler instability. In liquid metals, the instabilitydevelops on the magnetic response time scale, which depends on the conductivityand is much longer than the Alfv\'en time scale, on which the Taylerinstability develops in well conducting fluids. Secondly, we show that thisinstability is an edge effect caused by the curvature of the magnetic field,and its growth rate is determined by the linear current density and independentof the system size. Our results suggest that this instability may affect futureliquid metal batteries when their size reaches a few meters.
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