http://arxiv.org/abs/1503.07887
This paper presents numerical analysis a pinch-type instability in a semi-infinite planar layer of inviscid conducting liquid bounded by solid walls and carrying a uniform electric current. The instability resembles the Tayler instability in astrophysics and can presumably disrupt the operation of the recently developed liquid metal batteries (Wang et al. 2014 Nature 514, 348). We show that the instability in liquid metals, which are relatively poor conductors, significantly differs from that in a well conducting fluid. In the latter, instability is dominated by the current perturbation resulting from the advection of the magnetic field. In the former, the instability is dominated by the magnetic field perturbation resulting from the diffusion of the electric current perturbation. As a result, in liquid metals, instability develops on the magnetic response time scale, which depends on the conductivity, and is much longer than the Alfv\’en time scale, on which the instability develops in a well conducting fluid. The instability threshold in viscous fluid resulting from our model is comparable with the numerical as well as experimental results for liquid metals in cylindrical geometries.
J. Priede
Mon, 30 Mar 15
33/65
Comments: 15 pages, 3 figures
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