July 23, 2016 Other Open Access

Stability of fluid layers carrying a normal electric current revisited

Priede, Jānis

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In this report we revisit the basic model of electromagnetic interfacial instability originally due to Sneyd (1985). The model consists of horizontally unbounded fluid layers carrying a uniform normal current in the presence of a co-planar vertically invariant magnetic field. The absence of lateral boundaries in this model leaves the self-magnetic field determined up to a gradient of the scalar magnetic potential. This was deemed a major deficiency of the model in our first report. In particular, it was not obvious that the perturbation of magnetic field, which is postulated by Sneyd in terms of the electric potential perturbation satisfies not only Ampère’s law but also the continuity of tangential electric field across the interface. On the other hand, Sneyd’s solution is rather specific and limited by several assumptions typical for aluminium reduction cells and electric-arc furnaces. Therefore it may be worthwhile to revisit Sneyd’s model in a more general set-up and using alternative more transparent approach.