Elementary model of internal electromagnetic pinch-type instability

TL;DR

This paper presents a simplified numerical model of a pinch-type electromagnetic instability in liquid metals, highlighting its edge effect nature, dependence on current density, and potential impact on liquid metal batteries.

Contribution

It introduces a minimalistic model capturing key features of the instability, distinguishing it from astrophysical analogs and emphasizing its relevance to practical applications.

Findings

Instability differs from Tayler instability in liquid metals.

Growth rate depends on current density, not system size.

Potential impact on large-scale liquid metal batteries.

Abstract

We analyse numerically a pinch-type instability in a semi-infinite planar layer of inviscid conducting liquid bounded by solid walls and carrying a uniform electric current. Our model is as simple as possible but still captures the salient features of the instability which otherwise may be obscured by the technical details of more comprehensive numerical models and laboratory experiments. Firstly, we show the instability in liquid metals, which are relatively poor conductors, differs significantly from the astrophysically-relevant Tayler instability. In liquid metals, the 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 Tayler instability develops in well conducting fluids. Secondly, we show that this instability is an edge effect caused by the curvature of the magnetic field, and its growth rate is determined by the linear current density and independent of the system size. Our results suggest that this instability may affect future liquid metal batteries when their size reaches a few meters.