Elementary model of internal electromagnetic pinchtype instability
Abstract
We analyse numerically a pinchtype instability in a semiinfinite 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 astrophysicallyrelevant 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 Alfvén 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.
 Publication:

arXiv eprints
 Pub Date:
 March 2015
 DOI:
 10.48550/arXiv.1503.07887
 arXiv:
 arXiv:1503.07887
 Bibcode:
 2015arXiv150307887P
 Keywords:

 Physics  Fluid Dynamics;
 Astrophysics  Solar and Stellar Astrophysics;
 Physics  Plasma Physics
 EPrint:
 14 pages, 5 figures (to appear in J Fluid Mech)