A shallow water model for the instability of a liquid metal jet crossed by an axial electrical current

E. Zienicke¹ - A. Thess¹ - A. Krätzschmar² - P. Terhoeven²

¹ Fakultät Maschinenbau, Technische Universität Ilmenau, PF 100565, D-98684 Ilmenau, Germany
² Moeller GmbH, Hein Moeller Str. 7-11, D-53115 Bonn, Germany

Abstract
A liquid metal jet, passed through by an axial electrical current, is unstable against the MHD-pinch instability that is caused by the Lorentz force from the self-created magnetic field inside the current carrying jet. This effect has drawn attention in electrical engineering, because it can be used in the construction of liquid metal current limiters with self-healing properties. Using an analytical approximation for the Lorentz force for small deviations from a constant radius, a shallow water model of the liquid metal jet is developed for a rotationally symmetric case. In this way a one-dimensional closed system of two dynamical equations, namely for the axial velocity and the radius of the jet, is derived from the Euler equation and the evolution equation for the free surface. Starting from these much simpler equations, a stability analysis of this model is lead through, by which the critical current density for the pinch instability and the reaction time, in which the liquid jet is pinched off, can be determined. Figs 74, Refs 12.