Self-consistent Computations of the Geometries of Magnetically Confined Liquid Metal Columns

Abstract

In this paper, a modeling methodology is described which permits the computation of the cross-sectional geometry of a two dimensional column of perfectly conducting liquid in the presence of a magnetic field imposed by specified configurations of source conductors. The description is self-consistent in the sense that the column geometry results from a magnetic pressure corresponding to a magnetic field determined by the column geometry. Solutions are obained by iteratively calculating the magnetic field structure for a given column geometry and source conductors, and then calculating a new column geometry based on the magnetic stresses, surface tension, and pressure jump at the liquid-air interface. This loop is continued until a self-consistent solution is obtained. A quadrupole source magnetic shaping problem solved by Shercliff ushing conformal mapping is duplicated using the methodology described in this paper. The results obtained are in good agreement with those published by Shercliff. In addition, results are shown for arbitrary shaping problems, including levitation of horizontal columns, that are too complex for analytic solutions.