Stability of melt flow during magnetic sonication in a floating zone configuration

This paper considers the linear stability of a liquid metal flow driven by superimposed alternating and static axial magnetic fields in the floating zone configuration. A simple model is constructed that assumes a slight axial variation of the flow-driving radial magnetic force and a low-to-moderate skin effect. This force drives two symmetrical flow tori. Formation of the field-parallel layer is observed for a strong static field. In this regime the instability sets in as a standing azimuthal wave around the circumference of the cylindrical melt volume near its midplane. The length of this wave scales with the thickness of the parallel layer. The instability criterion may be formulated in terms of an interaction parameter reaching its critical value at around 525.