Metal pad roll instability threshold with magnetic damping in shallow cylindrical cells

I. Krastins - A. Bojarevics

MHD Technology Laboratory, Institute of Physics, University of Latvia, 32 Miera str., Salaspils LV-2169, Latvia

Abstract
This work discusses the metal pad roll instability and the means of quantifying it for two-layer and some three-layer cell systems. We extend the work of Herreman etal. [1] and calculate the critical beta-number considering magnetic damping in shallow cylindrical cells. The results show that the critical beta-number can be written as a sum of its contributions, viscous and magnetic dissipation. The viscous threshold is that derived in [1]. The critical magnetic beta-number is directly proportional to the radius meaning that its impact increases with the cell size. The quadratic dependence on the vertical magnetic field suggests that it can be neglected at small field values but becomes more dominant and suppresses flow at stronger magnetic fields. Tables 1, Figs 3, Refs 16.