Magnetic damping of buoyant convection during semiconductor crystal growth in microgravity: Spikes of residual acceleration

Abstract

This paper treats the decay of the buoyant convection in a circular cylinder after a brief spike of large acceleration. There is a steady, uniform, axial magnetic field which is sufficiently strong that nonlinear inertial effects and convective heat transfer are negligible. Since the governing equations are linear, the solution for a spike at any angle to the cylinder’s axis is given by the superposition of two solutions for an axial spike and a transverse spike. The flows are axisymmetric and three-dimensional for the axial and transverse spikes, respectively. With the transverse spike, the axial temperature gradient drives a single cell of circulation with transverse vorticity, and the radial temperature gradient drives two opposite cells of circulation with axial vorticity on opposite sides of the diameter parallel to the acceleration. Although the axial temperature gradient is larger than the radial one in the Bridgman crystal-growth process, the damping of transverse vorticity with an axial magnetic field is much stronger than the magnetic damping of the axial vorticity, so that the two-cell axial-vorticity circulation dominates. For a typical Bridgman process with a 0.2 T magnetic field and with silicon, the buoyant convections driven by the axial and transverse spikes of acceleration decay to one percent of their magnitudes immediately after the spikes in 3 and 14 s, respectively.