Magnetic Damping of Buoyant Convection During Semiconductor Crystal Growth in Microgravity. Steady Transverse Residual Acceleration

In this paper we treat the steady, three-dimensional buoyant convection in a circular cylinder with an axisymmetric temperature, with a uniform axial magnetic field, and with a steady transverse acceleration or gravitational force. The magnetic field is sufficiently strong that inertial effects and convective heat transfer are negligible for the typical residual accelerations on an earth-orbiting vehicle. Since the governing equations are linear, the solution for any steady acceleration or gravitational vector is given by the superposition of the solutions for an axial acceleration and for a transverse acceleration. The solution for an axial acceleration is given by a rescaling of the well-known solution for a terrestrial vertical Bridgman crystal-growth process, and in this paper we present the solution for a transverse acceleration. With an axial magnetic field, the melt motion consists of two circulations in opposite directions around two axial lines on opposite sides of the diameter plane which is parallel to the transverse acceleration vector a: both circulations involve flows in the direction opposite to a near the diameter plane and flows in the same direction as a near the cylinder wall. The small electrical conductivity of the crystal is important because the crystal provides a path for a major part of the electric current responsible for the magnetic damping