Magnetic damping of buoyant convection during semiconductor crystal growth in microgravity. Continuous random g-jitters

Abstract

This paper treats the buoyant convection of a liquid metal in a circular cylinder with a uniform, steady, axial magnetic field and with the random residual accelerations encountered on earth-orbiting vehicles. The objective is to model the magnetic damping of the melt motion during semiconductor crystal growth by the Bridgman process in space. For a typical process with a magnetic flux density of 0.2 T, the convective heat transfer and the nonlinear inertial effects are negligible, so that the governing equations are linear. Therefore, for residual accelerations or ‘‘g-jitters’’ whose directions are random functions of time, the buoyant convection is given by a superposition of the convections for two unidirectional accelerations: an axial acceleration which is parallel to the cylinder’s axis and a transverse acceleration which is perpendicular to this axis. Similarly, the response to accelerations whose amplitudes are random functions of time is given by a Fourier-transform superposition of the buoyant convections for sinusoidally periodic accelerations for all frequencies. Since the temperature gradient in the Bridgman process is primarily axial, the magnitude of the three-dimensional buoyant convection for the transverse acceleration is much larger than the magnitude of the axisymmetric convection for the axial acceleration. At a low frequency, only the magnetic damping limits the magnitude of the buoyant convection. As the frequency is increased, linear inertial effects augment the magnetic damping, so that the magnitude of the convection decreases, and its phase shifts to a quarter-period lag after the acceleration.