Geostrophic turbulence in CZ silicon melt under CUSP magnetic field

Due to the Coriolis force caused by crucible rotation, the CZ silicon melt convection develops into a geostrophic turbulence (J. Crystal Growth 116 (1992) 447) at higher Taylor number conditions (J. Crystal Growth 198/199 (1999) 135). This study investigates the effect of a CUSP magnetic field on the geostrophic turbulence by CCD melt surface observations (J. Crystal Growth 180 (1997) 487) in a conventional CZ furnace and corresponding numerical fluid simulations. The estimated Taylor number of the present study lies between 3×109 and 2×1012, Hartmann number lies between 0 and 2000, and Rayleigh number lies between 2×107 and 2×108. CCD melt surface observations indicated that the fluctuating polka dot patterns consisting of a high temperature spot, which is a typical property of the geostrophic turbulence, were not broken by the CUSP magnetic field. Moreover, increasing of the magnetic field intensity enhanced the size and amplitude of the polka dots. On the other hand, increasing of crucible rotation caused the polka dot pattern to fade, which is similar to the case of zero magnetic field conditions. As regard the numerical fluid dynamic simulation, 3D differential equations containing the magnetic induction equation were solved on a cylindrical lattice of 80×60×65 points. The result of the simulations agreed with the melt surface observations mentioned above, and indicated the reduction in the kinetic energy of the entire melt. These facts delineates that a CUSP magnetic field will suppress the averaged fluctuation of the melt convection as expected by the usual understanding (J. Crystal Growth 113 (1991) 305), but will enhance the melt surface fluctuation in a geostrophic turbulence regime of a large crucible.