Centrifugal pumping during Czochralski silicon growth with a strong, non-uniform, axisymmetric magnetic field

Centrifugal pumping flows are produced in the melt by the rotations of crystal and crucible during the Czochralski growth of silicon crystals. This paper treats the centrifugal pumping effects with a steady, strong, non-uniform axisymmetric magnetic field. We consider a family of magnetic fields ranging from a uniform axial field to a ''cusp'' field, which has a purely radial field at the crystal-melt interface and free surface. We present the numerical solutions for the centrifugal pumping flows as the magnetic field is changed continuously from a uniform axial field to a cusp one, and for arbitrary Hartmann number. Since the perfect alignment between the local magnetic field vector and the crystal-melt interface or free surface is not likely, we also investigate the effects of a slight misalignment.