Transverse rotating magnetic fields (B-max = 7.5 mT, f(rot) = 50 Hz) were applied to the floating zone growth of doped silicon. Non-periodic dopant fluctuations caused by time-dependent thermocapillary convection were considerably reduced by the rotating field. The radial segregation profiles (measured by a spreading resistance probe) became more homogeneous and more symmetric. The transition from a regime dominated by time-dependent thermocapillary convection to a flow state characterized by the rotating magnetic field was determined. This threshold depends on the height of the melt as well as the melt diameter (crystals between 8 and 14 mm have been investigated) and the efficiency of the applied field increases with larger melt zones. For a melt of 14 mm in diameter and an aspect ratio of I it is in the range of 2.5-3.75 mT/50 Hz (corresponding to a Taylor number of Ta = 9.3 x 10(3) -2.1 x 10(-4)). The change from a time-dependent 3D-flow without field to a quasi-axisymmetric 2D-flow with the magnetic field is corroborated by numerical simulations of the flow field: the thermocapillary driven irregular flow rolls are transformed to a nearly axisymmetric flow with high azimuthal flow velocities but reduced axial and radial components.