Silicon single crystals are grown from the melt by providing the melt in a crucible; imposing a horizontal magnetic field on the melt; directing a gas between the single crystal and a heat shield to a melt free surface, and controlling the gas to flow over a region of the melt free surface extending in a direction substantially perpendicular to the magnetic induction. A suitable apparatus has a crucible for holding the melt; a heat shield surrounding the silicon single crystal having a lower end which is connected to a bottom cover facing a melt free surface and a non-axisymmetric shape with respect to a crucible axis, such that gas which is directed between the crystal and the heat shield to the melt free surface is forced to flow over a region of the melt which extends substantially perpendicular to the magnetic induction.