The surface of a metal workpiece is remelted by a heat producing energy beam so as to form a molten metal layer thereon. While remelting the surface, a magnetic field is generated coaxially with the energy beam and is applied across the molten metal layer so as to cause the heat energy to flare and, thereby, produce a Lorentz force in the molten metal layer. By the Lorentz force, the molten metal is agitated. The heat energy and magnetic field are oscillated, or reciprocally moved, relative to the surface so as to cause a flow of the molten metal from the edges of the molten metal layer toward the center, thereby providing a uniform chilled layer thickness.