This work deals with the numerical investigation of the development of a laser molten aluminum pool under the influence of static magnetic fields with different strengths. Special attention has been paid to laser surface alloying by means of nickel. It was observed that thermocapillary forces drive two counter-rotating vortices which by themselves induce two secondary vortices at the free surface. This scenario yields an alloyed layer with an extension of about half the maximum pool depth. In the presence of a static magnetic field applied perpendicular to the plane of interest, the system of vortices is suppressed. This damped Row situation in the melt results in a variation of the solute distribution in the solid and in shallower alloyed layers depending upon the applied magnetic induction.