Absorption of the laser beam by the plasma in deep laser beam welding of metals

We present a simple model for the keyhole plasma in deep penetration welding with a laser beam. Simplifying the complete set of transport equations investigated by C. Tix and G. Simon [Phys. Rev. E 50, 453 (1994)] for high laser powers yields an energy balance for the plasma, which can be treated analytically. The mean plasma temperature is calculated accounting for higher charge states of the ions. For high laser intensities double and higher charged ions dominate in the plasma bulk in the case of iron. The degree of absorption remains approximately constant for increasing laser power. The critical Péclét number for which the absorbed laser energy is able to maintain a keyhole increases strongly with increasing laser power. The energy absorption by the plasma is enhanced for higher modes of the laser intensity distribution.