Model of a laser heated plasma interacting with walls arising in laser keyhole welding

In laser welding with laser intensities of approximately ${10}^{11}$ W/${\mathrm{m}}^2$, a hole, called a keyhole, is formed in the material. In this keyhole a plasma is detected, which is characterized by high pressure as well as being influenced by the boundary of the keyhole. Experimental data on plasma parameters are rare and difficult to obtain [W. Sokolowski, G. Herziger, and E. Beyer, in High Power Lasers and Laser Machining Technology, edited by A. Quenzer, SPIE Proc. Vol. 1132 (SPIE, Bellingham, WA, 1989), pp. 288–295]. In a previous paper [C. Tix and G. Simon, J. Phys. D 26, 2066 (1993)] we considered just a simple plasma model without excited states and with constant ion–neutral-atom temperature. Therefore we neglected radiative transport of excitations and underestimated the ion–neutral-atom temperature and the ionization rate. Here we extend our previous model for a continuous ${\mathrm{CO}}_2$ laser and iron and take into account radiative transfer of excitations and a variable ion–neutral-atom temperature. We consider singly charged ions, electrons, and three excitation states of neutral atoms. The plasma is divided in plasma bulk, presheath, and sheath. The transport equations are solved with boundary conditions mainly determined through the appearance of walls. Some effort is made to clarify the energy transport mechanism from the laser beam into the material. Dependent on the incident laser power, the mean electron temperature and density are obtained to be 1.0–1.3 eV and 2.5×${10}^{23}$–3×${10}^{23}$ ${\mathrm{m}}^{\mathrm{-}3}$. Radiative transport of excitations does not contribute significantly to the energy transport.