## 3 Results and Discussion
A comparison of the two temperature measurements obtained during the weld processes executed under equal conditions and with the same set of process parameters is given in Figure 13. In both experiments, a blow-out occurred when the keyhole reached the approximate position of the refractory probe; thus, the measurements are comparable judging by the apparent outer circumstances. Although the curves exhibit deviations of up to \(\Delta T=800\) K at certain points, qualitatively, they show significant similarities. Apparently, the temperature profile represented by the red curve in Figure 13 shows a rather smooth course in contrast to the second curve. This is an indicator that noisy temperature curves in this region of measuring may indeed be ascribed to an imperfect sample design rather than indicating physical phenomena in the investigated system. Figure 12: Temperature course from the prerunning melt to the probe destruction, i.e., within the keyhole prerunning region. Considering the estimated size of the keyhole of about \(d_{\text{key}}\approx 600\)\(\upmu\)m to \(900\)\(\upmu\)m at the top and regarding the typical shape becoming narrower with the increasing depth, the inner probe diameter of \(d_{\text{probe}}=600\)\(\upmu\)m is too large to perform a pointwise measurement at the keyhole front, as depicted schematically in Figure 14. Instead, it is likely that the recorded temperatures correspond to the average heat radiation \(\overline{I}\) emitted from the tantalum screen. The real temperature of the foil, in turn, results, on the one hand, from the heat transfer mechanisms acting on its outside surface, i.e., of the region of interest within the melt pool in the vicinity of the keyhole front wall, and, on the other hand, from heat propagation inside the tantalum foil. Based on Equation (2) and using the notations as shown in Figure 14, the average intensity on the temperature screen is given by:  
\[ \begin{split}\overline{T}\Bigg{\{}\begin{array}{l}T_{\text{foil}} \bigvee y,z\in A_{\text{foil}}\\ T_{\text{cross}}\bigvee y,z\in A_{\text{cross}}\end{array}\text{ and }A_{\text{tot}}=A_{\text{foil}}+A_{\text{cross}}\\ \overline{I}_{\text{pyro}}=\iint_{y,z\in A_{\text{tot}}}\Bigl{[}\epsilon \Bigl{(}\overline{T}(y,z)\Bigr{)}\cdot\int_{\lambda_{1}}^{\lambda_{2}}S\Bigl{(} \overline{T}(y,z),\lambda\Bigr{)}d\lambda\Bigr{]}dydz\end{split}  \tag{10}\]  
Figure 14: Geometric relation between keyhole and temperature screen: (**a**) view along the laser beam axis on the geometric intersection of the keyhole and the Ta foil, and (**b**) section between the keyhole and the temperature screen as seen by the pyrometer. Figure 13: Comparative temperature curves of two independent measurements with the same process parameters. Clearly, as the melt flowing around the keyhole is assumed to be significantly colder than the keyhole itself and contributing to the measured temperature and due to the spatial expanse of the temperature screen, the introduced measuring method inherently underestimates the real temperature at the point of interest. \[T\big{(}\overline{I}_{\text{pyro}}\big{)}<T(I(y,z))\ \forall\ y,z\in A_{\text{cross}} \tag{11}\]  
Furthermore, due to effects like temperature diffusion on time scales matching the measuring intervals for certain regions, the temporal and spatial resolutions of the measurements in the welding direction are blurred. Under those terms, a color pyrometer is the better choice for measuring the wall temperature. In a second experimental series for the validation of the obtained results, a Sensorthem H322+ two-color pyrometer was employed, as described in Section 2.3. Hereby, in the valid RoM, as referred to in Figure 10, the temperatures show maximum values of \(T_{\text{high}}=3110\) K to 3292 K. Considering that, in color pyrometry, values close to the maximum temperature inside the measuring spot are always obtained and there is no need to know the exact temperature-dependent emissivities, the absolute measured temperatures are more reliable than those obtained using small-band pyrometry.