## 3 Results
### Stability of the capillary  
As mentioned in the introduction, partial penetration welding of aluminum alloys leads to fluctuation and collapse of the capillary, which result in the formation of pores [1; 2; 3]. However, the single frames of the X-ray video shown in Figure 3 did not show any capillary collapse; pores, nevertheless, still formed. Different from Section 3.1, the entire image sequence of the X-ray videos had to be analyzed in order to quantify the stability of the capillary. Figure 5 shows the distribution of the average intensity and its corresponding temporal standard deviation of greyscale values of the X-ray video, which result from the same experiments as the cross sections shown in Figure 1.  
The vertical dash-dotted line represents the axis of the laser beam. The average intensity images (avg. intensity) represent the mean greyscale of each pixel averaged over all frames of the X-ray videos after the process reached steady-state condition. White areas highlight locations that exhibit a low density in the majority of the frames, like the capillary. The standard deviation images (std. deviation) represent the temporal standard deviation of the greyscale of each pixel over all frames of the X-ray videos after the process reached steady-state condition. The greyscale of the standard deviation images quantifies the local fluctuations. White areas highlight locations with strong process fluctuations, like the fluctuations of the capillary or the moving pores. The white areas, which surround the beam axis in the average intensity distribution images, show the average shape of the capillary in the x-z-plane. The distribution of the standard deviation showed that the majority of the capillary's fluctuations were located at a significant distance behind the beam axis. The comparison between the average intensity images and their corresponding standard deviation images pointed out that this location coincided with the average position of the rear wall of  
Figure 4: Average diameter, (**a**), and average growth velocity, (**b**), of bubbles “a”, “b”, and “c” during welding in overlap configuration of uncleaned AA6016 sheets with a feed rate of 12 m/min, a beam diameter of about 500 μm, and a laser power of 8.5 kW. the capillary. The standard deviation images further proved that the rear wall of the capillary was the only fluctuating part of the capillary, regardless of whether the samples that were welded were uncleaned (Figure 5a) or cleaned (Figure 5b). A comparison of these results with Figure 1 showed that porosity in a full penetration weld was not connected with the presence of the fluctuation in the rear wall of the capillary. In the standard deviation images of Figure 5a, an additional region of strong fluctuations can be identified on the left-hand side, far behind the capillary. This resulted from a high number of moving and growing pores located in this position and was only observed when welding uncleaned sheets. In order to quantitatively compare the fluctuations observed during welding sheets with different surface conditions, the average greyscale of each vertical pixel column was determined from the standard deviation images shown in Figure 5. Figure 6 shows the resulting mean standard deviation as a function of the distance x from the beam axis when welding sheets with cleaned (blue curve) or uncleaned (red curve) surfaces. The position of the beam axis, i.e., the position of the capillary, is represented by the vertical dash-dotted line at x = 0 mm. The curves represent the average of three values of the mean standard deviation of three investigated welds for each corresponding surface condition. Large values indicate locations with strong process fluctuations, like the fluctuations of the capillary or moving pores. The scatter band represents the minimum and maximum determined values of three investigated welds for each surface condition. Figure 5: Distribution of the standard deviation (std.