**4. Discussion**

It should be noted that the proposed dynamic model could not be used for precise data on the thermal history and simulation of the thermal stresses. The point was in researching an optimal laser power density distribution for the engineering tasks of LPBF. As known, the optimal melt pool configuration for the tasks of thick (more than 10 mm in thickness) material laser cutting or welding is torch-like (Figure 11) [25] and has a certain disadvantage when the laser power exceeds 100 W [26]. For laser scribing, surface treatment, and LPBF [40,41], the optimal one can be a more surface-like uniform distribution related to the following issues [60]:


c. melt ejection under steam pressure.

**Figure 11.** Melt pool formation: (**a**) torch-like; (**b**) torch-like with an increase of energy in the laser beam; (**c**) more uniform surface-like with an increase of redistributed energy in the melt pool.

The conducted research confirmed the effectiveness of the proposed approach not only for static modeling but for a dynamic one, as well. Achieved laser beam profiles are presented in Figure 12. As can be seen (Figure 12c), the flat-top profile is practically hard to be achieved close to the theoretical profile using the existed optical means [60]. The provided Figure 12d–f are reconstructed from the formed CoCr single tracks (Figure 12g–i) [61,62]. A detailed description of the developed LPBF setup equipped with an optical laser beam profiler and expander and optical diagnostics are presented in [26]. The experimental conditions are presented in [57]. Figure 13 presents the optical and modulation systems of LPBF setup.

The dynamic melt pool evaluation during experiments with metallic powders by optical diagnostic means [63,64] is expected for further research.

It should be noted that TEMFT cannot be called a "desirable intensity distribution" since it was a theoretical proposal [50]. The idea was to achieve a more uniform energy density instead of peaks in the centrum of the laser beam spot. The picture of energy distribution in the laser beam spot and adsorbed energy by powder material is different. However, it can be even more varied, considering the dynamic factor (Pe number). Desirability can only be called a distribution that allows the achievement of uniform energy

adsorption in the laser beam spot [57], taking into account the used material's thermal conductivity and dynamic factor. Definitely, it will be already varied for metallic [65,66] and ceramic [67–69] groups of materials. However, it can also vary depending on granulomorphometric parameters of the powder, mainly shape and reflect ability [45,70,71], which was not considered in the article. The TEM00 + TEM01\* equation is the only way to achieve approximate TEMFT by existing optical means [72,73].

**Figure 12.** Laser beam profiles (objective control data achieved experimentally): (**a**) TEM00 (Gaussian); (**b**) TEM01\* (donut); (**c**) TEMFT (flat-top); reconstruction of the temperature fields' features in the formed melt pools: (**d**) TEM00 (Gaussian); (**e**) TEM01\* (donut); (**f**) TEMFT (flat-top); formed experimental tracks: (**g**) TEM00 (Gaussian); (**h**) TEM01\* (donut); (**i**) TEMFT (flat-top), where *W* is a track's width, *Cz* is powder consolidation zone's width.

Comparing two radiation beams with different profiles is possible only with the different values for laser beam spot radii (Table 7). The same LPBF setup with a similar laser beam diameter provided technically and focused on a plane for all cases is practically used in the conditions of real production. Laser beam diameter corresponds to the main characteristics of the LPBF equipment (in our case, it is up to 100 μm) and cannot be changed quickly. The alternative laser beam profiles are experimentally achieved using a laser beam profiler and an expander and optically evaluated [60]. That was taken as a basis for theoretical evaluation of the dynamic factor to be closer to the common industrial conditions.

**Figure 13.** Modulation and optical control systems in-build into LPBF setup.

The average laser beam power distribution (*E*, J/m2) will not be similar in these cases as it was previously evaluated and compared (Table 5). Still, the question is not in the energy density in the laser beam spot radii, but in the practically achievable profile that can be useful and implemented in standard or experimental LPBF equipment (Figure 13).

Practically, the achievable profile by mixing TEM00 and TEM01\* is far from the profile simulated based on Equation (2) due to the use available for market optical means. Moreover, as it was shown theoretically, the TEMFT profile is not the one that corresponds the most to the technological tasks of LPBF of metallic powder with the high material thermal conductivity (*λ*).
