## 4 Discussion
### Beam Diameter and Energy Input  
For the theoretical calculations concerning the beam diameter and energy input, the beam is assumed to be perfectly round and its diameter is calculated according to Equation (5). The values presented here are for this specific case, an A2X from GE Additive. However, it is strongly recommended to consider the beam diameter as an important scanning parameter for all PBF-EB machines. The beam power density \(q_{A}\) is described in Equation (6). The absorption coefficient \(\eta\) is set to 0.85 [4; 12].  
\[q_{A}=\frac{\eta*P}{\pi*\left(\frac{d}{2}\right)^{2}} \tag{6}\]  
The dependence of the beam power density on the beam power is shown in Figure 8. Additionally, a cut in the \(x\)-\(z\)-plane (\(y=0\) and \(y_{0}=0\)) for a resting beam (\(x_{0}=0\)) of the Gaussian beam power distribution \(q_{A}\)(\(x\),\(y\)) within the electron beam is plotted according to Equations (7) and (8) [3; 4; 18]. The variance \(\sigma\) is \(\frac{1}{4}\)\(d\).  
\[q_{A}(x,y)=\eta*I(x,y)*P_{B} \tag{7}\]  
\[I(x,y)=\frac{1}{2\pi\sigma^{2}}\exp\left(\frac{(x-x_{0})^{2}+(y-y_{0})^{2}}{2 \sigma^{2}}\right) \tag{8}\]  
Figure 8 displays a rise in the beam power density, which is a measure of the energy density of the electron beam from 180-780 W. Simultaneously, the electron beam widens and the energy density in the center of the beam rises (see Gaussian beam power distribution in Figure 8). This leads to higher peak temperatures and a broader melt pool, enhancing aluminum evaporation and reducing gas porosity. This agrees well with the experimental findings.  
Figure 7: The correlation between melt pool depth, lateral extension, gas porosity, aluminum evaporation, and the nearly lamellar area is shown. Average experimental values are given by the symbols, while the dotted lines represent the overall trend. The area energy \(E_{A}\), line energy \(E_{L}\), return time \(t_{r}\), and lateral velocity \(v_{Lat}\) are constant. For small beam powers up to 900 W, the gas porosity (black) and nearly lamellar area (grey) decrease, whereas the lateral extension (red) and aluminum evaporation (blue) increase. The gas porosity and nearly lamellar area rise for higher beam powers, while the Al evaporation is reduced. At the same time, the lateral extension of the melt pool is constant.  
For beam powers larger than 780 W, the beam power density decreases. At the same time, the beam widening is enhanced and the energy density in the center of the electron beam is reduced. The lower peak energy input leads to less overheating during the initial melting and therefore reduces the peak temperatures. Consequently, the aluminum evaporation decreases and the melt pool solidifies faster, which results in more gas porosity. Meanwhile, the broadening electron beam increases the interaction area with the powder bed and melt pool, resulting in a more horizontal distribution of the energy and finally leading to a wider melt pool. In conclusion, the melt pool possesses lower peak temperatures and is shorter-lived, leading to less aluminum evaporation and more gas porosity, while the lateral extension rises due to the wider spread energy input.  
The simultaneous development of the beam power density and peak power (Figure 8, black and grey) to the aluminum evaporation, gas porosity, and nearly lamellar area (Figure 7, blue, black, and grey) is striking. Moreover, the development of the lateral melt pool extension (Figure 7, red) can be connected to the increase in the beam diameter (Figure 8, red). Overall, these results show a strong correlation between the energy input via the electron beam and the resulting melt pool and microstructure.