## 1 Introduction
\[E_{L}=\frac{U_{B}*I_{B}}{v_{B}}=\frac{P}{v_{B}} \tag{3}\]  
\[E_{A}=\frac{E_{L}}{l_{o}}=\frac{U_{B}*I_{B}}{v_{B}*l_{o}} \tag{4}\]  
This scaling approach was successfully used for a fourth generation \(\gamma\)-TiAl alloy in the author's previous work. Cylinders with scan lengths of roughly 3-17 mm were manufactured without misconnections and displayed a homogenous microstructure and isotropic mechanical properties [14]. Similar findings have been reported in a numerical study conducted with a semi-empirical heat conduction model on Ti-6 Al-4V by [PERSON] et al. [4]. Based on his results, the melt pool depth and width remain the same over a large range of scan lengths if the line energy and lateral velocity are kept constant [4]. In contrast, experimental studies showed that the scaling of process parameters can cause defects and influence the microstructure [15; 16]. An important process parameter is the beam diameter. Although this is known in the PBF-EB community, very little has been published on this topic. One rare exception is the formulation for beam widening on an _Arcam AB_ PBF-EB system suggested by [PERSON] et al. (Equation (5)) [12]. \[d=4\sigma=\left\{ \begin{array}{ll}342.5\ \mu\mathrm{m}+0.11\frac{\mu m}{W}*P,&P \ \leq\ 675\ W\\ 20.6\ \mu\mathrm{m}+0.58\frac{\mu m}{W}*P,&P>675\ W\end{array} \right. \tag{5}\]Based on these values the beam diameter \(d\), defined as 4\(\sigma\) of a Gaussian distribution, increases from 350 \(\upmu\)m at 60 W beam power to 845 \(\upmu\)m at 1500 W beam power (Figure 2). This means that the energy of the electron beam is distributed over a strongly increased surface for higher beam powers. However, the energy density is not only dependent on the beam diameter and the Gaussian distribution but also the power of the electron beam and hence is strongly influenced by the method of scaling the scanning parameters. To summarize, a wider electron beam is expected to influence the energy density and energy distribution of the electron beam and potentially can influence the melt pool. The objective of this study is to improve the general understanding of how the beam diameter, which changes with beam power, influences PBF-EB. Therefore, not only the bulk properties such as misconnections, gas porosity, and aluminum content are examined but also the width and depth of the melt pool. By scaling previously determined scanning parameters [14], the energy input is kept constant while the beam power and beam velocity are adapted to the various scan length. Consequently, the beam diameter is the only remaining parameter, which can influence the resulting part properties. For the first time, the connection between beam diameter, power density, melt pool, and microstructure is systematically analyzed for PBF-EB. The influence of the beam diameter is not limited to the machine and material presented here, but has to be taken into account for every PBF-EB process on any machine. In the future, on-demand microstructure via electron-beam powder bed fusion will enable tailoring the mechanical properties of certain areas in complex parts towards their specific requirements [17]. Hence, this novel approach  
Figure 1: (**a**) Scaled schematic of the samples for determining the melt pool width and depth. Thirteen stripes (dark grey) consisting of 35 scan lines (orientation indicated by orange arrows) per examined beam power are molten for the x- and y-deflection of the electron beam. The single, 100 \(\upmu\)m layer is molten on top of a 45 mm \(\times\) 45 mm \(\times\) 5 mm base plate (light grey) to reach common PBF-EB process conditions as close as possible. The section plane is indicated by the dotted lines (black). (**b**) Exemplary image of the persistent melt pool taken in the middle of the stripe. The melt pool width is defined as depicted. (**c**) Snake scan strategy used to build the samples. The beam velocity \(v_{B}\), line offset \(l_{o}\), scan length \(l_{s}\), and lateral velocity \(v_{lat}\) are indicated. (**d**) 3D CAD model of the geometry for melt pool investigations.