## 1 Introduction
Unfortunately, this procedure is not applicable in thick section welding, where the typical weld length is several meters, because scanning mirrors are unable to handle the power levels needed [14; 18]. Large components such as scanning optics also limit the degree of freedom and flexibility of the welding process as regards positioning. Determining the operational window for a good quality weld accounts for three main process parameters: laser power, welding speed and focal point position. These three easily adjustable parameters affect the power density at the top of workpiece, and therefore melt flow and distribution of the energy inside the keyhole, which have a major influence on the geometry of the weld. A certain threshold value of power density must be reached in order to be able to form the keyhole [19]. Figure 1: Comparison of weld joint geometries produced with: (**a**) arc welding; (**b**) autogenous laser welding; and (**c**) laser-arc hybrid welding, and stress concentration locations. The threshold is typically defined as \(10^{6}\) W/cm\({}^{2}\), or more commonly \(10^{3}\) W/mm\({}^{2}\), with typical dimensions of laser beam focal point. The power density is calculated as follows:  
\[E=\frac{P}{\pi r^{2}}, \tag{1}\]  
where \(P\) is laser power and \(r\) radius of the beam on the surface of the workpiece. The above-mentioned power density threshold is valid for CO\({}_{2}\) laser welding, whereas when using solid state lasers with wavelengths around 1000 nm the threshold is lower [20; 21]. The lower threshold is a result of higher absorption of shorter wavelengths, and it gives extra flexibility to parameter selection and greater freedom to tailor parameters to specific applications, for example, with static or dynamic beam formation. [PERSON] and [PERSON] et al. [22] developed the concept of Specific Point Energy (\(E_{\text{SP}}\)). In addition to energy density (power density \(\times\) interaction time), \(E_{\text{SP}}\) includes also beam diameter on the surface:  
\[E_{\text{SP}}=\rho_{P}T_{i}A=P_{L}T_{i}=\frac{Pd}{v}, \tag{2}\]  
where \(\rho_{P}\) is average power density of the beam (mW/cm\({}^{2}\)), \(T_{i}\) is interaction time (s), \(A\) is area of the beam on the surface (mm\({}^{2}\)), \(P_{L}\) is laser power (W), \(d\) is beam diameter on the surface (mm), and \(v\) is welding speed (mm/s). Experiments performed with bead-on-plate joints have shown that power density and \(E_{\text{SP}}\) control the depth of penetration and interaction time controls the bead width [22; 23; 24]. \(E_{\text{SP}}\) has also been shown to be suitable for evaluating the efficiency of laser cutting [25; 26]. The relationship between spot size and welding performance in steel and aluminum welding has been addressed in several studies [27; 28; 29; 30], and it has been found that small spot size produces deeper welds yet is accompanied by defects such as undercut and porosity. A study by [PERSON] [14] showed that in some cases the keyhole welding mode changes between selected parameter values, resulting in different weld cross section shape in butt joint welding of stainless steel with a disk laser. Lap and butt joints produced with CO\({}_{2}\) and solid-state laser sources have been characterized and compared [20]; for example, [PERSON] et al. [28] addressed the effect of focal spot size on weld defects and showed that, of the four sizes studied, welds with highest quality were obtained using the two larger spot sizes. The effect of focal point diameter on beam intensity on surface is much stronger than the effect via laser power. A simple way to manipulate the focal point diameter is to change the focal length of the focusing lens. A problem with this approach is that the focusing angle, i.e., the angle at which the beam enters the keyhole, changes as the focal length is changed, and the effect of focal point diameter is influenced by the effect of focusing angle and changes in the shielding gas arrangement.