## 1 Introduction
Spatter detachment in dependence on the required laser energies was described in [17]: to detach a spatter from the melt pool the kinetic energy of the fluid element \(\mathrm{E_{kin,fl}}\) must be equal or greater than the sum of the kinetic energy of the spatter \(\mathrm{E_{kin,sp}}\) and the surface energy of the melt \(\mathrm{E_{sur}}\). To determine the prerequisite for the spatter detachment the kinetic energies were calculated from the melt density \(\rho\), the spatter volume \(\mathrm{V_{sp}}\), and the upward melt flow velocity \(\mathrm{v_{fl}}\) or the spatter velocity \(\mathrm{v_{sp}}\). The surface energy was determined on the basis of the surface tension \(\sigma\) and the spatter surface \(\mathrm{S_{sp}}\)[17]. A similar condition for spatter detachment was published in [10], but an additional momentum transfer based on the escaping metal vapor \(\mathrm{E_{vap}}\) was added. Thus, the authors transformed the condition into an energy balance (see Equation (1)). \[\mathrm{E_{vap}}+\underbrace{\rho\mathrm{V_{sp}}\mathrm{v_{fl}^{2}}}_{\mathrm{ E_{kin,fl}}}=\underbrace{\rho\mathrm{V_{sp}}\mathrm{v_{sp}}^{2}}_{\mathrm{ E_{kin,sp}}}+\underbrace{2\sigma\mathrm{S_{sp}}}_{E_{sur}} \tag{1}\]  
The flow velocity of the fluid element \(\mathrm{v_{fl}}\) corresponds to the upward melt flow velocity at the keyhole rear wall for welding speeds \(\leq\)6 m/min [17]. This melt flow mainly contributes to the spatter detachment from the melt pool swellings. Various experimental studies have dealt with the measurement of melt flow velocities. Using tracer particles and x-ray imaging, the flow velocity at the keyhole opening was determined to be 1.65 m/s in the event of a spatter detachment at the keyhole front for welding pure titanium. A lower flow velocity of 1.37 m/s did not result in a detachment [18]. For the joining process of aluminum with a tophat distribution, spatter velocities up to 10 m/s with an average spatter diameter of less than 0.11 mm were measured [19]. Investigations on steel showed maximum spatter velocities of 4.1 m/s for low welding speeds (\(\leq\)3 m/min) [20]. For welding AISI 304 with welding speeds \(\geq\)8 m/min, the spatters detached from the melt pool swellings with a velocity of 3.5 m/s [21]. However, the flow around the keyhole increases with the welding speed [8] and should be taken into account when investigating spatter detachment at high welding speeds. When the critical energy for spatter detachment is exceeded, a melt column is formed and a spatter is detached by necking. The necking of a droplet from the melt column can be described by the Plateau-Rayleigh instability [22] which is determined by the surface tension. It describes how a liquid stream breaks up into drops due to a reduction in surface area [23]. Due to the emission of the melt in the spectral range of 820 nm to 980 nm, the occurring spatters can be observed by high-speed imaging using an appropriate optical filter. Subsequently, a suitable algorithm detects them in the recordings [24] and thus their trajectories can be tracked [25]. Various approaches to reduce the spatter formation for high welding speeds are already known. In addition to reducing the ambient pressure [9], the superposition of laser intensities [26], the change of the focal position of the laser beam [27], and laser beam oscillations [28], the use of a gas flow already showed a positive effect for welding with CO\({}_{2}\) lasers in 1984 [29]. In addition to suppressing the plasma by changing the flow direction of the metal vapor for CO\({}_{2}\) lasers, the spatter reduction with solid-state lasers while using a gas flow was investigated in [30]. For welding speeds \(\leq\)5 m/min the melt flow was stabilized due to the gas flow and spatter ejections were completely suppressed [31]. Recent investigations obtained a loss of mass reduction of up to 91% with an argon gas flow under low flow rates (\(\leq\)4.8 L/min) [32].