## 1 Introduction  
The stainless steel AISI 304 is widely used in home appliances, the food industry, and many engineering applications due to corrosion resistance and weldability [1]. A typical application for the use of AISI 304 is the production of continuously manufactured tubes for heating systems, water supply, and further technical applications [2]. Most industrially available AISI 304 tubes have diameters <110 mm [2] and wall thicknesses \(\leq\)4 mm [3]. The production of such tubes can be carried out continuously in a single production line, i.e., a strip of steel coming from a coil is formed into an open-seam tube by multi-stage forming rolls and welded with a longitudinal seam from one side in a single pass [4]. Tungsten inert gas and laser beam welding are usually used for the single-pass welding process [5]. However, the process speed of the tube manufacturing is limited to \(\leq\)5 m/min using tungsten inert gas welding [5]. Other arc welding processes would limit the welding speed even further, such as metal inert gas welding (<2 m/min [6]) or submerged arc welding (<1 m/min [7]) as used in automated processing of AISI 304 components. Manual welding processes, like manual metal arc welding, are also not applicable to automated production. In contrast, laser and electron beam welding of AISI 304 enables high welding speeds of 10 m/min and above [5] due to their high power intensities [8]. Unlike electron beam welding, laser beam welding does not normally operate under a vacuum and therefore requires less effort in industrial production [9]. Therefore, an enhanced cost-benefit efficiency of the laser welding process for the automated welding of continuously formed open-seam tubes is recognizable [10]. In addition, modern solid-state lasers offer an increasing maximum power that could reach even higher welding speeds for AISI 304 [8] but result in an enhanced spatter formation [11]. Spatter formation leads to a loss of mass, i.e., the cross-section of the weld is reduced, and requires reworking of components due to adhering spatters [11]. A number of methods are already demonstrating the potential to reduce spatter formation and thus enable high welding speeds. In order to describe the behavior of AISI 304 during laser deep penetration welding (also known as laser keyhole welding) in the context of spatter formation, a wide range of welding speeds is described to enable a discussion of underlying phenomena and to determine different welding regimes. For lower welding speeds (typically below 5 m/min for AISI 304L) spatters are formed at the keyhole rim [12]. This spatter formation and detachment is undirected in contrast to higher welding speeds [13] and shows a comparatively small spatter size [10]. Here a uniform heating of the keyhole surface is observed. Laser welding under this condition is called the \"Rosenthal\" regime [14]. However, at high welding speeds (6 m/min [11] to 10 m/min [15]) the laser welding of AISI 304 results in spatter detachments from the highly fluctuating melt pool swellings at the keyhole rear wall [11]. This phenomenon is referred to as a \"single wave\" regime [12]. Spatter formation reduces the seam cross-section and adherent spatters have to be removed from the sample surface after the welding process [10]. An increased welding speed causes an enlargement of the keyhole area and so this process is referred to as an \"elongated keyhole\" regime. Both, the oscillation of the melt pool swellings and its elevation are decreased in this regime. In all different process regimes, the loss of mass increases with increasing welding speed until the spatter detachment changes to the formation of humps [16]. This transition occurs in the \"pre-humping\" regime and results in the \"humping\" regime [12].