## 1 Introduction  
Laser beam cutting is a highly complex process that has not yet been fully understood. The principle of laser beam fusion cutting (LBFC) is to melt material using a laser beam, superimposed by a coaxially high pressure gas jet that ejects the melt [1; 2; 3; 4]. The inclined cutting front throughout the plate thickness characterizes the transition from solid to molten phase [1; 2; 3]. There are many properties, such as focal radius, laser power, gas flow, etc., affecting the LBFC [1; 2; 3; 4; 5; 6]. In general, two main criteria evaluate the cutting result: productivity and cut edge quality. For productivity, the cutting speed is decisive. Furthermore, a cut edge is of high quality by absence of burr, together with a homogenous smooth surface [7; 8; 6; 9]. To increase the process productivity, higher energy input is necessary. This could be achieved by either decreasing the focal radius or increasing the laser power [1; 2; 3; 4; 5]. Both options accelerate the cutting speed; however, the quality of the cut parts is affected [3; 4; 5]. For instance, the faster the cutting speed, the shorter the interaction time is between the laser beam and gas jet in respect to the material. This leads to reduced melt ejection, with the result that the melt film thickness increases [10; 11; 12]. The liquid melt gathers particularly in the lower part of the plate thickness. That forces a flattening of the cut front [1; 11; 12; 13]. In turn, this results in a larger interaction area between laser beam and material,so that more laser energy is absorbed [11; 12]. Heat conduction transports the absorbed laser energy into the material. This creates a melt film with a defined thickness. In consequence, as the melt film thickness increases due to the faster cutting speed, the heat conduction proceeds over a longer distance. Since the resulting heat flow is inversely proportional to the melt film thickness, an increase in the temperature difference and an increase in the interaction area between laser beam and material is required to ensure the melting process [1; 10; 11; 12; 13; 14]. The accumulated melt as well as a high temperature difference causes a turbulent melt flow. This is reflected as striations on the finished cut edge [1; 11; 13]. A reduced melt volume accompanies also the increasing cutting speed in order to maintain the energetic balance [15]. This means that the cut kerf width narrows as the cutting speed increases. Correspondingly, less of the gas jet couples into the cut kerf and thus the melt ejection is inhibited [11; 13; 16; 17]. The incomplete ejected melt attaches as burr at the bottom part and as a recast layer of the finished cut edge. The described striations as well as the burr, caused by faster cutting speed, are contrary to the specifications of a high-quality cut edge. Many researchers are attempting to solve the conflict between productivity and quality in LBFC of thick metal plates. They have detected that striations could be avoided by a laminar melt flow. For this purpose, the melt film must be thin and exhibit only a minimal thermal difference [18; 19; 20]. A complete melt ejection prevents burr, whereby a sufficient cut kerf width is advantageous [3]. Other researchers have investigated various methods to combine the demands of high productivity and high cut quality, such as controlling the intensity distribution [21; 22; 23], spot size [8; 24; 25], spot shape [22; 26], and focal position [8; 15; 27; 28; 29]. All these methods have in common that they belong to static beam shaping methods. This means that the properties of the laser beam are modified before the cutting process takes place [30; 31]. One of the most promising methods to improve LBFC of thick metal plates is the enlargement of the focal radius [8; 32]. As a result, the interaction area and kerf width increases, which is favorable for reducing burr formation. However, when the laser power remains constant, the intensity decreases, which reduces the cutting speed.