## 1 Introduction  
Deep-penetration laser welding is a well-established yet still promising joining technology with a broad field of applications in the automotive, aerospace, and many other industries of great economic significance. Allowing for high-aspect ratios, it has proven to be an ideal method for generating deep and narrow weld seams at comparatively low energy inputs [1]. High welding velocities and low thermal distortion of the joined parts qualify this technology for applications in manufacturing processes, e.g., for automated welding tasks or complex welding contours [2]. At a certain material-dependent intensity threshold of the laser beam, the material evaporation induces a recoil pressure onto the molten material, allowing the laser to penetrate the formerly flat workpiece surface [3]. Thereby, a long and narrow vapor capillary, also referred to as a keyhole, is formed in which the laser beam can propagate through multiple reflections so that the energy is absorbed along the complete depth of the capillary [4]. The keyhole diameter is approximately one to one and a half times the size of the beam diameter at the material surface [5] and is filled with metal vapor and shielding gas. Although the keyhole formation has been well-explained, its dynamic behavior is not fully understood; this is, at least from an experimental point of view, also due to the difficult accessibility of the system. Temperatures exceeding 2000 K are too high for conventional tactile temperature measurements, and optical accessibility through the keyhole opening is impeded due to the strong emissions caused by the laser-material interaction. The metal vapor, which is partially ionized by the laser beam, can also disturb optical measurements in the vapor capillary, as can the complicated geometrical accessibility due to the small diameter of the keyhole and the fluctuations of the melt pool on short time scales. The temperature of the keyhole wall is assumed to be a parameter of fundamental importance to the keyhole behavior and, thus, to the welding process. As the layer thickness of the melt film, its viscosity, and the surface tension strongly depend on the temperature of the surface material, it is obvious that, in order to predict or even control the dynamics of the keyhole, and accordingly, part of the melt pool dynamics, knowledge of the temperature distribution at the keyhole wall is crucial. The small layer of evaporation at the keyhole wall where the material particles are accelerated from the melt film towards the center of the keyhole contributing to the metallic vapor is known as the Knudsen layer [PERSON] (1958). Previous surveys conducted in the field of the numerical simulation of deep-penetration laser welding have already addressed this quantity. For example, it has been predicted by [PERSON] et al. [PERSON] et al. (2018) that the melt surface inside the keyhole is overheated, leading to temperatures far beyond the evaporation temperature of the weld material. The model created by [PERSON] et al. [PERSON] et al. (2018) used to investigate keyhole stability supports this prediction by calculating the temperature at the transition layer between the liquid and gaseous phase as ranging from 3400 K to 3800 K, thereby significantly exceeding the evaporation temperature of the examined material. According to [PERSON] et al. [PERSON] et al. (2018), the deep welding process can be divided into different regimes corresponding to the welding velocity \(v_{\text{weld}}\). The velocity range below \(v_{\text{weld}}=5\) m/s is referred to as the Rosenthal regime, which is characterized by an almost vertical keyhole with circular cross-sections along the laser beam axis. The temperature is thought to be homogeneously distributed along the contour of each cross-section and, therefore, is only spatially dependent on the keyhole depth. For higher welding speeds, the keyhole is tilted and elongated in the welding direction.