## 4 Discussion
### Estimated Energy Deposition Related to Temperature Evaluation
This was already noticeable within the temperature sequences of \(\overline{\mathrm{T_{P,P}}}(\mathrm{t})\) in Figure 18. As the position of \(\overline{\mathrm{T_{P,P}}}(\mathrm{t})\) has a fixed relation to the cut front, only the volatility is evaluable. To consider the interaction time and the heat up phase, a fixed material position with a shifting pixel index needs to be evaluated. This was done with the temporally resolved submatrix \(\overline{\mathrm{T_{P}}}_{(\mathrm{t}),\mathrm{P}}(\mathrm{t})\). The result is visualized in Figure 21.  
Comparing Figures 20 and 21 reveals similarities, which support the assumption of temperature volatility in dependence of energy deposition. The heat up for static beam shaping (Figure 21a) remains almost uniform until it reaches its maximum of 1975 \({}^{\circ}\)C after 75 ms. Set #2 (Figure 21b) reaches the maximum temperature of 2570 \({}^{\circ}\)C already after 25 ms. In contrast to static beam shaping, the heat up phase of beam oscillation includes several cooling periods. These cooling periods occur due to the oscillating laser beam, as demonstrated in Figure 20. The decreased laser beam intensity is linked to the moments when the laser beam is not positioned at the cut front. Consequently, the temperature decreases, too (see Figure 21). The increased maximum temperature is also related to the higher laser beam intensity due to the changed focal position. The fact that a high temperature is reached much faster is based on the oscillation movement. As a result, the peak intensity is immediately applied and, due to its plateau-like characteristics (see Figure 20c,d), it is active for a longer period. Increasing the amplitude as in set #3 (Figure 21c), the heat up to 2470 \({}^{\circ}\)C takes  
Figure 21: Comparison of the local temperature for the submatrix \(\overline{\mathrm{T_{P(t),P}}}(\mathrm{t})\) calculated with \(\mathrm{e}=1\) showing one certain material position of 12 mm stainless steel along the cut path as function of time for the following: (**a**) Static beam shaping; and different values of the longitudinal, linear beam oscillation parameters: (**b**) 300 \(\mathrm{\SIUnitSymbolMicro m}\) amplitude and 500 Hz frequency; (**c**) 550 \(\mathrm{\SIUnitSymbolMicro m}\) amplitude and 500 Hz frequency; (**d**) 300 \(\mathrm{\SIUnitSymbolMicro m}\) amplitude and 2000 Hz frequency. around 30 ms. The denser pulses due to the high frequency in set #4 (Figure 21d) enables peak temperatures of 2835 \({}^{\circ}\)C even after 20 ms. The interaction times shown in Figure 20 may only qualitatively correspond with the periods shown in Figure 21. Meanwhile, the temperature measurement in Figure 21 represents the real melting process that is also influenced by heat conduction, melt ejection, plate thickness, etc. The estimated energy deposition in Figure 20 does not consider all those circumstances. The important fact is to prove that the interaction time is high for beam oscillation, despite the adjusted focal plane and increased cutting speed. As a general result, the cut front temperature exceeds that of static beam shaping. The following section discusses effects on the cut edge quality.