## 4 Discussion  
### Estimated Energy Deposition Related to Temperature Evaluation  
As stated in the previous publication [24], the energy deposition by applying beam oscillation is no longer uniform but gradual. Analyzing an infinitesimal small part of the workpiece shows this characteristic in Figure 20. For each setup (set #1... #4), the operative part of the laser beam intensity was calculated as a function of time. This was done considering the real laser beam geometry and cutting parameters, according to Table 4. The  
Figure 19: Global histogram of the temperature distribution, averaged for a period of 500 ms of 12 mm stainless steel cut with static beam shaping (set #1) and different values of the longitudinal, linear beam oscillation: 300 \(\upmu\)m amplitude and 500 Hz frequency (set #2), 550 \(\upmu\)m amplitude and 500 Hz frequency (set #3), 300 \(\upmu\)m amplitude and 2000 Hz frequency (set #4). resulting energy deposition is the cumulative effect of the laser beam intensity. A sufficient energy deposition combined with an adequate interaction time is mandatory to obtain the melting process. Furthermore, a long interaction time is advantageous for an effective melt ejection. The interaction time of the laser beam at a fixed position corresponds to the time starting from the first impact of radiation until the intensity has dropped to zero. This value indicates the maximum interaction time to melt and eject the material. This consideration does not include a real melting process, as well as heat conduction. Therefore, the interaction time is only used as a comparative parameter. For this approach, it suits very well, as it combines the influence of the beam geometry, the beam quality, the focal position, the cutting speed, and the oscillation parameters. For static beam shaping (Figure 20a), the laser beam intensity steadily increases until the evaluated material position is passed. Subsequently, the intensity decreases in the same manner. During the whole sequence, with an interaction time of about 132 ms, energy is continuously deposited onto the material. Applying beam oscillation, several effects influence the energy deposition. As the focal plane is adapted for set #2, the absolute value of effective intensity clearly increases in Figure 20b. In combination with the increased cutting speed and the oscillating beam, this leads to a shortened interaction time of about 70 ms. The highest intensity is not only valid for one moment, rather, for a long period. This is visible as a kind of intensity plateau in Figure 20b. The increased intensity also leads to a higher amount of deposited energy. The characteristic of energy deposition is obviously gradual due to the pulse-like intensity sequence. Changing the amplitude and focal plane as in set #3 (Figure 20c) results in a slightly decreased cutting speed compared to set #2 (see Table 4). The interaction time significantly increases to 132 ms and is comparable with static beam shaping. However, the intensity and the amount of deposited energy are still  
Figure 20: Comparison of the local intensity profile and energy deposition for one certain material position along the cut path as function of time for the following parameters: (**a**) Static beam shaping; and different values of the longitudinal, linear beam oscillation parameters: (**b**) 300 \(\upmu\)m amplitude and 500 Hz frequency; (**c**) 550 \(\upmu\)m amplitude and 500 Hz frequency; (**d**) 300 \(\upmu\)m amplitude and 2000 Hz frequency; heat conduction as well as melt ejection have been disregard. at a high level. Applying a high frequency as in set #4 (Figure 20d), the interaction time results in 84 ms due to the decreased cutting speed and the changed focal plane compared to set #2. The denser pulse characteristic and as a result the steadier energy deposition are both remarkable. It is assumed that the described behavior of gradual energy deposition leads to a distinct volatile temperature profile at the cut front.