## 3 Analysis of the Transition between Shock Reflections
### Position (b)  
[PERSON] et al. [30] conducted a study on the transition of regular reflection to Mach reflections by changing the location of the deposition between the wedge surface and oblique shock. A similar analysis was performed by moving the deposition position inside the contraction region (position (b) in Figure 8) to examine the effect of the position of the laser energy deposition on the transition characteristics. Figure 12 shows the computational results from when 107.5 mJ of energy is deposited at position (b). The intermediate collapse and regeneration process of the shock wave due to the blast wave can be considered to be qualitatively the same as the result of position (a). However, as the time for the blast wave to reach the upper oblique shock wave decreases, the last intersection of the blast wave and Mach reflection occurs between 150 us and 180 us in the expanded region.  
In these conditions, the transition occurs very slowly compared to the case of position (a), even after the disturbance disappears. However, the time for the transition to the regular reflection to be completed decreases by about 80 \(\upmu\)s from T = 600 \(\upmu\)s to T = 520 \(\upmu\)s. It seems that this mainly results from the time difference of when the blast wave begins to interact with the oblique shock wave. Thus, it is expected that moving the focus of energy deposition into the contraction zone may contribute to promoting the transition from Mach reflection to regular reflection.  
Figure 13 shows the results from doubling the energy of the laser to 215 mJ. Compared to Figure 12, the time that is required to complete the transition is increased due to the formation of a strong blast wave, which is the same tendency that was obtained from the result for position (a). In this case, disturbances from the blast wave passed through the computational domain faster than in the case of position (a). Compared with Figure 10, the transition time is 800 \(\upmu\)s, which is 150 \(\upmu\)s less than the energy applied to position (a). Thus, by moving the energy deposition point downstream from position (a) to position (b) in Figure 8, the transition can be promoted.  
The deposition energy was increased further to 430 mJ, as shown in Figure 14. The simulation results are very similar to those in Figure 11. As the strong blast wave reaches the lower wedge surface, the reflected wave from this region influences the shock wave regeneration process. Similar to Figure 11, multiple normal shock waves are generated on the wedge. In this case, Mach reflection is maintained after the regeneration of the shock wave, which supports the previous claim that excessive energy deposition may have a negative impact on the shock wave transition in the dual solution domain.  
Considering that a transition occurs at 215 mJ despite the strong Mach reflections, the following differences can be found in the simulation results. The final state of the shock reflection seems to be significantly affected by the position of the Mach reflection that occurs during the transition process. This means that a complex shock system that is caused by a disturbance should undergo interference from an expansion wave that is generated at the end of the wedge for a transition of the shock system. This is supported by the results obtained with 430 mJ of energy, where the effect of a disturbance only ends at the contraction zone. In that case, there is no interference with the expansion wave before it was stabilized and no transition is produced.