## 3 Dynamic Heterogeneity Investigation into Debris Bed Safety Analysis
### Results and Discussion  
#### 3.3.1 Transformation of Heterogeneous Configuration  
Figure 7 displays the transformation processes of the bed configuration during the particle redistribution on these three debris bed models, including the Homogeneous, Mixed, and Stratified models. The particle in the grey in Figure 7 stands for the Homogeneous particle as the element of the Homogenous model. On the other hand, the black and white particles in the Mixed and Stratified model represent the Fuel particle and Structure particle, respectively.  
In the beginning, since the slope angle of the conical debris bed model was higher than the stable repose angle, particle avalanching was induced, letting particles slide downwards and being redistributed in all three models. During the particle redistribution, all three debris bed models exhibited a similar trend of being flattened gradually, suppressing their slope angles and the heights of the debris beds. In the end, particle redistribution in all three models ceased after a new stable bed configuration with lower slope angles and bed heights within 10 s had been achieved, as shown in Figure 7.  
Meanwhile, the heterogeneous debris bed models (Mixed model and Stratified model) revealed different characteristics of the bed configuration's transformation during particle redistribution from the Homogeneous model. As for the Mixed model, both light Structure particles and weighty Fuel particles moved downwards during particle redistribution, and the light Structure particles tended to gradually disperse outwards in the debris  
Figure 7: Transient process of the particle redistribution among three debris bed models: (**a**) Homogeneous model, (**b**) Mixed model, and (**c**) Stratified model.  
\begin{table}
\begin{tabular}{c c c} \hline
**Material** & **Fuel Particle \({}^{*}\)** & **Structure Particle \({}^{*}\)** & **Homogeneous Particle \({}^{*}\)** \\ \hline Cr & - & \(1.20\times 10^{-2}\) & \(4.38\times 10^{-3}\) \\ W & - & \(7.19\times 10^{-4}\) & \(2.63\times 10^{-4}\) \\ Ti & - & \(9.87\times 10^{-4}\) & \(3.61\times 10^{-4}\) \\ \hline \end{tabular} \({}^{*}\)Unit: Atomic number density [10\({}^{24}\) atoms/cm\({}^{3}\)].  
\end{table}
Table 5: _Cont._bed after a series of particle-particle collisions with density differences, as shown in Figure 7b. In addition, this indicated that the weighty Fuel particles tended to stay and be concentrated within the debris bed. The characteristics of the Mixed model's configuration transformation also reflect the previous experimental results, which demonstrated that heavier particles take over the bottom layer's larger ratio after the sedimentation of binary-density particles [14,15]. Finally, because of the effect of the dispersed light Structure particles, the height of the debris (\(H_{bd}\) [m]) was lower than the other two models after particle redistribution, as shown in Figure 8. For the Stratified model, although both Fuel particles and Structure particles also moved downwards, the initial stratified configuration was not altered during the particle redistribution since the Structure particles with lower density on the upper layer found it tough to intrude into the bottom high-density layer of the Fuel particles, as in Figure 7c. In the end, the \(H_{bed}\) of the Stratified model was higher than the other two models after particle redistribution, as demonstrated in Figure 8. The values of the \(H_{bed}\) after particle redistribution among the three models are also listed in Table 6.