## 3 Results and Discussion
### Experimental Results at Non-Ambient Temperature
When the reflected wave reaches the bottom of the PMMA, its pressure is greater than the actual critical initiation pressure of the acceptor. If the acceptor is not detonated, the reflected wave produced has little effect on the PMMA. There are calculated shock pressure profiles at various depths of SSGT for the Go case of 7.20 mm and No-go case of 7.30 mm PMMA gaps shown in Figure 9. At 4.60 \(\upmu\)s, the donor explosive RDX reacted completely, and the stable detonation pressure was approximately 21.7 GPa. The theoretical detonation velocity of the donor RDX is approximately 8200 m/s. The time for the shock wave running in the depth of the RDX was approximately 4.65 \(\upmu\)s. It was consistent with the actual situation. Due to the deformation of the PMMA and the different impedance of the contact material, the detonation wave is attenuated when it  
Figure 8: Simulation results of shock initiation process and detonation pressure progress for SSGT: **(a)** Go case at 7.2 mm PMMA thickness; **(b)** No-go case at 7.3 mm PMMA thickness. contacts the top of the PMMA, and it is transmitted to the acceptor. The critical initiation pressure of HMX-based booster is approximately 3.6 GPa at 25 \({}^{\circ}\)C.  
The ignition and growth simulation of the shock initiation for HMX-based booster at \(-25\), 88 and 120 \({}^{\circ}\)C is illustrated in Figure 10, respectively. The calculation SSGT results of the booster were consistent with the actual situation. From Figure 10, it is quite evident that the ignition and growth model simulates experimental records quite well and can be reliably used to describe the shock ignition process involving HMX-based booster at a temperature range from \(-25\) to 120 \({}^{\circ}\)C.  
While most of the modeling constants remain unchanged, only a few of them require a change depending on the temperature. The parameters of the shock initiation equation for HMX-based booster with non-ambient temperature were optimized by changing two parameters: \(B\) in the JWL equation of state and G\({}_{1}\) in the ignition and growth reactive rate equation. These constants are shown in Table 8.  
Contrary to the experiments, which provide limited data on critical gap thickness G\({}_{50}\) at only four temperature positions of HMX-based booster shock sensitivity test, the numerical simulations provide more detailed information on the shock initiation processes. Figure 8 shows the calculated shock pressure profiles at various depths of HMX-based booster for \(-25\), 88 and 120 \({}^{\circ}\)C conditions. As the temperature increases, the critical initiation pressure of HMX-based booster gradually decreases, which is approximately 4.6 GPa (\(-25\)\({}^{\circ}\)C), 2.7 GPa (88 \({}^{\circ}\)C) and 2.2 GPa (120 \({}^{\circ}\)C), respectively. \begin{table}
\begin{tabular}{c c c} \hline \hline \(T_{0}\) (\({}^{\circ}\)C) & **Unreacted \(B\) (GPa)** & \(G_{1}\) (GPa/\(\updownarrow\)s) \\ \hline \(-25\) & \(-5.0750\)\(\pm\) 0.104 & 95,000 \(\pm\) 2058 \\ \(25\) & \(-5.9440\)\(\pm\) 0.128 & 100,000 \(\pm\) 3359 \\ \(88\) & \(-7.0384\)\(\pm\) 0.136 & 112,500 \(\pm\) 4740 \\ \(120\) & \(-7.5425\)\(\pm\) 0.141 & 145,000 \(\pm\) 5061 \\ \hline \hline \end{tabular}
\end{table} 
Table 8: Ignition and growth parameter change for HMX–based booster at different temperatures. Figure 9: Calculated pressure profile for SSGT simulation: (**a**) Calculated pressure profile with a gap thickness of 7.2 mm; (**b**) Calculated pressure profile with a gap thickness of 7.3 mm.