## 3 Results
### Plume Parameters  
Figure 6 shows the fitting plot of plume length for carbon-doped composite propellants. It can be seen that three different composite propellant samples exhibited varying trends. The plume length of the nano-carbon-doped composite propellant sample presented approximately linear growth, as can also be seen in Figure 5a, indicating a consistently stable expansion rate. At the end of a laser pulse, the plume length reached a maximum of 11 cm, with a corresponding plume expansion rate of 22 m/s. The plume length of the graphite-doped composite propellant sample exhibited parabolic growth before the ablation time of 1 ms, as can also be observed in Figure 5b. Subsequently, it increased linearly to reach a maximum length of 8 cm. The average plume expansion rate was 16 m/s. Variation in the plume length of the graphene-doped composite propellant sample was similar to that of the graphite-doped composite propellant sample, as can also be seen in Figure 5c. It exhibited parabolic growth before the ablation time of 1.5 ms, followed by a nearly linear increase. The maximum length of its plume reached 12 cm, with an average expansion rate of 24 m/s. After comparing the three sets of experiments, we can conclude that the plume length of carbon-doped composite propellant samples primarily displayed a linear growth, indicating a stable expansion rate of the plume, which further suggests that the addition of carbon particles had significantly enhanced the optical absorption coefficient of the PTFE. Of the three composite propellant samples, the graphene-doped one exhibited the greatest plume length and the highest expansion rate, primarily attributable to the higher melting point of graphene compared to nano-carbon powder and graphite, which is significantly greater than that for PTFE. When exposed to laser irradiation, the dispersed graphene in PTFE facilitated the deposition of laser energy, thereby intensifying ionization through reactions with the excited products of PTFE in the plume. Despite graphite having a higher melling point than nano-carbon powder, the graphite-doped composite propellant sample demonstrated the smallest plume length and expansion rate due to its flame retardancy. Figure 7 shows variation in the plume area of carbon-doped composite propellant samples. During the early ablation stage, the plume area continued to increase with time until it reached a certain value and then fluctuated around this level. For the nano-carbon-doped composite propellant sample, its plume area kept increasing to a maximum of 15 cm\({}^{2}\), before 3 ms and then remained dynamically stable until the end of the laser pulse width. As for the graphite-doped composite propellant sample, its plume area continued to increase before 2 ms and then remained constant at 7 cm\({}^{2}\) until the end of the laser pulse width. In the case of the graphene-doped composite propellant sample, the area kept increasing until 3.5 ms, after which it fluctuated and stabilized at 10 cm\({}^{2}\). Once the laser stopped irradiating the propellant, although the plume area of three composite propellant samples was unequal, they all took roughly the same time to decrease to 0. Throughout the ablation process, the plume area of the nano-carbon-doped composite propellant sample was the greatest, followed by that of the graphene-doped sample. The plume area of the graphite-doped composite propellant sample was the smallest. Figure 6: Plume lengths of different carbon-doped composite propellant samples. Figure 7: Plume areas of different carbon-doped composite propellant samples. Based on the analysis of the plume images, it was observed that the jet of the carbon-doped composite propellant sample continued to spread during the ablation process but the plume cluster at the tail end gradually darkened and eventually vanished. In the case of tradeoffs, there was no significant increase in the plume area at the late stage of the ablation.