# Monte Carlo Study of Imaging Plate Response to Laser-Driven Aluminum Ion Beams
## 6 IP Sensitivity  
We examined how IP sensitivities at different incident Al ion energy deviate from the IP sensitivity obtained by least squares method in each model. Figure 5 shows the IP sensitivities as functions of the incident Al ion energy for both the linear model and the exponential model. The IP sensitivities calculated using the exponential model are shown as hollow red circles, and those calculated using the linear model are plotted as hollow black circles. These values are derived from experimentally measured IP responses and the calculated deposited energy from the incident Al ions using each model. In Figure 5, the IP sensitivity fluctuation in the exponential model is less than that in the linear model. The IP sensitivity is nearly constant at \(\alpha_{exp}=0.019\) in the exponential model with a standard deviation of 5% of \(\alpha_{exp}\). In the linear model, the IP sensitivity is \(\alpha_{lin}=0.013\) with a standard deviation of 21% of \(\alpha_{lin}\). This suggests that the exponential model describes the IP response better.  
Since the IP sensitivity in the exponential model remains nearly unchanged regardless of the incident kinetic energy of Al ions in Figure 5, we can treat \(\alpha_{exp}\) as a constant value in Equation (3) and determine the IP response function by multiplying the deposited energy function calculated from the Monte Carlo simulations. This implies that the IP response function can be calculated even with little experimental data.  
The overall sensitivity of BAS-TR IP to Al ions is found to be much smaller than the known sensitivity of IPs to electrons, protons, and alpha particles. This is consistent with the findings reported by [PERSON] et al. [23] and [PERSON] et al. [16] for alpha particles. [PERSON] et al. report that the IP sensitivity to \({}^{4}\)He ions is about 10 times smaller than the IP sensitivity to protons with BAS-MS and BAS-SR IPs and around five times smaller than the IP sensitivity to protons with BAS-TR IP [16]. [PERSON] et al. explain this using a quenching effect. According to their study, the IP sensitivity depends on both the type of incident ions and the stopping power of IPs for those ions [16; 23].  
In our experiment, a similar quenching effect is also observed. The measured sensitivity of BAS-TR IP to Al ions is about 13 times less than the known IP sensitivity to protons, and it is about half of the known IP sensitivity to \({}^{4}\)He [16]. As shown in Figure 5, IP sensitivities decrease with increasing incident Al ion energy. This decrease is larger in the linear model than in the exponential model. The large variations of the IP sensitivities in the linear model seem to be caused by the quenching effect, which results in large discrepancy with the experimental IP response data. In comparison, the exponential model has smaller variations of the IP sensitivity and agrees well with the experimental data. The exponential factor in Equation (5) offsets the IP sensitivity decline coming from the stopping power increase of Al ions.  
Figure 5: Sensitivity of BAS-TR IP is shown as a function of the incident Al ion energy on the IP surface.