# The DREAM Endstation at the Linac Coherent Light Source
## 3 Performance and Simulations
### Simulation for Coulomb Explosion Imaging Experiments
(**c**) The dependence of the required electric field strength (V/mm) on the acceleration length \(\mathrm{L}_{a}\) and acceleration-plus-drift length \(\mathrm{L}_{ad}\). Figure 7: Ion trajectory simulation for CEI-type experiments. The electric filed strength is 460 V/cm. The trajectories of \(\mathrm{C}^{2+}\) with kinetic energy of 150 eV and \(\mathrm{C}^{3+}\) with kinetic energy of 250 eV are shown in orange and blue, respectively. The ejection angles relative to the spectrometer axis range from 0 to 360 degrees. (**a**) Side display of spectrometer equipotential lines (red) and particle trajectories. (**b**) Spectrometer equipotential lines (red) and particle trajectories along the potential energy surface (green). A similar dependence trend emerges in resolving the ionic mass for different electric fields, as shown in Figure 8b,c, as is expected. When the kinetic energy acquired by the charged particle from the spectrometer field is much larger than that gained from the interaction, which is often the case in CEI experiments, the TOF spread of each ion species with a fixed momentum distribution can be approximated to be inversely proportional to the electric field strength. Since the larger the TOF spread is, the smaller is \(\sum_{i=1}^{3}\overrightarrow{T_{i}}\), the mass resolving power should follow the same dependence trend as the electric field strength. Thus, increasing the electric field strength can be an effective way to increase the separations between ion species in the \"TOF vs. R\" plot. However, it can also degrade the momentum resolution, as we will illustrate with the simulation results using the dimensions of the DREAM spectrometer. Figure 10 shows the simulated \"TOF vs. R\" ((a) and (c)) and ion momentum/energy resolution ((b) and (d)) plots for the DREAM spectrometer, with L\({}_{ad}\) = 275 mm and L\({}_{a}\) = 99 mm. A position resolution of 250 \(\upmu\)m and time resolution of 0.25 ns were assumed in the simulation. Figure 10a,b are obtained with the spectrometer voltage only high enough to detect the charged particles over 4\(\pi\) solid angle. There are overlaps between different ion distributions in the \"TOF vs. R\" plot, which typically would require the additional step of applying coincidence or momentum-conservation conditions to fully disentangle distinct ion species. The momentum resolution for C\({}^{\prime+}\) and O\({}^{\prime+}\) ions ranges from sub-one to a few atomic units, and the kinetic energy resolution ranges from sub-one to a few electron Volts. The simulation results after scaling the voltage up by a factor of 1.3 are shown in Figure 10c,d. Due to the electric field dependence discussed before, the separation between ion distributions grows larger with the increased voltage setting. However, the momentum and energy resolution is slightly degraded. The increased electric field compresses the spread of the charged particles on the detector in the directions along and perpendicular to the spectrometer axis, which would in turn make the smallest resolvable momenta and kinetic energy values larger. Therefore, the trade-off between mass resolving power and momentum resolution should be taken into account when choosing the electric field for the DREAM CEI experiments.