# The DREAM Endstation at the Linac Coherent Light Source
## 3 Performance and Simulations
### Simulation for Coulomb Explosion Imaging Experiments  
Coulomb explosion imaging experiments performed at X-ray free-electron (XFEL) laser facilities demand special spectrometer considerations compared with those with table-top lasers or synchrotron light sources. With the number of photons typically on the order of \(10^{12}\), a femtosecond XFEL pulse with \(\sim\)\(\upmu\)m focal spot size can drive a molecule into extremely high charge states and induces the molecule into an almost instantaneous explosion. Therefore, the kinetic energy of the resulting ion fragments is typically much larger than in the experiments with conventional light sources. The spectrometer is required to collect such highly energetic particles over a 4\(\pi\) solid angle, while simultaneously preserving the mass and momentum resolution adequate for the imaging purposes. Carbon and oxygen ions C\({}^{i+}\) and O\({}^{i+}\) with \(i=1,2,\) and 3 are chosen for simulating the spectrometer performance in CEI experiment as shown in Figure 7. The kinetic energies of C\({}^{i+}\)/O\({}^{i+}\) ions are set to be i \(\times\) 100 eV, based on data from a previous CEI experiment performed at the European X-ray Free-Electron Laser Facility. In the simulation under each setting, the spectrometer voltage is set such that it is sufficient to detect the charged particles over a 4\(\pi\) solid angle. A typical charged particle \"time of flight (TOF) versus detector hit position (R)\" plot from the simulation is shown in Figure 8a. A \"TOF vs. R\" plot is often used for identifying and isolating different ion species. Thus, for a cleaner separation, decreasing the overlap between different species in such plots, which is equivalent to increasing the mass resolving power, is needed. As shown in Figure 8a, we define \(\sum_{i=1}^{3}\overrightarrow{T}_{i}^{i}\) as the metric for the mass resolving power, with the vector \(\overrightarrow{T}_{i}\) connecting the point of the largest C\({}^{i+}\) TOF to the point of the smallest O\({}^{i+}\) TOF. Figure 8b displays \(\sum_{i=1}^{3}\overrightarrow{T}_{i}^{i}\) as a function of the acceleration length L\({}_{a}\) and acceleration-plus-drift length L\({}_{ad}\). At fixed L\({}_{a}\), the mass resolving power increases with increasing L\({}_{ad}\), and at fixed L\({}_{ad}\), the mass resolving power increases with decreasing L\({}_{a}\). This dependence is better visualized in Figure 9. With L\({}_{ad}\) fixed at 270 mm and as L\({}_{a}\) is decreased from 270 mm to 10 mm, the distribution of each ion species is more compressed in the TOF direction, making adjacent distributions better separated from each other. Figure 8c displays the required electric field strength as a function of the acceleration length L\({}_{a}\) and acceleration-plus-drift length L\({}_{ad}\). At fixed L\({}_{a}\), the field strength increases with increasing L\({}_{ad}\), and at fixed L\({}_{ad}\), the field strength increases with decreasing L\({}_{a}\). As  
Figure 6: DREAM spectrometer model used by the SIMION simulation. (**a**) 3D isometric display of the model by SIMION. (**b**) Side display of the model by SIMION. \(\mathrm{L}_{a}\) is decreased from 270 mm to 10 mm, the electric field is required to be increased from 35 V/mm to 256 V/mm. Figure 8: Mass resolving power and electric field dependence on the acceleration length \(\mathrm{L}_{a}\) and acceleration-plus-drift length \(\mathrm{L}_{ad}\). (**a**) Simulated “TOF vs. \(\mathrm{R}^{\prime}\) plot of \(\mathrm{C}^{\dagger+}\) and \(\mathrm{O}^{\dagger+}\) ions detected with a certain spectrometer configuration, with \(q=1\), 2 and 3. The vector \(\overline{T}_{i}\) connects the point of the largest \(\mathrm{C}^{i+}\) TOF to the point of the smallest \(\mathrm{O}^{i+}\) TOF. \(\sum_{i=1}^{3}\overline{T}_{i}^{\prime}\) is used as the metric for the mass resolving power. (**b**) The dependence of the mass resolving power \(\sum_{i=1}^{3}\overline{T}_{i}\) (ns) on the acceleration length \(\mathrm{L}_{a}\) and acceleration-plus-drift length \(\mathrm{L}_{ad}\).