## 2 Apparatus
### Simulations  
To evaluate the expected performance of the spectrometer, simulations were carried out using SIMION [45] for the different operation modes listed above. An interaction region, defined by the overlap between the laser beam and the molecular beam, with a conservatively chosen size of \((100\,\times 100\times 2000)\)\(\upmu\)m\({}^{3}\) was used. For the VMI calculations, electron kinetic energies were chosen in steps of 5 eV from 10-90 eV and ion kinetic energies in steps of 1 eV from 2 to 10 eV. For each operation mode, we found optimum voltages, defined as the voltages for which the best resolution is obtained for electrons with a kinetic energy of 30 eV and singly-charged ions with a kinetic energy of 6 eV and a mass of \(m=100\) u. The kinetic energies were chosen based on the typical energies of the photoelectrons and photoions of interest using high-order harmonics generated in argon to ionize molecules with ionization potentials in the 10-20-eV range, and the mass was chosen because it is typical for systems that are of current scientific interest, like small polycyclic aromatic hydrocarbons.  
To find the optimum voltages for the VMI modes, a simplified simulation procedure was used, in which the trajectories of 27 particles arranged on a \(3\times 3\times 3\) grid covering the interaction region and with their velocity component perpendicular to the detector axis were calculated and the energy or mass resolution calculated from the particle impact position distribution on the detector. For the optimum voltages found (summarized in Table 1), a procedure based on Monte Carlo sampling was used [46], resulting in more realistic resolution estimates. The method consisted of launching a large number of electrons or ions (\(\sim\)10\({}^{6}\)) with a random starting position chosen from a Gaussian distribution over the interaction volume and with a random, isotropically-distributed 3D initial momentum. The particle impacts on the detector were then sampled to generate a simulated detector image or TOF trace, which was treated similarly to experimental data in order to extract the resolution. The simulated images were inverted using an iterative algorithm [23] to retrieve the 3D momentum distribution from the 2D image. From the 3D momentum distribution, the energy spectrum was calculated, and the energy resolution, \(\Delta E/E\), was estimated by obtaining \(\Delta E\) from the full width at half maximum of a Gaussian fit to the peaks in the spectrum. For the TOF simulations, only the Monte Carlo method was used, and the mass resolution, \(m/\Delta m\), was calculated by obtaining \(\Delta m\) from the full width at half maximum of a Gaussian fit to the peaks in the mass spectrum. They were performed both for ions with zero kinetic energy and for ions with an initial velocity in the direction of the molecular beam. The latter represents the more realistic scenario of target molecules with a mass of 100 u that are brought into the interaction region by a carrier gas, e.g., helium. This carrier gas typically travels at a speed of 1000 m/s, which corresponds to a kinetic energy of 520 meV for molecules with a mass of 100 u.