## 3 Lens Design  
Figure 2a shows the dimensions of the electron-optical lens, which consists of 27 independently tunable electrodes. high voltages are supplied by Iseg EHS40200x power supplies. The interaction region is located between \(e^{-}\) pusher and \(e^{-}\) extractor. The right side is the electron arm, while the left side is the ion arm. The electrodes are made of aluminum plate with a thickness of either 5 mm or 1 mm. The gap between the electrodes is normally either 6 mm or 3 mm except the one between \(e^{-}\) pusher and \(e^{-}\) extractor, which is 18 mm so that the 800 nm femtosecond laser can be back-focused and the strayed X-ray photon would be less likely to see the electrodes. Figure 1: Schematic view of the CpVMI spectrometer. The gas sample can be prepared as either a supersonic molecular beam or an effusive molecular beam. Charged particles produced in the interaction region are projected onto the detector (stacked MCPs with a P46 phosphor screen), and the images are recorded by a camera. The ion TOF signals are recorded using an oscilloscope. Figure 2: (**a**) The geometry of the electrostatic lens (length unit: mm). The electron arm and ion arm sit at the right and left sides, respectively. (**b**) SIMON simulated trajectories of the electrons with the kinetic energy of 1000 eV in the strong focusing mode and ions with the kinetic energy of 20 eV. The emission angles are \(0^{\circ}\), \(30^{\circ}\), \(60^{\circ}\), \(90^{\circ}\), \(120^{\circ}\), \(150^{\circ}\), and \(180^{\circ}\) with respect to the lens axis. The source region is defined as 9 particles emitted from a 1 \(\times\) 3 mm\({}^{2}\) rectangle. In the lens there are four ultrafine stainless steel meshes with an 80% transparency. Mesh I and II separate the spectrometer into three parts, ion focusing region, reaction/1 st electron focusing region, and 2 nd electron focusing region. The electron arm can work in either strong or weak focusing mode. In the strong focusing mode, both the 1 st and the 2 nd regions are used for focusing. In the weak focusing mode, while the 1 st region is set in a uniform electric field, only the 2 nd region is used for focusing. As described before, there are two ways to introduce the gas into the main chamber: the supersonic molecular beam and the effusive molecular beam. Because the supersonic molecular beam does not affect the electric field, the electron arm can be set in the strong focusing mode. On the contrary, the effusive molecular beam will strongly distort the electric field if the interaction region is not set in a homogeneous field, so the electron arm needs to work in the weak focusing mode. Mesh III and IV are used to prevent the detector voltage from distorting the electric field in the lens. The distance between the reaction point and mesh II is half of that between mesh II and mesh III, as required by the Wiley-McLaren condition [26]. Figure 2b shows the simulated trajectories of electrons with a kinetic energy of 1000 eV in the strong focusing mode and ions with a kinetic energy of 20 eV using SIMION software, the source region is defined as 9 particles emitted from a 1 \(\times\) 3 mm\({}^{2}\) rectangle. The optimization is separated into two steps. The first step is to optimize the electron arm. We set the \(e^{-}\) pusher grounded, then find the voltage setting of the electron arm in either weak or strong focusing mode. The maximum voltage in simulation is 17 kV when the electron arm can detect 1000 eV electrons with a 4\(\pi\) acceptance angle. 17 kV can cause discharge easily, so we shifted all voltages negatively. For experiments that produce low kinetic energy electrons, we reduce all voltages proportionally. The second step is to find the voltage setting of the ion arm. Since the ion arm and the electron arm share the interaction region, the setting of the ion arm will be affected by that of the electron arm. Therefore, we fixed the voltage setting of the electron arm according to different experimental conditions, then found the voltage setting of the ion arm.