## 2 Apparatus
### Design  
The design of the double VMIS was made with the following goals: First, we wanted to add the capability to detect positively-charged ions without compromising the resolution on the electron side as compared to a standard VMIS. Second, as molecules have a typical ionization potential of 7-15 eV and, with HHG, the typical photon energies are up to 100 eV, the spectrometer should be able to focus electrons with energies up to \(\approx\)90 eV and ions with kinetic energies up to \(\approx\)10 eV, typical for, e.g., Coulomb explosion. Third, the spectrometer had to be compatible with the existing experimental chamber of the high-intensity XUV beamline at the Lund Attosecond Science Center containing the all-reflective short focal length XUV focusing optics [42; 43]. Extending the single-sided spectrometer to be able to record positively-charged ions and electrons simultaneously was the aim of this work. To that end, the design of the electron side, adapted from [44], was retained and the repeller electrode replaced by an electrode with a mesh, as shown in Figure 1b. On the ion side, an open extractor electrode and a flight tube, similar to that on the electron side, were added. There are two advantages with this choice of design. First, we are not changing the imaging conditions on the electron side, and second, once the optimum voltages have been found for the electrons, the voltages on the ion side can be tuned independently without affecting the electron image quality. The drawbacks are that the ions are to some extent scattered by the mesh, which has a transmission of \(\sim\)80%, and that they pass through a drift region before they pass the repeller and are focused by the fields on the ion side. This affects the energy resolution that can be achieved for the ion imaging, which will be discussed in Section 2.3. The maximum electron or ion energy is restricted by the fact that the electrons or ions move away from the detector axis due to their initial velocity perpendicular to it. To increase the maximum detectable energy, one needs to either decrease the flight tube length, increase the flight tube and detector diameters or use higher acceleration voltages. In our case, the maximum detector size and the flight tube diameters were set by the existing chamber to \(\sim\)100 mm, leading to the choice of a standard MCP detector with a diameter of 75 mm, mounted on a CF160 flange. Similarly, the minimum flight tube lengths were set by the flange-to-flange distance (690 mm) of the existing experimental chamber to 345 mm. In principle, shorter flight tube lengths could have been achieved by a design where the MCPs are mounted inside the vacuum chamber, but this would have led to a more complicated design and a deteriorated TOF resolution, and was thus avoided. With restrictions imposed on the detector size and flight tube length, the ratio between the maximum detectable kinetic energy and the acceleration voltage scales approximately as \((r/L)^{2}\), where \(r\) is the detector radius and \(L\) is the flight tube length. Under the chosen conditions, this means that particles with kinetic energies up to \(\approx\)1% of the acceleration voltage can be detected, meaning that a total voltage difference of almost 10 kV between the front of the electron MCP and the front of the ion MCP is required to detect electrons and ions with 90 eV and 10 eV of kinetic energy, respectively. The design of the assembly was made in such a way that both detectors, electrodes and flight tubes could be supplied with floating voltages of \(\pm\)10 kV. While the front of the MCPs are not electrically connected to the flight tubes, for the following discussion and simulations, we assume that the same voltage is applied to the front of the MCP and the flight tube. The resulting design of the double VMIS is shown in Figure 1 together with the relevant dimensions.