## EUV Beamline Experimental Characterization
### Space Charge Effect at the Sample Material  
While the EUV photon flux of \(>\)10\({}^{10}\) ph/s after the monochromator is comparable to the flux of synchrotron radiation source beamlines, the number of photons per pulse is much higher because of the lower pulse repetition rate of the laser, compared with the synchrotron. The large photons density incident on the sample surface during the ultrashort EUV pulse can lead to the space charge effect, which can distort photoelectron emission. A single-crystal copper Cu (111) as the sample was inserted into the ARPES chamber and its Fermi-edge photoemission spectra were measured in order to measure the influence of space charge on the ARPES spectra and characterize the energy resolution of the EUV beamline. The H13 (20.15 eV) is chosen with grating G2 as photon source and the slit width is \(\sim\)100 \(\upmu\)m. The photon flux was varied from 5.7 \(\times\) 10\({}^{9}\) to 6 \(\times\) 10\({}^{8}\) ph/s. Figure 11 shows the effect of space charge on the ARPES measurements of the copper crystal. In Figure 11a, we observe space charge broadening and shifting of the Fermi-edge for higher photon fluxes. The space charge effect is minimized for F\({}_{\rm ph}\)\(\sim\) 3.6 \(\times\) 10\({}^{9}\) ph/s, which corresponds to a pulse photon density of 180 ph/\(\upmu\)m/pulse in the EUV focal spot with dimensions of 170 \(\upmu\)m \(\times\) 120 \(\upmu\)m. The Fermi-edge spectrum was fitted with Fermi-Dirac function, convolved with a 190 meV-width Gaussian function (black line in Figure 11b). The good fitting shows that energy resolution of the EUV beamline is \(\sim\)190 meV for H13, when space charge effects are minimized. This spectral resolution is in agreement with the design resolution of grating G2. In order to minimize the space charge effects, we need to reduce the EUV pulse photon density on the sample to \(<\)180 ph/\(\upmu\)m\({}^{2}\)/pulse. This pulse photon density is in good agreement with the space-charge measurements in Ref. [23] and is typical for TR-ARPES measurements reported in Refs. [28; 29] for example. The reduction in photon density is obtained by increasing the EUV focal spot area at the sample, to a maximum of 170 \(\upmu\)m \(\times\) 120 \(\upmu\)m, and/or reducing the photon flux at the sample. The EUV spot size of an average diameter of \(\sim\)150 \(\upmu\)m has a negligible contribution to the angular resolution and hence to the momentum measurement. On SRS, the EUV spot size is around 50 \(\upmu\)m and the effect of the 150 \(\upmu\)m in the TR-ARPES is negligible due to the low energy resolution (190 meV). Essentially in TR-ARPES, the momentum resolution is dominated by the energy resolution of the photon beam. Figure 10: EUV spot size measurement (**a**) CCD image of the fluorescence of the CE:YAG crystal, irradiated with EUV beam; scale bar is 100 \(\upmu\)m; (**b**) the measured focal spot profiles D\({}_{\rm x-FWHM}\)\(\sim\) 170 \(\upmu\)m and D\({}_{\rm y-FWHM}\)\(\sim\) 120 \(\upmu\)m.  
In angular resolving lens modes, the emission angle distribution is imaged on the detector. Here, the finite spot size of the photon beam on the sample contributes to the angular resolution and therefore to the momentum resolution. Theoretically, all electrons with the same escape angle excited from within the photon beam spot should be focused into an infinitely small spot on the detector. In reality, this spot on the detector will have a certain lateral spread M, which could also be viewed as a magnification. The contribution of the photon beam spot size S to the angular resolution A may be described by  
\[\text{A}=\frac{\text{M}}{\text{D}}\times\text{S},\]  
where D is the angular dispersion of the lens mode. For example, the Wide Angle Mode (WAM) of the PHOIBOS 150 analyzer has an angular acceptance of \(\pm 15^{\circ}\) with D = 0.75 mm/\({}^{\circ}\). The values for M depend on the lens mode and the retardation ratio R = kinetic energy/pass energy.