# Characterization of Ultra-High-Dose Rate Electron Beams with ElectronFlash [PERSON]
## 2 Materials and Methods
### Monte-Carlo Dose Simulations  
Experimental measurements were compared with simulations obtained by means of the MC software 2020.0.10 FLUKA version [27; 28]. In particular, the accelerator beam optics from the titanium window (at the end of the linac) to the end of the applicator was simulated.  
As mentioned previously, the A-d30 and A-d120 applicators were chosen to validate the EF dosimetric proprieties according to the foreseen radio-biology experiments.  
In the simulations, the electron beam exits from the linac and goes through a 55 \(\upmu\)m-thick titanium window that seals the linac vacuum. Depending on the applicator, the source-to-surface distances (SSDs) are 55 cm and 110 cm for the A-d30 and A-d120, respectively, (Figures 2 and 3).  
The A-d120 applicator was modeled as a series of three PMMA cylinders centered on the beam axis (z axis), with diameters of 50, 120, and 120.4 mm, a wall thickness of 5 mm and lengths of 62.6, 155.4, and 852.0 mm, and one truncated cone 30 mm long parallel to the z axis, with the larger and smaller circular base of 120.4 mm and 120 mm in diameter, respectively. The A-d30 applicator was modeled in the same way using three PMMA cylinders with diameters of 50 mm, 120 mm, and 30 mm, having 5 mm wall thickness and lengths of 62.6 mm, 155.4 mm, and 332.0 mm, and one truncated cone 43 mm long with the larger and smaller circular base of 120 mm and 30 mm diameter, respectively.  
A PMMA phantom 40 \(\times\) 40 \(\times\) 40 cm\({}^{3}\) was placed in both simulations at the exit of the applicator, according to the setup used for the experimental data acquisition.  
The specification of the electron beam arriving on the titanium window was provided by the manufacturers and thus defined as a Gaussian distributed electron profile with  
Figure 3: Two-dimensional visualization of FLUKA simulation geometry used for the A-d120 simulation. The beam travels in the z direction.  
Figure 2: Two-dimensional visualization of FLUKA simulation geometry used for the A-d120 simulation. The beam travels in the z direction.  
full-width of half-maximum (FWHM) on the x and y planes of 3.4 mm and a negligible mean angular spread. Figure 4 reports the energy distributions of EF electron beams at 5 MeV and 7 MeV. As shown in Figure 4, two types of electron beam energy spectra are obtained, i.e., a single peak and a double peak case for the 5 MeV and 7 MeV, respectively. The difference between the two cases is due to the phasing between the electron bunch and the RF fields inside the linac. Since the RF field behaves as a cosine function in time and the bunch length is large compared to the RF wavelength, it is possible to have a situation in which the electrons experience two different stable points in terms of capture, at two different energies, for example, on the crest and slightly before or after. Nevertheless, these two points are so close in energy that no dosimetry change is expected between the single-peak and the double-peak cases. Indeed, we performed simulations with these types of beam spectra but no difference in the absorbed doses was appreciable between the two cases.  
The energy cut-offs for the transport and production of both electrons and photons were set to EMFCUT = 10 keV (kinetic energy). Particles with an energy below this threshold are not transported further and their energy is locally deposited. The expected dose per electron was evaluated in the PMMA phantom. In order to score the energy deposition, the 40 \(\times\) 40 \(\times\) 20 cm\({}^{3}\) phantom was divided into 201 \(\times\) 201 \(\times\) 200 voxels of size 2 \(\times\) 2 \(\times\) 1 mm\({}^{3}\). In the next section, the results of the simulations are compared with measurements.