# Dosimetric Optimization of a Laser-Driven Irradiation Facility Using the G4-ELIMED Application
## 2 Materials and Methods
### Depth-Dose Profile Generation  
Clinical irradiations with ion beams are usually carried out using a Spread-Out Bragg Peak (or SOBP), i.e., a flat depth dose distribution is needed to uniformly irradiate a solid tumor.  
The SOBP is the result of many beams of different energies and intensities added up with an appropriate weighting function. Usually, the energy change is done by some passive energy modulation system (e.g., a wheel modulator [31] or a ridge filter [32]) coupled with additional range shifters. These components are not required along the ELIMED beamline because the initial energy spectrum of laser-accelerated beams is intrinsically poly-energetic and the ESS can be used as an active energy modulator.  
The only problem with such an approach is that the configuration of the focusing system needs to be changed to properly inject protons at different kinetic energies into the ESS. This will increase the time required to perform a certain experiment. For this reason, only the configurations to focus four different energies (18, 20, 22, and 25 MeV) were considered in this work. These changes have been calculated keeping the same sequence of magnets and limiting the displacement as much as possible in order to reduce the time necessary for repositioning the magnets. In such a way the transmission efficiency is not optimal, but the full irradiation time is limited to about 6 min. On the other hand, four setups calculated to maximize the transmission efficiency would require changing the sequence of the magnets, which means several hours because this operation cannot be performed under vacuum and involves the manipulation of heavy objects (the weight of the smaller quadrupole is about 70 kg).  
In the simulated configurations, the first and the fourth PMQs have a length equal to 120 mm and positive polarity, while the second and the third PMQs have a length of 80 mm and negative polarity. The initial positions of the PMQs to transport the different energies are summarized in Table 2 and the relative distances between elements (D1, D2, D3, and D4) are clarified in Figure 2 where the generic scheme of the setup is presented.  
Figure 1: Distributions of the implemented source: (**a**) Initial kinetic energy distribution following the data presented in [PERSON] et al. [30]; (**b**) Initial angular distribution. Protons at different energies have a maximum half-angle between 2.4 (highest energy) and 21 (lowest energy) degrees according to the data presented in [PERSON] et al. [30]; (**c**) Initial position of the protons in the XY plane.  
As mentioned above, the ESS can be used as an active energy modulator. This is realized by changing the magnetic field, i.e., the current intensity, of the dipoles to select different energies at different shots. Herein, the magnetic field values used in the energy selector are 0.243 T, 0.257 T, 0.269 T, and 0.287 T which are the necessary parameters to obtain protons with energies of 18 MeV, 20 MeV, 22 MeV, and 25 MeV, respectively, streaming on the reference trajectory. On the other hand, both the energy spread and the transmission efficiency depend on the aperture of the slit placed in the center of the ESS to select ions at different kinetic energies. Thus, a slit aperture equal to 30 mm was used to increase the transmission of protons, except in the 25 MeV case where a 20 mm slit aperture was used to reduce the energy spread and, hence, the distal fall-off of the SOBP.