## 2 Materials and Methods
### Radiochromic Film  
Corresponding film measurements were simultaneously performed for each of the calorimeter irradiations by placing a single RCF on the front surface of the calorimeter jacket--i.e., the surface which was directly exposed to the incoming proton beam. Singular sheets of GaFChromic EBT3 films [39] were cut to approximate dimensions of 3 cm \(\times\) 3 cm, sufficient to fully encompass the entirety of the sensitive region of the SPGC core. Prior to irradiation, the outer circumference of the calorimeter jacket was marked on the attached film, allowing the volume averaged dose region to be analysed. This is highlighted in Figure 4.  
As observed from Figure 4, the dose distribution deposited on the EBT3 film is the result of the magnetic dispersion system that was employed, giving a horizontal spread of energy components. The deflection of proton kinetic energies is demonstrated in the schematic shown in Figure 5. The least energetic protons should experience the greatest deflection corresponding to those deposited leftmost on the film shown in Figure 4, with the most energetic being deposited further across the horizontal direction. The significant darkening on the left-hand side of the dose profile on the EBT3 film in Figure 4 indicates that the least energetic protons are the most populous and are being stopped by the film. A \"line-out\" of the dose profile was calculated and examined from the irradiated RCF, as shown in Figure 6. This is taken as a line directly across the horizontal geometrical distance of the irradiated region, from which the dose is analysed. Figure 5: Schematic showing the deflection of protons contained within the laser-accelerated beam, with the degree of deflection dependent on the incident particle kinetic energy. The colours highlight the fact that particles are deflected onto the irradiation point according to their energy, with the higher energies (red) deflecting least and the lower energies (purple) the most. The proton energy dispersion was investigated through Monte Carlo simulations using the Geant4 code (applying the QGSP_BERT_HP physics list for all processes) [39; 40; 41]. A proton source, variable in its distribution of particle kinetic energy (ranging from 0 to 45 MeV at the source), was simulated using Geant4. Through the use of particle scoring, the cartesian coordinates in addition to the initial kinetic energy of each component of this simulated proton beam were recorded at a position corresponding to that of the exact entrance of the jacket of the small-body portable graphite calorimeter. This setup was simulated to replicate that of the calorimeter system within the beamline at the RAL. The plot shown in Figure 7, in addition to that in Figure 8, highlights that within the proton bunch accelerated from the laser system, the particle kinetic energies at the lower end of the spectrum (\(-\)0-10 MeV) are the most populous. It was anticipated that this lower end of the spectrum would comprise those particles that are stopped within the initial RCF and graphite jacket. This was confirmed through calculations performed with the LISE++ software (Michigan State University, [[https://lise.nscl.msu.edu/lise.html](https://lise.nscl.msu.edu/lise.html)]([https://lise.nscl.msu.edu/lise.html](https://lise.nscl.msu.edu/lise.html)), accessed on 18 September 2023) [42]. Using this toolkit, the proton energy required to penetrate a structure composed of 350 \(\upmu\)m water equivalent thickness RCF (EBT3) material, followed immediately by 0.75 mm of graphite of density 2 g/cm\({}^{3}\), was obtained. Proton energies of between 12.1 and 12.2 MeV were calculated with the LISE++ setup, indicating this energy is required to reach the SPGC core after initially traversing both the film and jacket layers. Figure 6: Horizontal dose profile taken from the EBT3 layer attached to the SPGC for the first shot. The blue line indicates the dose line-out taking across the film horizontal.