## 2 Materials and Methods  
### Calorimetry  
The small-body portable graphite calorimeter (SPGC, National Physical Laboratory, NPL, Teddington, UK) is a smaller derivative of the previous portable graphite calorimeter reported in the literature [31, 36], with both devices developed from the same materials at the NPL. The intended purpose for the SPGC was the measurement of low energy, clinical proton beams, but more recently it has been refurbished to enable use with laser-driven protons. A schematic of the graphite components of the SPGC is shown in Figure 1. The SPGC comprises a cylindrical arrangement of graphite structures, with the innermost component, the core, containing thermistors used to detect the radiation-induced temperature rise from which the absorbed dose is measured. The core has a 20 mm diameter and 2 mm thickness and is separated from a jacket of 30 mm external diameter and 4 mm depth by a 1 mm air cavity. Both the core and jacket are composed almost exclusively of graphite. This graphite arrangement of components is enclosed within a Styrofoam structure, with the outer surface of the graphite lid exposed to the incoming radiation beam. These two outermost components (graphite jacket and Styrofoam enclosure) are designed to enhance thermal isolation of the core by reducing heat exchange with the surrounding environment. The structure of the small portable graphite calorimeter, in addition to its placement within the irradiation pipe, are shown in Figures 2-4. The first recorded measurements of the absorbed dose of a laser-driven proton beam using the calorimeter system as reported here were conducted with the high-power VULCAN-PW laser system at the CLF, Rutherford Appleton Laboratory, United Kingdom. This system is capable of producing pulses with wavelength \(\lambda\) = 1.054 \(\upmu\)m duration \(\sim\)500-700 ps and energy up to 600 J. The laser pulses were focused with an f/3 Off Axis Parabola onto the surface of thin foils at an intensity of \(\sim\)5 \(\times\) 10\({}^{20}\) W/cm\({}^{2}\). Upon irradiation, protons were  
Figure 1: Configuration of the graphite components of the SPGC for measurements within a radiation beam. The red dots on the right indicate the relative locations of the thermistors within the body of the calorimeter. Dimensional metrology of the graphite components was carried out during the refurbishment of the calorimeter. The SPGC prepared for use with the VULCAN-PW system can be seen in Figure 2a. accelerated from the rear of the foils through the target normal sheath acceleration (TNSA) process [11]. As shown in Figure 2a, a dipole magnet system was placed downstream of the target within the interaction chamber, generating a magnetic field of 0.9 T, thus allowing for the energy dispersion of the protons before they reach a sample located in a re-entrance tube. This setup, designed for radiobiology measurements [37], was adapted to fit the SPGC system within the in-air irradiation pipe, as shown in the schematic included in Figure 2b. Figure 2: (**a**). Schematic showing the layout and components of the VULCAN-PW beamline at CLF (RAL) used in the irradiation of both biological sample/calorimeter system. The rail and re-entrance pipe connecting the sample to be irradiated to the interaction chamber are identified as the furthermost right components. (**b**). Alternative perspective of the beamline at RAL, with the small portable graphite calorimeter positioned at the irradiation point through the use of the pipe and rail system. The dashed lines indicate the relative paths of the X-rays (black) and protons (red), respectively. Proton bunches are generated through intense laser-target interactions impinging on the SPGC core, inducing a temperature rise in the graphite which is detected by the embedded thermistors.