## 2 Description of the Simulation Models and Experimental Set up
Description of Electron and Proton Sources Used for Calculation of Electron, Proton and Photon Spectra and Fluencies, around the High Power Laser--Thin Solid Target Interaction Point  
The simulation model used for calculation of angular distribution of laser driven accelerated particles was developed considering mainly the above formulas (Equations (1)-(6)). A 2 MeV temperature for the hot electrons was calculated using Formula (1) and the following experimental parameters [24]: \(5\times 10^{19}\) W/cm\({}^{2}\) laser intensity, 40 fs laser pulse duration, 207 \(\upmu\)m\({}^{2}\) laser spot area. Two volume sources of radiation were considered in order to compute the spectra of electrons, protons and photons emitted in the 0-360\({}^{\circ}\) range (with a 5-degree angular step) at 3 cm distance, around the interaction point. The first source represents the source of electrons (a disk of 9 \(\upmu\)m radius) generated in the pre-plasma obtained after the interaction of the PW laser with the target surface. It provides the electrons for the simulation of radiation transport. The electrons were considered to have a Maxwellian energy distribution in accordance with Equations (4) and (5). This source is position in front of the target [28; 29; 30; 31]. The energy distribution of electrons was calculated, based on mathematical equations from (1) to (5). The angular distribution of electron source was assumed isotropic. The electrons generated in the pre-plasma which emit in 4\(\uppi\) are the main source for radiation in the vacuum chamber [7; 8]. The energy distribution of photons has been calculated considering the hot electrons interaction with the target nuclei. The second source (a disk of 9-\(\upmu\)m radius) of radiation included in the simulation was placed behind the target and provides the accelerated protons. There are considered the TNSA mechanism (Equations (1)-(3) and (6)) and the plasma expansion model [1; 28; 29]. The divergence of this source is an independent parameter and is defined through its half angle which was 25\({}^{\circ}\) in accordance with [1]. The incidence angle of the laser beam on the target was not considered in these simulations. Previously, in the paper of [PERSON]'s et al. [32] by Particle in Cell simulations it was shown that an oblique incidence angle of laser on the target increases the energy of accelerated protons without changing the distribution of electrons. At laser intensities of \(\sim\)10\({}^{19}\) W/cm\({}^{2}\), the incidence angle of the laser beam on the target influences only the efficiency of the energy transfer from photons to electrons into the pre-plasma. The characteristics of source terms are summarized in Table 1.  
The two volume sources described above were used to compute the angular and energy spectral distributions of electrons, protons and photons around the high power laser-thin solid target interaction point using the GEANT4 simulation toolkit [25; 33; 34]. Particle fluencies were also determined. The general particle sources (GPS) defined in GEANT4 provide a complex environment which allows the inclusion into the simulation of both proton and electron sources, with a specific ratio of particle numbers. It was considered a \(1.97\times 10^{12}\) total events number, (\(1.97\times 10^{12}\) electron events number and \(1.29\times 10^{9}\) proton events number) and a proton to electron number ratio of \(1.53\times 10^{3}\). The total events number and the ratio between electron and proton events number were generated by analytical calculations using the TNSA model (Equations (1)-(6)) for the experimental parameters mentioned above. Geant4 simulations were performed using the G4 EmLivermore interaction library for electromagnetic radiation and QGSP_BIC_HP for proton interaction. Binary cascade models were activated for Ion interactions [33; 34]. Monte Carlo algorithms provide a statistical approach for radiation transport within environments and detectors, the uncertainties being lower than 1% for simulations that runs for \(10^{12}\) events number.