Table A.1: Uncertainties of the measured lateral deflection Δ y$_{80}$ and range retraction Δ R$_{80}$ of the Bragg peak. Lower and upper limits are given for energy-dependent effects, where lower energies are related to smaller uncertainties. Appendix B. Monte Carlo Simulations Simulations were conducted on our high-performance computing cluster. Data analysis was performed using the Python programming language (Python Software Foundation. Python Language Reference, version 3.4.3, www.python.org). As the proton beam is not mono-energetic, beam energy distributions corresponding to the facility’s nominal beam energies E$_{nom}$ needed to be determined. For this purpose, in-water depth-dose curves were measured for 24 energies between 100 MeV and 215 MeV using a multi-layer ionization chamber with 6 cm radius and an effective depth resolution of 1 mm (Giraffe, IBA Dosimetry, Schwarzenbruck, Germany) [30]. An analytical approximation of the Bragg curve [31] was fitted to the measured data, yielding the proton range R$_{80}$ and its energy spread σ$_{E}$ . Ranges R$_{80}$ were converted to mean initial proton energies E$_{0}$ using tabulated stopping power data [32]. E$_{0}$ and σ$_{E}$ are given in Table B.2 for all studied energies. The obtained energies E$_{0}$ exceeded the nominal energies E$_{nom}$ by 1 MeV to 2 MeV, which can be explained by the fact that the beam line is calibrated to produce certain beam ranges, whereas the nominal energies serve as labels. The measured energy spread σ$_{E}$ ranged between 0 . 8 MeV and 1 . 2 MeV. E$_{0}$ and σ$_{E}$ were used to define the beam for the Monte Carlo simulations. If not stated differently, energies mentioned throughout this work refer to the nominal energies. To acquire a realistic model of the source, 2D beam profiles were measured close to the beam exit window (in a distance of 8 cm) using a the pixelated scintillation detector for seven energies between 100 MeV and 215 MeV. A fit of a two-dimensional Gaussian function to the data yielded a mean lateral spread of σ$_{0}$ yz = (4 . 7 ± 0 . 7)mm with a small trend of decreasing σ$_{0}$ yz with increasing energy and a slightly higher spread in vertical ( z -) direction than in horizontal ( y -) direction. Appendix B.1. Beam model definition 17 Source of uncertainty Δ R$_{80}$ /mm Δ y$_{80}$ /mm Statistical 0.4 0.2 Sytematic 0.3 ... 0.4 0.4 Thereof: LET dependence 0.0 ... 0.2 0.0 ... 0.2 Setup axis alignment 0.3 0.3 Beam achromaticity < 0.01 0.2 Total 0.5 0.4 ... 0.5