Table B.4: Uncertainties of the predicted 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. Almost none of the individual uncertainty contributions exceeded the resolution of the dose scoring grid (0 . 1 mm). The only exception to this is the uncertainty caused by the magnetic field map, with an uncertainty of 0 . 2 mm for the Bragg peak deflection at 180 MeV. With a relative uncertainty of 2 %, the magnetic field map is the largest factor of uncertainty to this study. The fact that it causes an uncertainty of approximately 2 % in the Bragg peak deflection is consistent with the proportionality of the two as found in a previous study [13]. Absolute uncertainties tend to increase with increasing energy, whereas relative uncertainties tend to decrease. Note that, as the systematic uncertainties were gained in analogous simulations as the main simulations, they are themselves subject to a statistical uncertainty of up to 0 . 1 mm. Two-dimensional dose distributions D ( x, y ) were obtained from the film plane. From these, the lateral ( y -) deflection and longitudinal ( x -) retraction of the Bragg peak due to the magnetic field were extracted as follows. For each depth x , a univariate Gaussian function was fitted to the lateral beam profile and the maximum position y$_{T}$ was extracted. This yielded a function for the lateral maximum dependent on depth, the beam trajectory y$_{T}$ ( x ). To mimic a depth-dose curve measured by an ionization chamber of 8 cm diameter, for each depth the predicted dose was integrated radially around y$_{T}$ with an integration radius of r = 4 cm. This resulted in a function for the integrated lateral dose dependent on depth, the integral depth-dose curve with r ′ and φ the polar coordinates. Both y$_{T}$ ( x ) and IDD ( x ) were smoothed to reduce statistical noise using a univariate spline fit. The range R$_{80}$ was calculated from IDD ( x ) as the depth of the beam at the 80 % IDD ( x ) = ∫ 2 π 0 ∫ r 0 D ( r $^{′}$, φ ) r $^{′}$dr$^{′}$dφ = π$^{∫}$ r − r D ( x, y ) | y − y$_{T}$ ( x ) | dy 22 Appendix C. Depth dose and trajectory reconstruction Source of uncertainty Δ R$_{80}$ /mm y$_{80}$ /mm Systematic 0.1 ... 0.2 0.1 ... 0.3 Thereof: Beam energy 0.1 0.0 ... 0.1 Phantom density 0.0 0.1 Magnetic field 0.0 ... 0.1 0.0 ... 0.2 Physics modelling 0.0 ... 0.1 0.0 ... 0.1 Statistical 0.0 ... 0.1 0.0 ... 0.1 Total 0.1 ... 0.2 0.1 ... 0.3