distal end of the IDD maximum. The longitudinal Bragg peak retraction Δ R$_{80}$ was defined as the difference between R$_{80}$ with and without magnetic field. The lateral Bragg peak deflection y$_{80}$ was determined from the trajectory obtained with magnetic field as y$_{T}$ ( R$_{80}$ ). Measured and simulated Bragg peak deflection and retraction values and their uncertainties are summa- rized in Supporting Table D.5. Table D.5: Bragg peak displacement caused by the magnetic field in lateral (Δ y$_{80}$ ) and longitudinal (Δ R$_{80}$ ) direction for different proton energies. Positive retraction values indicate that the range with magnetic field is reduced compared to the reference range without field. Measurement (EBT3) Simulation (Geant4) E$_{nom}$ / MeV Δ y$_{80}$ / mm Δ R$_{80}$ / mm Δ y$_{80}$ / mm Δ R$_{80}$ / mm 80 1 . 0 ± 0 . 4 0 . 0 ± 0 . 5 1 . 0 ± 0 . 1 0 . 1 ± 0 . 1 100 1 . 7 ± 0 . 4 − 0 . 5 ± 0 . 5 1 . 7 ± 0 . 1 0 . 0 ± 0 . 1 120 3 . 2 ± 0 . 4 0 . 3 ± 0 . 5 2 . 9 ± 0 . 2 0 . 1 ± 0 . 1 140 4 . 3 ± 0 . 4 − 0 . 2 ± 0 . 5 4 . 6 ± 0 . 2 0 . 2 ± 0 . 2 160 6 . 9 ± 0 . 4 − 0 . 2 ± 0 . 5 6 . 7 ± 0 . 3 0 . 2 ± 0 . 2 180 10 . 1 ± 0 . 5 0 . 4 ± 0 . 5 9 . 3 ± 0 . 3 0 . 3 ± 0 . 2 23 Appendix D. Bragg peak displacement