is clinically acceptable. These results were shown to agree within 0 . 8 mm with Monte Carlo based particle tracking simulations. The obtained range of 1 mm to 10 mm Bragg peak displacement corresponds very well with previous theoretical studies in a homogeneous magnetic field in water [17, 18]. For inhomogeneous media, a magnetic field induced dose increase at medium-air material boundaries in the order of 2 % has been predicted caused by electrons returning to the material boundary after being deflected by Lorentz force in air (electron return effect [17]). The experimental verification thereof is subject of an ongoing study. This study showed for the first time that the magnetic field induced proton dose distortion is both measurable and accurately predictable in a tissue-like beam stopping medium. This validates the models used by Monte Carlo simulations and allows them to be used for accurate dose prediction in future treatment planning studies on MR-integrated proton therapy. Details on the experimental setup and the Monte Carlo model as well as an estimation of sources of uncertainty can be found in the Supplementary Information section. The authors thank Wolfgang Enghardt, Stephan Helmbrecht, J¨ org Pawelke, Elke Beyreuther and Leonard Karsch (OncoRay, Germany) for discussing the experimental setup. We thank Patrick Wohlfahrt (OncoRay, Germany) for providing depth-dose curves of the beam line, Florian Brack (HZDR, Dresden) for providing the magnetic finite element model, and Susanna Guatelli (UOW, Australia), Henrik Schulz, Richard Pausch, Carlchristian Eckert and Alexander Matthes (HZDR, Germany) for support with the Geant4 software and the high performance cluster. We thank Jan Pipek (INFN, Czech Republic) for testing and implementing our bug fix to the next Geant4 release, and Susanna Guatelli (UOW, Australia), Andreas Resch (MedUni Wien, Austria), Brent Huisman (INSA, France) and Loic Grevillot (MedAustron, Austria) for advice on Geant4 physics lists. We thank Michael Knobel (HZDR, Dresden) for performing the phantom density determination, and Norbert M¨ ullner (Vacuumschmelze GmbH, Germany) for providing data on the magnet material composition. We thank Karl Zeil (HZDR, Dresden, Germany) for providing the magnet assembly, Robert Sch¨ onert (HZDR, Dresden, Germany) for manufacturing the phantom and Elke Beyreuther (HZDR, Dresden, Germany) for practical advice on film dosimetry. 8 Ackowledgements Methods