based radiation therapy, proton therapy utilizes the electromagnetic properties of charged particles giving rise to a depth-dose distribution that is characterized by a steep dose maximum at the so-called Bragg peak, with almost no dose beyond the peak. The Bragg peak can be positioned to cover the tumour volume in depth by adjustment of its energy, and laterally by use of dipole magnets or collimation devices. This allows to deliver dose distributions with improved conformality to the tumour volume and hence a better sparing of healthy tissue, especially beyond the tumour. At the same time, the steepness of the Bragg peak and its positional dependence on the material compo- sition in the beam path make proton treatment far more sensitive to morphological changes in the patient than photon (or X-ray) therapy. Possible anatomical alterations and differences in patient positioning be- tween irradiations (interfractional uncertainties), as well as organ motion and deformation during irradiation (intrafractional uncertainties, e.g. due to respiration, muscle tension and digestion) lead to considerable un- certainties in the dose delivery. These uncertainties currently translate into large treatment margins around the tumour und thus compromise the dosimetric benefit of proton therapy, which may lead to undesired side effects for the patients (treatment toxicity). One strategy to reduce such side effects is to monitor the patient’s anatomy during dose delivery in real- time and to adapt the beam accordingly. Providing unmatched soft-tissue contrast, subsecond temporal resolution and freedom from ionizing radiation dose, Magnetic Resonance Imaging (MRI) appears to be an ideal candidate for anatomy monitoring during treatment delivery [4, 5]. For photon beam therapy, the integration of both modalities has already been realized, and first-generation hybrid systems have recently found their way into clinical application [6, 7, 8, 9]. Because of the high anatomical sensitivity of proton therapy mentioned above, the integration of MRI into proton therapy (MRiPT) is expected to be even more beneficial than for photon therapy and thus has gained interest in the last years [10]. However, MRiPT has only been studied on a conceptual level thus far, as a number of technical and physical challenges need to be overcome. Complex mutual interactions are expected between the transient electromagnetic fields of the MR scanner and the proton beam line [11]. Furthermore, unlike photons, protons being charged particles are subject to the Lorentz force when traversing the magnetic field of an MRI scanner, causing the beam to be deflected from its otherwise straight path. This is a well-understood and benchmarked phenomenon in vacuum. However, for protons interacting with substances of the human body (e.g. tissue, bone, air, fat, blood), a continuous energy loss will affect the local curvature of the beam as it penetrates the body. So far, only simulation studies exist investigating this effect using particle tracking algorithms in a water phantom or patient geometry. Severe distortions 2