Particle tracking and beam optics analysis on a toroidal gantry for proton therapy

GaToroid is a concept of toroidal gantry for hadron therapy under investigation at CERN It makes use of the toroidal magnetic field between each pair of coils to steer and focus the particle beams down to the patient. This peculiar concept requires detailed studies on particle tracking and beam optics to optimise the winding geometry and explore the properties of the system. The work presented in this manuscript is focused on the features of a GaToroid system for protons, specifically designed to minimise the footprint and weight of the gantry. Firstly, a two-dimensional single particle tracking was developed to optimise the coil geometry and the toroidal magnetic field, aiming to the maximisation of the energy acceptance of the magnet. Particles over the whole spectrum of treatment energy are directed at isocenter within 1 mm of precision. This procedure, restricted to the symmetry plane between each pair of coils, defines different beam orbits, function of the beam energy. Subsequently, a three-dimensional particle tracking was implemented to evaluate the interaction of a beam of finite dimensions with the complete magnetic field map in vacuum. The parameters of the simulated beam at the isocenter are coherent with the clinical requirements. The results of the three-dimensional tracking were then used to calculate the linear transfer matrix associated to each beam orbit. Finally, the option of performing the beam spot scanning at the isocenter by acting on the upstream steering magnet has been investigated, highlighting the potential of the concept, as well as the limitations related to the scanning field dimension and source-to-axis distance. In conclusion, the results described in this paper represent a crucial step toward the understanding of the beam optics properties of a GaToroid gantry.