Nonlinear Effects and Higher-Order Aberrations on Beam Optics of Energy Selection System for Proton Therapy

The energy selection system (ESS) with achromatic capability is essential for a cyclotron-based proton therapy facility. Its purpose is to match the degraded beam to the downstream beam delivery system. In contrast to beam optics calculations using hard-edge and linear transport, the actual fringe field of the magnet and higher-order aberrations of the particle motion lead to a mismatch between the original design and the real situation. In this study, we perform a 3-D magnet simulation with ANSYS Maxwell to evaluate the field distribution of the ESS. The multipole components are realistically included. The transfer matrices are determined from the particle equations of motion using the fourth-order Runge–Kutta (RK4) method. The beam properties at the exit of the ESS are then calculated by transfer mapping. The results show that the beam spot size of the third-order optics approximately doubles in the
$x$
-plane compared to the hard-edge model. The fringe fields contribute most to the beam spot deformation, while the variation caused by higher-order aberrations accounts for about 4%. Imaged optics are represented to reduce distortion by refitting the magnetic fields using the COZY INFINITY code with the Enge function. The analysis and results provide a more accurate representation of the fringe field and its effect on the beam, which can be used as a reference for field optimization during beam commissioning. Realistic field distributions should be considered when designing lattices to obtain reasonable beam transport predictions.