Methods comparison for the emittance computation of a charged particle beam in a lithium-like magnetic lens and comparison of different degrader systems

In proton therapy, the energy degradation process that occurs after the cyclotron accelerator is essential to deliver the appropriate beam energy to the patient. However, degradation of energy increases the beam divergence, leading to particle losses and activation of the surrounding material. To mitigate this divergence, a collimator is placed downstream of the degrader, but it further increases beam losses. To enhance transmission and reduce activation, a magnetic lens can be positioned after the degrader—or even replace it entirely. In this work, we demonstrate the equivalence between two deterministic methods for modeling the emittance evolution of a proton beam in a lithium-like magnetic lens, accounting for both multiple Coulomb scattering within the material and the influence of the magnetic field on charged particle trajectories. Comparisons with numerical simulations performed using the BDSIM software identify the deterministic method and scattering power that best reproduce the simulated results. Using this validated deterministic approach, we investigate improved solutions for minimizing the emittance of the primary beam. These include degraders composed of various materials, stand-alone magnetic lenses, and combined configurations. We show that a typical medical degrader can be optimized by employing a fully beryllium-based design. Further enhancement is achieved by adding a low-field (0.4 T) beryllium lens downstream of the beryllium degrader. For research applications, optimal performance is obtained with a 10 T lithium lens placed upstream of a beryllium degrader or with a lithium lens featuring a variable length at 10 T. • Farley method with ICRU scattering power is compared to BDSIM with success. • A discretization method is validated and provides more flexibility. • Using a magnetic lens in front of a passive degrader reduces the emittance growth. • Using a varying-length lithium lens of 10T decreases further the emittance.