Modeling and optimization of a multiple-ring double scattering system for proton therapy

This study investigates proton beam scattering systems with the aim of improving beam-shaping efficiency and increasing transmission within the radiation field for low-energy beams under intensity-limited conditions. These improvements are particularly relevant for delivering radiation fields at high dose rates for ocular proton therapy (OPT) and even at ultra-high dose rates for potential FLASH radiotherapy applications. A systematic methodology was developed to design multiple-ring double-scattering systems that maximize transmission under a field-homogeneity constraint while controlling the outgoing kinetic energy after each ring. Although generally applicable, the framework was specifically motivated by clinical and experimental requirements for proton-based ocular therapy using a 70 MeV cyclotron at the Helmholtz-Zentrum Berlin für Materialien und Energie (HZB). A Python-based graphical user interface (GUI) was implemented to integrate a mathematical optimization model for two to four concentric rings that maximizes transmission under homogeneity constraints. The software incorporates energy degradation, range shifting, and the conversion of optimized scattering angles into physical dimensions. The mathematical optimization accurately reproduced the two-ring results reported by Takada (1994) and extended the approach to three- and four-ring configurations. The four-ring system achieved a transmission of 53±2% with a dose homogeneity of ±3%, corresponding to a dose rate of 77Gy/s at 100nA for a 30 mm field size, exceeding the threshold for FLASH conditions. Bragg-peak measurements and Monte Carlo simulations using TOPAS showed a distal penumbra below 1 mm and a water range agreement within 0.1 mm of predictions, supporting the adopted energy degradation methodology. The developed GUI provides a practical tool for designing and refining double-scattering systems, significantly improving transmission compared with single-scattering approaches. The four-ring design increased beam transmission more than tenfold compared with single scattering, making it a promising candidate for high-dose-rate irradiation in small fields.