Modeling proton acceleration and penetration: A Python-based approach for medical physics applications

Existing platforms (GEANT4, FLUKA, and GATE) for proton beam simulation are computationally intensive and difficult to adapt for early stage design. This study presents an open-source Python framework for modeling proton focusing and penetration in laser-plasma acceleration systems, providing a lightweight alternative for medical physics research and education. The framework uses fourth-order Runge–Kutta (RK45) integration and stepwise magnetic tracking to solve Lorentz force trajectories through permanent magnet quadrupole (PMQ) lattices across 70–500 MeV. Lower energies (70–260 MeV) with fixed gradients demonstrated optimal focusing at 200 MeV (7.35 μm diameter). Higher energies (300–500 MeV) with optimized gradients achieved 86% transmission efficiency to target spots of 10–100 μm. Tissue penetration was assessed via Bethe–Bloch analytical modeling and stopping and range of ions in matter/transport of ions in matter Monte Carlo simulation. Bethe–Bloch consistently overestimated range by ∼13% at 300 MeV (53.3 vs 47.09 cm) due to idealized assumptions, though both confirmed Bragg peak behavior. The results validate compact PMQ systems for high-precision beam control and support the development of hospital-based laser-driven proton therapy, offering an accessible tool for resource-limited settings.