Geoffrey Vandeplas

Higher-order beam tracking models for proton therapy beamlines

Abstract

Numerical simulations have proved to be very useful for the design of charged particle systems. In low-energy charged particle machines, such as proton therapy beamlines, proton beams are propagated through multipolar magnetic elements. An accurate modelling of the beam interaction with such multipolar components magnetic fields is required to allow predictive simulations of the dosimetric properties of the beamlines. This project aims to implement second-order integration methods to track charged particles through hadron therapy beamlines, with a particular focus on capabilities required by proton therapy tracking codes. The tracking formalism implemented is based on the Taylor expansion of the particles output coordinates, in power series of the input coordinates, truncated at the second-order. Based on the work presented in [6], we first derived the differential equations for the coefficients in the Taylor expansion from the equation of motion of charged particles in magnetic fields. These equations were then solved analytically using Sympy, a python library, to find the expression of the terms up to second order. From these symbolic expressions, first and second-order tracking maps were derived for the simple cases of ideal magnets (dipoles, quadrupoles, sextupoles). Fringe field maps were also derived up to the second-order, enabling the modeling of more realistic magnets, with pole face angles and fringe fields. The formalism implemented was added into Manzoni, a python fast-tracking code developed in the "Service de Métrologie Nucléaire" department of ULB. The tracking routines were compared to an already existing implementation, to highlight the benefits of the second-order. Moreover, the implementation was applied to a simplified model of the IBA Proteus One Pencil Beam Scanning (PBS) system and the impacts of second-order terms, including fringe field effects, not only on the beam position but also on the beam sizes, were quantified and discussed in detail.