A general solution to charged particle beam flattening using an optimized dual-scattering-foil technique, with...

This paper describes a dual-scattering-foil technique for flattening of radiotherapeutic charged particle beams. A theory for optimization of shapes and thicknesses of the scattering foils is presented. The result is a universal optimal secondary-scatterer profile, which can be adapted to any charged particle beam by a simple scaling procedure. The calculation of the mean square scattering angle of the beam after passing through the scattering foils is done using the generalized Fermi-Eyges model for charged particle transport. It is shown that the fluence profile in the plane of interest can be made flat to better than 1% inside a predefined beam radius provided the shaped secondary scatterer has the universal radial thickness profile. The thicknesses of the two foils are optimized to minimize the total energy loss. The theory has been tested experimentally in an 180 MeV clinical proton beam. The measured distributions agree well with the calculations.