Proton dose approximation in arbitrary convex geometry

Abstract

An expansion is derived for the solution to the transport equation in two dimensions subject to boundary conditions given for an arbitrary convex region. Questions of high-energy transport are considered along with the properties of the dose response function. The expansion of the solution of the transport equation is presented in terms of a parameter which measures the lateral dispersion of an unidirectional beam. This parameter is usually small and the expansion is expected to converge rapidly. The dominant term in the expansion is related to fluence-to-dose conversion factors in a semiinfinite slab for normal incidence. A convenient parameterization of the conversion factors is provided along with numerical examples.