Woodcock tracking with arbitrary sampling cross section using negative weights

The paper presents a variant of the Woodcock free flight distance sampling algorithm. Instead of a majorant cross section of the whole system, an arbitrarily chosen cross section can be used for sampling the free flight distance. As the sampling cross section is permitted to be smaller than the maximum of the cross sections, the novel algorithm may cause particle weights to become negative. This technique circumvents the major drawback of conventional Woodcock sampling when a localized heavy absorber implies much more frequent path sampling than required thereby rendering the calculation ineffective. Theoretical derivation is shown for heterogeneous medium. A one dimensional analytical and numerical model is presented for basic optimization study of the free sampling parameters and an applied case illustration is shown using a GPU-based radiotherapy Monte Carlo code.