Monte Carlo Electron Dose Calculations Using Discrete Scattering Angles and Discrete Energy Losses

We present a computationally efficient single event Monte Carlo approach for calculating dose from electrons. Analog elastic scattering and inelastic energy-loss differential cross sections for electrons are converted into corresponding discrete cross sections that are constrained to exactly preserve low-order moments of the analog cross sections. While the method has been implemented and tested for the Rutherford model for scattering and energy loss, its dependence solely on cross-section moments makes our approach arbitrarily general. By comparison with analog Monte Carlo calculations, we demonstrate that few discrete angles and energies are required to achieve accurate dose distributions, and the calculations are fast. The method is capable of yielding accurate results across the entire spatial extent of the transport problem, from relatively isotropic scattering to highly forward-peaked scattering. We compare the accuracy of the angular approximation with the GoudsmitSaunderson angular approximation commonly used by condensed history methods and similarly analyze the energy approximation. Finally, we present an investigation of the combined approximations and illustrate the accuracy of this method in the presence of a material interface. The computational efficiency of each method is explicitly compared using timing studies.