SU‐E‐T‐489: Quantum versus Classical Trajectory Monte Carlo Simulations of Low Energy Electron Transport
Purpose: Widely‐used classical trajectory Monte Carlo simulations of low energy electron transport neglect the quantum nature of electrons; however, at sub‐1 keV energies quantum effects have the potential to become significant. This work compares quantum and classical simulations within a simplified model of electron transport in water. Methods: Electron transport is modeled in water droplets using quantum mechanical (QM) and classical trajectory Monte Carlo (MC) methods. Water droplets are modeled as collections of point scatterers representing water molecules from which electrons may be isotropically scattered. The role of inelastic scattering is investigated by introducing absorption. QM calculations involve numerically solving a system of coupled equations for the electron wavefield incident on each scatterer. A minimum distance between scatterers is introduced to approximate structured water. The average QM water droplet incoherent cross section is compared with the MC cross section; a relative error (RE) on the MC results is computed. Results: RE varies with electron energy, average and minimum distances between scatterers, and scattering amplitude. The mean free path is generally the relevant length scale for estimating RE. The introduction of a minimum distance between scatterers increases RE substantially (factors of 5 to 10), suggesting that the structure of water must be modeled for accurate simulations. Inelastic scattering does not improve agreement between QM and MC simulations: for the same magnitude of elastic scattering, the introduction of inelastic scattering increases RE. Droplet cross sections are sensitive to droplet size and shape; considerable variations in RE are observed with changing droplet size and shape. Conclusions: At sub‐1 keV energies, quantum effects may become non‐negligible for electron transport in condensed media. Electron transport is strongly affected by the structure of the medium. Inelastic scatter does not improve agreement between QM and MC simulations of low energy electron transport in condensed media.
Thomson, R.M, & Kawrakow, I. (2012). SU‐E‐T‐489: Quantum versus Classical Trajectory Monte Carlo Simulations of Low Energy Electron Transport. In Medical Physics (Vol. 39, pp. 3817–3818). doi:10.1118/1.4735578