Radial dose profiles for pencil electron beams

The relationship between the Boltzmann and Fermi-Eyges-Yang equations governing electron transport is examined. Radial dose profiles for a pencil beam obtained by numerical solution of the Boltzmann equation in the small angle approximation are compared with both the Gaussian approximation and with Monte Carlo simulations for a carbon medium. For energies ranging from 5 to 20 MeV and penetration depths up to 75% of the range the numerical results are within 10% of the Monte Carlo results for the radial distance encompassing 63% of the energy deposition.