A statistical model for electron transport and dose calculations

A statistical model for electron transport in homogeneous media is developed which assumes that electrons lose energy continuously between collisions by experiencing only small deflections around a straight path, and change their direction only at large-angle collisions without losing energy. The medium is characterized by its stopping power S(E), which is the energy loss per unit distance traveled by an electron, and by the energy-dependent scattering cross-section σ(E). The electron flux Ψ(x,E,t) due to a burst of electrons at T=0 at the origin; as a function of position, energy and time, and the steady state flux Φ(x,E) due to a time-independent point electron source; as a function of position and energy, are explicitly obtained. In this work, the diffusion equation which Φ(x,E) satisfies is valid at all energies during slowing down, and reduces to the Fermi-Eyges1 equation for pencil-like electron beams. In this sense the proposed stochastic model extends the Fermi-Eyges theory to the later stages of slowing down where electrons diffuse isotropically.