Electron dose calculations using the Method of Moments

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Abstract
TheMethod of Momentsis generalized to predict the dose deposited by a prescribed source of electrons in a homogeneous medium. The essence of this method is (i) to determine, directly from the linear Boltzmann equation, the exact mean fluence, mean spatial displacements, and mean‐squared spatial displacements, as functions of energy; and (ii) to represent the fluence and dose distributions accurately using this information. Unlike the Fermi–Eyges theory, the Method of Moments is not limited to small‐angle scattering and small angle of flight, nor does it require that all electrons at any specified depthzhave one specified energyE(z). The sole approximation in the present application is that for each electron energyE, the scalar fluence is represented as a spatial Gaussian, whose moments agree with those of the linear Boltzmann solution. Numerical comparisons with Monte Carlo calculations show that the Method of Moments yields expressions for the depth‐dose curve, radial dose profiles, and fluence that are significantly more accurate than those provided by the Fermi–Eyges theory.