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Electron dose calculations using the Method of Moments
Author(s) -
Larsen Edward W.,
Miften Moyed M.,
Fraass Benedick A.,
Bruinvis Iaı̈n A. D.
Publication year - 1997
Publication title -
medical physics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.473
H-Index - 180
eISSN - 2473-4209
pISSN - 0094-2405
DOI - 10.1118/1.597920
Subject(s) - monte carlo method , boltzmann equation , physics , electron , scattering , fluence , computational physics , gaussian , statistical physics , mathematics , quantum mechanics , statistics , ion
The Method of Moments is 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 depth z have one specified energy E(z) . The sole approximation in the present application is that for each electron energy E , 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.