An analysis of equivalent fields for electron beam central-axis dose calculations.

The concepts of the equivalent square or circular field have long been used in dose calculations for photon beams. These concepts allow data measured for square or circular fields to be extended to calculate, for example, the percentage depth doses or output factors of rectangular or irregular fields. It has been pointed out in the past that an electron beam equivalent field dimension varies with depth and, thus, will have questionable utility. As the equivalent square and circle have proven to be useful in photon beam dose calculations, the work described in this paper has sought to analyze conditions under which equivalent fields may be useful for electron beam dose calculations. Equivalent square field dimensions and circular field radii are derived using the Fermi-Eyges theory and are compared to a number of approximate equivalent fields that have been applied to electron dose calculations. Calculations are also compared with measurements presented in the literature. It is shown that the accuracy of an electron dose calculation using these approximate equivalent fields diminishes with a decreasing degree of lateral scatter equilibrium at the central axis and only becomes accurate once equilibrium is established. As the central-axis dose under this latter condition is in any event independent of field shape or size, the equivalent field approach becomes unnecessary. Because of this and other restrictions discussed, it is concluded that the equivalent fields analyzed here should not be used for electron beam dose calculations.