This paper uses a solution to the Fermi electron transport equation for an isotropic point source to characterize the magnetically scanned broad electron beams from the Sagittaire Therac 40 accelerator in the air space above patients. Thick lead collimation is shown to be adequately modeled by an infinitely thin absorbing plate when used to predict penumbra shape. A relationship between broad beam penumbra width and the value of the root-mean-square spatial Gaussian spread sigma (z) of an elementary pencil beam is derived. This relationship is applicable for any rectangular field size. Measurement of the variation in broad beam penumbra width with source-surface distance (SSD) for a 7-MeV beam locates the isotropic source to be coincident with the exit window of the accelerator and indicates that the scattering effect of the monitor chamber may be considered negligibly small. Using this source location accurate predictions of beam profile shape for any clinically used beam energy, SSD, or field size are made in the presence of lead trimmer collimation. Field penumbra beyond the photon collimation system is formed in each lateral direction by two lead blocks whose faces are aligned along a diverging ray emanating from the source. The photon collimator closest to the source restricts the field size causing a variation of both fluence and the mean square angle spread of the electrons across the plane at the level of the lower collimator. This variation is accounted for by introducing an empirical perturbation factor into the mathematical formalism. An interesting feature of this perturbation factor is that it is field size dependent and its effect on penumbra width may be scaled for both beam energy and SSD to accurately predict beam profile shape.