  Accurate antenna beam models are critical for radio observations aiming to
isolate the redshifted 21cm spectral line emission from the Dark Ages and the
Epoch of Reionization and unlock the scientific potential of 21cm cosmology.
Past work has focused on characterizing mean antenna beam models using either
satellite signals or astronomical sources as calibrators, but
antenna-to-antenna variation due to imperfect instrumentation has remained
unexplored. We characterize this variation for the Murchison Widefield Array
(MWA) through laboratory measurements and simulations, finding typical
deviations of order +/- 10-20% near the edges of the main lobe and in the
sidelobes. We consider the ramifications of these results for image- and power
spectrum-based science. In particular, we simulate visibilities measured by a
100m baseline and find that using an otherwise perfect foreground model,
unmodeled beamforming errors severely limit foreground subtraction accuracy
within the region of Fourier space contaminated by foreground emission (the
"wedge"). This region likely contains much of the cosmological signal, and
accessing it will require measurement of per-antenna beam patterns. However,
unmodeled beamforming errors do not contaminate the Fourier space region
expected to be free of foreground contamination (the "EOR window"), showing
that foreground avoidance remains a viable strategy.
