  Radio interferometer arrays such as HERA consist of many close-packed dishes
arranged in a regular pattern, giving rise to a large number of `redundant'
baselines with the same length and orientation. Since identical baselines
should see an identical sky signal, this provides a way of finding a relative
gain/bandpass calibration without needing an explicit sky model. In reality,
there are many reasons why baselines will not be exactly identical, giving rise
to a host of effects that spoil the redundancy of the array and induce spurious
structure in the calibration solutions if not accounted for. In this paper, we
seek to build an understanding of how differences in the primary beam response
between antennas affect redundantly-calibrated interferometric visibilities and
their resulting frequency (delay-space) power spectra. We use simulations to
study several generic types of primary beam variation, including differences in
the width of the main lobe, the angular and frequency structure of the
sidelobes, and the beam ellipticity and orientation. For all of these types, we
find that additional temporal structure is induced in the gain solutions,
particularly when bright point sources pass through the beam. In comparison,
only a low level of additional spectral structure is induced. The temporal
structure modulates the cosmological 21cm power spectrum, but only at the level
of a few percent in our simulations. We also investigate the possibility of
signal loss due to decoherence effects when non-redundant visibilities are
averaged together, finding that the decoherence is worst when bright point
sources pass through the beam, and that its magnitude varies significantly
between baseline groups and types of primary beam variation. Redundant
calibration absorbs some of the decoherence effect however, reducing its impact
compared to if the visibilities were perfectly calibrated.
