  We study the pair production of fermions in a time dependent axion background
with and without an electric background. We construct the adiabatic mode
functions which incorporate the gauge field and the axion velocity dependence
of the dispersion relation. The semiclassical approach using this adiabatic
basis shows two types of pair production. One is axion-assisted pair
production: the presence of the axion velocity gives enhancement and
interference effects on the pair production driven by the electric field. The
other is axion-driven pair production: the time variation of the axion velocity
causes the pair production even though the electric field is absent.
