  In order to describe magnetogenesis during inflation in the kinetic coupling
model, we utilize a gradient expansion which is based on the fact that only
long-wavelength (superhorizon) modes undergo amplification. For this purpose,
we introduce a set of functions (bilinear combinations of electromagnetic
fields with an arbitrary number of spatial curls) satisfying an infinite chain
of equations. Apart from the usual mode enhancement due to interaction with the
inflaton, these equations also take into account the fact that the number of
relevant modes constantly grows during inflation. Truncating this chain, we
show that even with a relatively small number of equations, it is possible to
describe the electric and magnetic energy densities with a few percent accuracy
during the whole inflation stage. We arrive at this conclusion for different
types of coupling functions (increasing, decreasing, and nonmonotonic) in the
regime with strong backreaction and its absence.
