  If the gauge fields are amplified from the inflationary vacuum, the quantum
mechanical initial data correspond to travelling waves that turn asymptotically
into standing waves whose phases only depend on the evolution of the gauge
coupling. We point out that these gauge analogs of the Sakharov oscillations
are exchanged by the duality symmetry and ultimately constrain both the
relative scaling of the hypermagnetic power spectra and their final asymptotic
values. Unlike the case of the density contrasts in a relativistic plasma, the
standing oscillations never develop since they are eventually overdamped by the
finite value of the conductivity as soon as the corresponding modes are
comparable with the expansion rates after inflation. We show that the late-time
value of the magnetic field is not determined at radiation dominance (and in
spite of the value of the wavenumber) but it depends on the moment when the
wavelengths (comparable with the Mpc) get of the order of the Hubble radius
before equality. This means that the magnetogenesis requirements are only
relaxed if the post-inflationary expansion rate is slower than radiation but
the opposite is true when the plasma expands faster than radiation and the
corresponding power spectra are further suppressed. After combining the present
findings with the evolution of the gauge coupling we show that these results
are consistent with a magnetogenesis scenario where the gauge coupling is
always perturbative during the inflationary stage while, in the dual case, the
same requirements cannot be satisfied.
