The nature of magnetic fields in the voids of the large-scale structure of the Universe has been a multifaceted open puzzle for decades. On one hand, their origin is not clear with most of the magnetogenesis models using physics beyond the standard model in the early Universe, and on the other hand, their existence and potential role in explaining the spectra of TeV blazars have been intensely debated in the past decade. Here, we propose a mechanism, within classical electrodynamics, that could fill the voids with late-Universe fields and, under certain conditions, dispel the need for primordial fields altogether to explain the void fields. Specifically, we use the dipole component of the galactic fields to generate space-filling magnetic fields in voids with white-noise spectrum and sufficient amplitude to explain the lack of GeV halos around TeV blazars observed by Fermi-LAT. A definitive test for such fields in the voids will be the white-noise spectral shape, which will constrain possible plasma processes in the voids to the ones that allow for the propagation of these dipole fields into the voids.

Cosmic voids are magnetized at the level of at least $10^{-17}$ G on Mpc scales, as implied by blazar observations. We show that an electrically conducting plasma is present in the voids, and that, because of the plasma, \emph{diffusion} into the voids of galactic fields generated by a mean-field dynamo is far too slow to explain the present-day void magnetization. Indeed, we show that even in the presence of turbulence in the voids, dynamo-generated galactic fields diffuse out to a galactocentric radius of only 200-400 kpc. Therefore, it is challenging to meet the required volume filling-factor of the void magnetic field. We conclude that a primordial origin remains the most natural explanation to the space-filling weak fields in voids.