We propose a novel mechanism for significantly enhancing the amplitude of
    primordial electromagnetic fields during inflation. Similar to existing
    proposals, our idea is based on parametric resonance effects due to
    conformal-symmetry-breaking coupling of the gauge field and the inflaton. Our
    proposed scenario, however, significantly differs from previously studied
    models, and avoids their shortcomings. We, particularly, construct a viable
    system where the gauge field is exponentially amplified on super-horizon
    scales, therefore evading the no-go theorem formulated on the basis of widely
    encountered drastic back-reaction of the magnetic field energy on the
    inflationary background. We compute the spectrum of the produced magnetic
    fields and demonstrate the compatibility with current observational

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