  Context: An electron-positron beam escaping from the magnetospheric vacuum
gap of an accreting black hole interacts with recombination-line photons from
surrounding gas clouds. Inverse-Compton scattering and subsequent pair
production initiate unsaturated electromagnetic cascades exhibiting a
characteristic spectral energy distribution. Aims: By modelling the
interactions of beam electrons (positrons) with hydrogen and helium
recombination-line photons, we seek to describe the spectral signature of
beam-driven cascades in the broad emission-line region of blazar jets. Methods:
Employing coupled kinetic equations for electrons (positrons) and photons
including an escape term, we numerically obtain their steady-state
distributions, and the escaping photon spectrum. Results: We find that cascade
emission resulting from beam interactions can produce a narrow spectral feature
at TeV energies. Indications of such an intermittent feature, which defies an
explanation in the standard shock-in-jet scenario, have been found at
$\approx\,4\,\sigma$ confidence level at an energy of $\approx$ 3 TeV in the
spectrum of the blazar Mrk 501. Conclusions: The energetic requirements for
explaining the intermittent 3 TeV bump with the beam-interaction model are
plausible: Gap discharges that lead to multi-TeV beam electrons (positrons)
carrying $\approx$ 0.1 % of the Blandford-Znajek luminosity, which interact
with recombination-line photons from gas clouds that reprocess $\approx$ 1 % of
the similar accretion luminosity are required.
