  The spectra of BL Lac objects and Fanaroff-Riley I radio galaxies are
commonly explained by the one-zone leptonic synchrotron self-Compton (SSC)
model. Spectral modeling of correlated multiwavelength data gives the comoving
magnetic field strength, the bulk outflow Lorentz factor and the emission
region size. Assuming the validity of the SSC model, the Hillas condition shows
that only in rare cases can such sources accelerate protons to much above 10^19
eV, so > 10^20 eV ultra-high-energy cosmic rays (UHECRs) are likely to be heavy
ions if powered by this type of radio-loud active galactic nuclei (AGN).
Survival of nuclei is shown to be possible in TeV BL Lacs and misaligned
counterparts with weak photohadronic emissions. Another signature of hadronic
production is intergalactic UHECR-induced cascade emission, which is an
alternative explanation of the TeV spectra of some extreme non-variable blazars
such as 1ES 0229+200 or 1ES 1101-232. We study this kind of cascade signal,
taking into account effects of the structured extragalactic magnetic fields in
which the sources should be embedded. We demonstrate the importance of
cosmic-ray deflections on the gamma-ray flux, and show that required absolute
cosmic-ray luminosities are larger than the average UHECR luminosity inferred
from UHECR observations and can even be comparable to the Eddington luminosity
of supermassive black holes. Future TeV gamma-ray observations using the
Cherenkov Telescope Array and the High Altitude Water Cherenkov detector array
can test for UHECR acceleration by observing >25 TeV photons from relatively
low-redshift sources such as 1ES 0229+200, and > TeV photons from more distant
radio-loud AGN.
