  It has been suggested that relativistic shocks in extragalactic sources may
accelerate the highest energy cosmic rays. The maximum energy to which cosmic
rays can be accelerated depends on the structure of magnetic turbulence near
the shock but recent theoretical advances indicate that relativistic shocks are
probably unable to accelerate particles to energies much larger than a PeV. We
study the hotspots of powerful radiogalaxies, where electrons accelerated at
the termination shock emit synchrotron radiation. The turnover of the
synchrotron spectrum is typically observed between infrared and optical
frequencies, indicating that the maximum energy of non-thermal electrons
accelerated at the shock is < TeV for a canonical magnetic field of ~100 micro
Gauss. Based on theoretical considerations we show that this maximum energy
cannot be constrained by synchrotron losses as usually assumed, unless the jet
density is unreasonably large and most of the jet upstream energy goes to
non-thermal particles. We test this result by considering a sample of hotspots
observed with high spatial resolution at radio, infrared and optical
wavelengths.
