  We calculate the severe radiative energy losses which occur at the base of
black hole jets using a relativistic fluid jet model, including in-situ
acceleration of non-thermal leptons by magnetic reconnection. Our results
demonstrate that including a self-consistent treatment of radiative energy
losses is necessary to perform accurate MHD simulations of powerful jets and
that jet spectra calculated via post-processing are liable to vastly
overestimate the amount of non-thermal emission. If no more than 95% of the
initial total jet power is radiated away by the plasma travels as it travels
along the length of the jet, we can place a lower bound on the magnetisation of
the jet plasma at the base of the jet. For typical powerful jets, we find that
the plasma at the jet base is required to be highly magnetised, with at least
10,000 times more energy contained in magnetic fields than in non-thermal
leptons. Using a simple power-law model of magnetic reconnection, motivated by
simulations of collisionless reconnection, we determine the allowed range of
the large-scale average reconnection rate along the jet, by restricting the
total radiative energy losses incurred and the distance at which the jet first
comes into equipartition. We calculate analytic expressions for the cumulative
radiative energy losses due to synchrotron and inverse-Compton emission along
jets, and derive analytic formulae for the constraint on the initial
magnetisation.
