Synchrotron and inverse-Compton emission from blazar jets I: a uniform
  conical jet model
  In the first of a series of papers investigating emission from blazar jets
from radio to high-energy {\gamma}-rays, we revisit the class of models where
the jet has a uniform conical ballistic structure. We argue that by using
simple developments of these models, in the context of new multi-frequency data
extending to gamma-ray energies, valuable insights may be obtained into the
properties that fully realistic models must ultimately have. In this paper we
consider the synchrotron and synchrotron-self-Compton emission from the jet,
modelling the recent simultaneous multi-wavelength observations of BL Lac. This
is the first time these components have been fitted simultaneously for a blazar
using a conical jet model.
  In the model we evolve the electron population dynamically along the jet
taking into account the synchrotron and inverse-Compton losses. The
inverse-Compton emission is calculated using the Klein-Nishina cross section
and a relativistic transformation into the jet frame, and we explicitly show
the seed photon population. We integrate synchrotron opacity along the line of
sight through the jet plasma, taking into account the emission and opacity of
each section of the jet. In agreement with previous studies of radio emission,
we find that a conical jet model which conserves magnetic energy produces the
characteristic blazar flat radio spectrum, however, we do not require any
fine-tuning of the model to achieve this. Of particular note, in our model fit
to BL Lac--which at ~10^37W is a relatively low jet-power source--we find no
requirement for significant re-acceleration within the jet to explain the
observed spectrum.
