  We extend previous work modeling the Galactic magnetic field in the plane
using synchrotron emission in total and polarised intensity. In this work, we
include a more realistic treatment of the cosmic-ray electrons using the
GALPROP propagation code optimized to match the existing high-energy data. This
addition reduces the degeneracies in our previous analysis and when combined
with an additional observed synchrotron frequency allows us to study the
low-energy end of the cosmic-ray electron spectrum in a way that has not
previously been done. For a pure diffusion propagation, we find a low-energy
injection spectrum slightly harder than generally assumed; for J(E) \propto
E^{\alpha}, we find {\alpha} = -1.34 \pm 0.12, implying a very sharp break with
the spectrum above a few GeV. This then predicts a synchrotron brightness
temperature spectral index, {\beta}, on the Galactic plane that is -2.8 <
{\beta} < -2.74 below a few GHz and -2.98 < {\beta} < -2.91 up to 23 GHz. We
find that models including cosmic-ray re-acceleration processes appear to be
incompatible with the synchrotron data.
