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.
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