  Key diagnostics of non-thermal plasmas, such as the position of the
synchrotron self-absorption turnover or the Faraday rotation optical depth,
depend crucially on the unobserved low-energy electron spectrum. We investigate
the effect of physically viable assumptions about the low-energy electron
spectrum on the magnetic field strength as inferred from the position of the
peak in the synchrotron spectrum marking the transition from optically thick to
optically thin radiation. To this end the kinetic equations are written down
and stationary solutions are given. In this context the inviability of the
delta function approximation of the synchrotron power spectrum is discussed.
Using two different approaches, we show that the field determination is
independent of the assumptions about the low energy electron spectrum within an
order of magnitude. As an example, we use our result to obtain a small
correction to the limiting brightness temperature.
