  I investigate the shape of the electron cosmic ray spectrum in the range up
to ~1000 keV, assuming that the acceleration process at the shock results in a
power law in momentum, and that downstream of the shock the spectrum is
affected by Coulomb interactions with background electrons only. In the
non-relativistic regime one can analytically determine the energy of an
electron starting with a certain energy, and use this result to produce an
electron cosmic ray spectrum, modified by Coulomb losses. An analytic
expression for the electron spectrum is obtained that depends on the parameter
n_e t, which can be estimated from a similar parameter used to characterize the
line spectra of supernova remnants. For the brightest supernova remnants n_e t
> 1e11 cm^-3 s,and most of the electrons accelerated to < 100 keV have lost
their energy. Because of its high radio flux, Cas A is the most likely
candidate for non-thermal bremsstrahlung. Although it has n_e t ~ 2e11 cm^-3 s,
one may expect to pick up non-thermal bremsstrahlung above 100 keV with current
hard X-ray detectors.
