2008A&A...486..837V

We investigate the shape of the electron cosmic ray spectrum in the range up to ∼1000keV, 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_et, which can be estimated from a similar parameter used to characterize the line spectra of supernova remnants. For the brightest supernova remnants n_et>10¹¹s/cm³, and most of the electrons accelerated to <100keV 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_et ∼2x10¹¹s/cm³, one may expect to pick up non-thermal bremsstrahlung above 100 keV with current hard X-ray detectors.