Extremely flat and inverted radio spectra as observed in galactic nuclei and BL Lac sources are still a challenge for fast-particle acceleration models. Continuous acceleration by electric fields in reconnection regions can result in almost-constant particle distributions and therefore in inverted synchrotron spectra independent of the details of the injected spectra. These spectra are calculated from a spatially averaged diffusion transport equation in momentum space that includes systematic momentum gains and losses as well as finite particle-escape lifetimes.
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Birk et al. (2001) studied this question.
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