Radio, X-ray, and gamma-ray observations provide us with strong evidence of particle acceleration to multi-TeV energies in various astrophysical sources. Diffusive shock acceleration is one of the most successful models explaining the presence of suc
h high-energy particles. We discuss the impact of inverse Compton losses on the shock acceleration of electrons that takes place in radiation dominated environments, i.e. in regions where the radiation energy density exceeds that of the magnetic field. We perform a numerical calculation, including an energy-loss term in the transport equation of accelerated particles. We discuss the implications of this effect on the hard X-ray synchrotron and gamma-ray inverse Compton radiation, produced by shock-accelerated electrons in young supernova remnants in the presence of large radiation fields (e.g. in the Galactic centre). We also discuss possible implications of our results for clusters of galaxies and gamma-ray binaries. We demonstrate that the inverse Compton losses of electrons, in the Klein-Nishina regime, lead to spectra of ultra-relativistic electrons that may significantly differ from classical diffusive shock acceleration solution. The most prominent feature is the appearance of a pile-up in the spectrum around the cut-off energy.
Recently, the MILAGRO collaboration reported on the detection of a diffuse multi-TeV emission from a region of the Galactic disk close to the inner Galaxy. The emission is in excess of what is predicted by conventional models for cosmic ray propagati
on, which are tuned to reproduce the spectrum of cosmic rays observed locally. By assuming that the excess detected by MILAGRO is of hadronic origin and that it is representative for the whole inner Galactic region, we estimate the expected diffuse flux of neutrinos from a region of the Galactic disk with coordinates $-40^{circ} < l < 40^{circ}$. Our estimate has to be considered as the maximal expected neutrino flux compatible with all the available gamma ray data, since any leptonic contribution to the observed gamma-ray emission would lower the neutrino flux. The diffuse flux of neutrinos, if close to the maximum allowed level, may be detected by a km$^3$--scale detector located in the northern hemisphere. A detection would unambiguously reveal the hadronic origin of the diffuse gamma-ray emission.
