Production of TeV-class photons via Compton back-scattering on proton beams of a keV high brilliance FEL

Present availability of high brilliance photon beams as those produced by X-ray Free Electron Lasers in combination with intense TeV proton beams like those available at SPS, LHC or in the future at FCC, makes possible to conceive the production of TeV-class photons by Compton back-scattering of keV photons carried by the FEL radiation pulse. We present here the study of spectra and fluxes of the TeV-class photons, which are collimated in the typical 1/γ forward angle with respect to the propagation of the proton beam (γ is the proton beam relativistic factor). Using a room-temperature Linac based X-ray FEL delivering radiation pulses at 100 Hz up to 6 keV photon energy (implying a Linac electron beam energy in the 5-8 GeV range), fluxes of tens photons/s are achievable. It is also shown that a proper control of proton beam emittance and focusing at the interaction point is crucial to assure a reasonable energy spread of the photons emitted within an angle smaller than 1/γ. Moreover, due to the reasonably small proton recoil, the back-scattering is actually in the Thomson regime, therefore the back-scattered photons retain the same polarization of the incident FEL beam (that is typically linear, but can be made circular too) even using unpolarized protons. The life-time of the proton beam circulating in the main ring is not affected at all by the interaction with the FEL beam due to the small number of Compton back-scattering events generated (maximum of 1 per bunch collision).