Design of the optical system for the gamma factory proof of principle experiment at the CERN Super Proton Synchrotron

The Gamma Factory proof of principle experiment aims at colliding laser pulses with ultrarelativistic partially stripped ion beams at the CERN Super Proton Synchrotron. Its goals include the first demonstration of fast cooling of ultrarelativistic ion beams and opening up many possibilities for new physics measurements in various domains from atomic physics to particle physics. A high average-power, pulsed laser system delivering approximately 200 kW needs to be implemented for this aim. This is possible thanks to state-of-the-art optical systems that recently demonstrated similar performances in the laboratory environment. Challenges lie in the implementation of this kind of laser system in the harsh environment of hadronic machines including their robust and fully remote operation. The design of this laser system, involving a high quality factor enhancement cavity, is drawn and described in this article. Mitigation procedures are proposed to overcome limitations imposed by the occurrence of degenerate highorder mode at high average power in such optical resonators. We show that the operation at average power above 200 kW is feasible.