# Multiple-Collision Free-Electron Laser Compton Backscattering for a High-Yield Gamma-Ray Source
## 1 Introduction  
Backward Compton scattering, which is inelastic scattering between a photon and a relativistic electron, can generate a high-energy photon [1]. In astronomy, backward Compton scattering is recognized as a factor that causes a spectral shift of the cosmic microwave background [2]. In actuality, it has been experimentally demonstrated using coherent synchrotron radiation and transition radiation that backward Compton scattering causes wavelength conversion to a broadband light beam [3, 4]. However, currently, a practical application of backward Compton scattering is to obtain quasi-monochromatic X-ray and gamma-ray beams using an intense laser as the incident light. This laser Compton scattering (LCS) gives the best quasi-monochromatic X-ray and gamma-ray sources which have sufficient intensity and controllable polarization in the energy region over keV [5, 6]. LCS gamma rays using electron beams of storage rings have long been applied to studies in the field of the nuclear physics [7, 8, 9, 10]. Recently, laser performance has been dramatically improved, and studies using electron beams with high-intensity and short-pulse lasers in linear accelerators have been actively promoted [6, 11, 12, 13].  
Free-electron laser (FEL) Compton backscattering, in which a resonator-type FEL generated by a relativistic electron beam is used as the incident photon, has been studied at several accelerator facilities [14, 15, 16, 17, 18, 19]. Because the resonator-type FEL oscillates in an optical cavity comprising high-reflectivity mirrors [20], there is no loss caused by transporting a laser to a relativistic electron beam, and the intracavity power of the resonator-type FEL is high enough to generate intense gamma rays via backward Compton scattering. The FEL-Compton backscattering gamma-ray beam has beenused as a high-yield, quasi-monochromatic, and wavelength-variable gamma-ray source [21]. However, in order to counter the LCS gamma-ray source using an external high-power laser, it is necessary to further increase the yield of the gamma rays. Multiple-collision FEL-Compton backscattering [22], in which a multi-bunch electron beam makes head-on collisions with multi-pulse FELs in an optical cavity, is one of the most effective solutions. By realizing multiple-collision FEL-Compton backscattering with a high-repetition electron beam of an energy recovery linac (ERL), it is possible to obtain a high-yield gamma-ray source far superior to existing quasi-monochromatic gamma-ray sources.  
Although it has been considered a priori that multiple-collision FEL-Compton backscattering gamma rays can be described as the superposition of the individual FEL-Compton backscattering gamma rays generated at each collision point, experimental results have not been reported in detail. It is important for the progress of science to show the evidence. We thus investigated the properties of multiple-collision FEL-Compton backscattering gamma rays using an infrared FEL system in the storage ring NJIJ-IV [23]. In this paper, we describe the expected spatial distribution and spectrum of the multiple-collision FEL-Compton backscattering gamma rays and explain the experimental setup using the infrared FEL system in the NJIJ-IV. Then, the measured spatial distributions and spectra of the multiple-collision FEL-Compton backscattering gamma rays are reported, and it is proved that the multiple-collision FEL-Compton backscattering gamma rays can be described as the superposition of the backward Compton scattering gamma rays generated at each collision point.