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We report a novel method for evaluating the energy spectrum of electrons emitting hard x-rays and gamma-rays in undulators and Compton sources. The method takes into account the quantum nature of recoils undergone by the electrons emitting high energy photons. The method is susceptible to evaluate a spectrum of electrons for the whole range of the emission rates per electron-pass through of the driving force, from much less than one emitted photon on average (Compton sources and short undulators) to many emitted photons (long undulators, relatively low-energy electrons). As shown in the former limiting case, the spectrum of electrons reflects the spectrum of emitted radiation whereas it is close to the Gaussian shape in the latter case. Limitation of coherency for the sources of high-energy electromagnetic radiation caused by recoils from emitted photons is also discussed.

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The International Linear Collider (ILC) is on the table now as a new global energyfrontier accelerator laboratory taking data in the 2030's. The ILC addresses key questions for our current understanding of particle physics. It is based on a proven accelerator technology. Its experiments will challenge the Standard Model of particle physics and will provide a new window to look beyond it. This document brings the story of the ILC up to date, emphasizing its strong physics motivation, its readiness for construction, and the opportunity it presents to the US and the global particle physics community.

The luminosity of Compton x-ray and sources depends on the average current in electron bunches, the energy of the laser pulses, and the geometry of the particle bunch to laser pulse collisions. To obtain high power photon pulses, these can be stacked in a passive optical resonator (Fabry-Perot cavity) especially when a high average flux is required. But, in this case, owing to the presence of the optical cavity mirrors, the electron bunches have to collide at an angle with the laser pulses with a consequent luminosity decrease. In this article a crab-crossing scheme is proposed for Compton sources, based on a laser amplified in a Fabry-Perot resonator, to eliminate the luminosity losses given by the crossing angle, taking into account that in laser-electron collisions only the electron bunches can be tilted at the collision point. We report the analytical study on the crab-crossing scheme for Compton gamma sources. The analytical expression for the total yield of photons generated in Compton sources with the crab-crossing scheme of collision is derived. The optimal collision angle of the bunch was found to be equal to half of the collision angle. At this crabbing angle, the maximal yield of scattered off laser photons is attained thanks to the maximization, in the collision process, of the time spent by the laser pulse in the electron bunch. Estimations for some Compton source projects are presented. Furthermore, some schemes of the optical cavities configuration are analyzed and the luminosity calculated. As illustrated, the four-mirror two-or three-dimensional scheme is the most appropriate for Compton sources.