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Closed analytical formulas describing the parameters of x rays, generated in Compton backscattering of laser pulse and electron beam, such as total yield and temporal duration of the x-ray pulse are presented. Despite the fact that maximal yield is attainable at the head-on collisions and the analytical expressions for this specific case were derived, for some technological reasons in the Compton sources, the head-on collision is not acceptable. In “laser wire” monitors the laser beam crosses the electron bunch at the right angle. A model comprising the ellipsoidal laser and electron bunches with tri-Gaussian density distribution is considered. For this model, the total yield of x-ray quanta and temporal duration is derived as functions of the (arbitrary) crossing angle and geometric dimensions of both the bunch and the pulse. As is shown, the yield is maximal for the head-on collision. With increase in the collision angle, the yield diminishes with rate determined by dimensions of the bunches. Duration of the x-ray pulse behaves in a similar way; minimal duration is attained near the back-on collisions

Parameters of Compton x-ray beams: Total yield and pulse duration