Optimization of iterative beam dynamic process

This article is devoted to intense beam dynamics optimization in resonance systems, where particles movement is effected by radio-frequency (RF) fields generated by the beam itself. Klystron or klystron-type buncher are the examples of such devices. Mathematical model of beam longitudinal dynamics is presented by the finite sequence of equations. At every iteration dynamic process is described by the system of integral-differential equations; right-hand part of this system depends on functionals values defined on beam trajectories at previous iteration. The controlled process efficiency is estimated by the criterion defined on trajectory ensemble of final iteration. Mathematical methods of trajectory ensemble control are developed and analytical expression of quality criterion variation is derived. This result makes it possible to obtain objective functional gradient and to use directed optimization methods. The approach suggested has been successfully applied for beam dynamics optimization in klystron-type buncher.