Discrete optimization problem in beam dynamics

Discrete systems of equations have been often used when considering charged particle dynamics in accelerating and focusing structures. In this paper, a discrete optimization approach is considered for a problem in beam dynamics. The conventional approach for the design of various controlled systems involves the initial calculation of programmed motion (e.g. motion of a synchronous particle) and subsequent examination of perturbed motion with the use of equations for deviations. This approach, however, does not always lead to satisfactory results. Thus, when analyzing perturbed motions significantly dependent on programmed motions, it can happen that the dynamic characteristics of the perturbed motions obtained are not satisfactory from one point of view or another. A mathematical model that allows simultaneous optimization of programmed motion and an ensemble of perturbed motions in discrete systems is suggested.