Beam dynamics optimization in a linear accelerator

The article is devoted to the problems of optimization of the charged particles' beam dynamics in accelerators. The increasing requirements to the output parameters of the accelerated particles call for the development of new methods and approaches in the field of beam control for charged particles. The present paper considers and sets out particular tasks of optimization of the longitudinal motion of the charged particles in an RFQ accelerator. The particles' dynamics is considered in the accelerating field of an equivalent travelling wave. As was shown earlier, that approach allows one to consider the longitudinal motion and the transverse motion separately. Besides, certain requirements for transverse motion can be considered in the study of the longitudinal motion, which facilitates further optimization of the transverse dynamics. Particular quality functionals are specified and explained in the article. What distinguishes the present work is that it considers non-smooth functionals in combination with smooth functionals, taking the particles distribution density along the beam of trajectories into consideration. The mathematical model of simultaneous optimization of smooth and non-smooth functionals is considered. The variation of the combined functional is obtained as well as the necessary optimality condition. It should be noted that the considered approach might be applied to the control problems in case of partial information about the initial conditions, i. e. the problems of control of the beam of trajectories of various dynamic systems. Refs 15. Figs 4.