Mathematical Methods of Optimization for Charged Particle Beams.

A nonlinear dynamics problem is considered in the framework of a self-consistent evolution of a charged particle beam distribution and a self-generated electric field. A concept from optimal control theory is employed for studying properties of the Vlasov-Poisson equation (VPE). It makes it possible to reduce the focusing and acceleration problem to an optimal control problem. We focus on a case when a nonlinear ordinary differential equation associated with VPE does not meet an integrability condition. In this paper it is shown that, in this case, the density distribution function over a phase space can be estimated using L-moment technique. [ABSTRACT FROM AUTHOR]