Optimization of Beam Dynamics in the Axially Symmetric Potential Field.
The problem of optimization of charged particle beam dynamics in an axially symmetric electric field is considered. The complex potential is represented with use Cauchy integral of a function defined on the boundary of the region and considered as the control function. Analytical representation for the variation of the optimized functional and the necessary optimality conditions are found. On the basis of the expression for the variation of the functional can be built directed methods of optimization. Various practical implementations of fields obtained in the optimization process are possible.