On optimization of charged particle dynamics in electrostatic field

The problem of optimization of charged particle dynamics in an electric potential field is considered. A planar problem, corresponding to the case of axial-symmetric field is investigated. Two-dimensional real linear space is identified with the complex plane. The complex potencial is given in an area in the form of an integral of Cauchy. As a control function is considered a function defined on the boundary of the area which defines an analytic function inside the area. Inside the area, dynamics of charged particle is considered and optimization problem is formulated. Use of complex representation of the field can get an explicit form of the dependence of the field inside the area from the control function on the boundary and obtain necessary optimality conditions for the entered functional. In the work an analytic representation of the variation of the investigated functional at a variation of the boundary conditions is found. On base of obtained analytical expression for the variation of the functional directed optimization methods can be constructed. Practical realization of optimized fields is possible in many ways. Bibliogr. 6.