New formulation of the synthesis problem in electron optics

We describe a new approach to solving the problem of harmonic field synthesis for electron-optical systems. Numerical solutions obtained in practice with the classical approach often lead to operational difficulties, such as numerical instability and vacuum breakdown. Our approach differs from the classical one in that it considers a mixed formulation where one part of the information is responsible for representing objective functionals—Cauchy data, while the other part of the information represents the boundary conditions defined on boundaries of specified geometry. This approach takes into account the a priori structural constraints of the synthesis problem, analytically extending the solution to the subdomain of synthesis as well as finding the tolerances for small perturbations of the objective functional. Numerical algorithms proposed in this work are based on the integral representation of a field by a potential of a single and double layer as well as by a volume potential for charged particle beams. A classification of the basic types of electronic lenses with minimal aberrations is given. Numerical examples of test and practical problems are presented. This approach is implemented in the code “Synthesis-2” of Computer Aided Design system “TOPAZ”.