Development of algorithm for tolerances calculation in accelerator systems

Being in a good progress, the particle accelerators start to penetrate deeply into different sectors of human social life. Application of accelerator technology, to address a variety of new tasks, places special demands on the characteristics of the charged particles beam, such as reducing the size of the beam, rigorous requirements for the form of the beam and the calibration of its energy. This paper proposes methods for determining tolerances in the parameters of the systems elements to accelerate and focus the charged particles beams. The offered methods are based on differential calculus, matrix formalism and algebraic techniques Lee, tensor matrix computation. The submitted mathematical apparatus represents the parallelization of computations on the presented methods.