Lego-technology Approach for Beam Line Design

In this paper we present an approach to study some problems of beam line modeling and optimization. We use a modular principle for all levels of the modeling and optimization procedures. The design code proposed by J.Irwin with colleagues is based on modular presentation only for beam line description. For every module (LEGO-module) they used numerical methods for equation motion integration and additional operations. In our approach we introduce LEGO-objects on all levels of the modeling and optimization processes. The beam line components each have two main sets of LEGO-objects: the first contains all necessary objects for beam line component description and the second all objects which correspond to a transfer map (a beam propagator) as an aggregate of two-dimensional matrices. These matrices are computed in symbolic forms up to some approximation order of the nonlinear aberrations. Similar approach we developed for the space charge forces description too. In this case a set of model distribution functions is used. Some examples of practical application are discussed.