A Modular Approach for Beam Lines Design
We discuss advantages of numerical simulation based on symbolic presentations of beam line dynamical models. In some previous papers, some of these features were discussed. In this paper, we demonstrate how the symbolic presentation of necessary information can provide an in-depth study of different features of complex systems. For this purpose, we suggest a modular principle for all levels of the modeling and optimization procedures. This principle is based on so-called LEGO objects, which have both symbolic and numerical representation. For beam line design, it is necessary to support three types of similar objects. The first of them contains all necessary objects for beam line components description, the second contains all objects which correspond to particle beam models, and the third contains all objects corresponding to a transfer map (“a beam propagator”). In the suggested approach, the beam propagator is presented as a set of two-dimensional matrices describing different kinds of beam or beam line properties up to some approximation order. These matrices can be computed both in symbolic and numerical forms up to the necessary approximation order of the nonlinear effects. An example of practical application is demonstrated.
KeywordsSymbolic algebra LEGO object Lie algebraic methods beam physics
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