CERN Accelerating science

Article
Title	Synthesis of Beam Lines with Necessary Properties
Author(s)	Andrianov, Serge
Affiliation	(St. Petersburg State University, St. Petersburg)
Publication	2005
In:	21st IEEE Particle Accelerator Conference, Knoxville, TN, USA, 16 - 20 May 2005, pp.1096
Subject category	Accelerators and Storage Rings
Abstract	In this paper a new approach to the problem of synthesis of beam lines is discussed. Usually this problem can be overcome by the use of numerical simulation and optimal control theory methods. But this results in sufficiently great number of variable parameters and functions. Obviously, that this degrades quality of a modeling procedure. The suggested approach is demonstrated on a problem of a microprobe design problem. Essence of the problem is that necessary to design a high precision focusing system which satisfies some additional conditions. For solution of this problem we use an algebraic treatment based on Lie algebraic methods and computer algebra techniques. Using the symmetry ideology this approach allows rewriting beam properties to enough simple conditions for control parameters and functions. This leads a set of desired solutions and show results in some most suitable form. Moreover, this approach decreases the number of variable parameters.