Root
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Conference Proceedings
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4th International Conference on Physics and Control (PhysCon 2009)
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Mathematical Modeling of Fringe Fields in Beam Line Control Systems
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Usually beam dynamic modeling in beam lines is implemented using a

piecewise approximation for of steering magnet fields. Real magnet

fields have a bell-shaped form, which describes a field distribution

along the electrical axis of a steering element. Influence of fringe

fields in beam lines is taken into account only on tuning stage,

practically on final steps before usage. This paper deals with

methodology, which allows including fringe field effects during an

initial stage of a modeling process. Also wide spectrum of modeling

functions for fringe field distributions is presented. It is known,

that fringe field effects are intrinsic and unremovable effects and

could heavily impact on the beam dynamic and corresponding beam

characteristics. Mathematical and computer models for fringe field

help to estimate their influence and include information of real

magnet field into the designing model. Research is based on the

matrix formalism for Lie algebraic tools. This approach gives large

flexibility, because it could admit the usage of computer algebra

methods and technologies. Computer algebra methods can be easily

paralleling, which gives line benefit with increasing number of

processors (cores).

Besides, this approach can be extended for

nonlinear aberrations without loss of generality.

piecewise approximation for of steering magnet fields. Real magnet

fields have a bell-shaped form, which describes a field distribution

along the electrical axis of a steering element. Influence of fringe

fields in beam lines is taken into account only on tuning stage,

practically on final steps before usage. This paper deals with

methodology, which allows including fringe field effects during an

initial stage of a modeling process. Also wide spectrum of modeling

functions for fringe field distributions is presented. It is known,

that fringe field effects are intrinsic and unremovable effects and

could heavily impact on the beam dynamic and corresponding beam

characteristics. Mathematical and computer models for fringe field

help to estimate their influence and include information of real

magnet field into the designing model. Research is based on the

matrix formalism for Lie algebraic tools. This approach gives large

flexibility, because it could admit the usage of computer algebra

methods and technologies. Computer algebra methods can be easily

paralleling, which gives line benefit with increasing number of

processors (cores).

Besides, this approach can be extended for

nonlinear aberrations without loss of generality.