Problems of Conservative Integration in Beam Physics

In this paper an approach to conservative integration methods development is discussed. This problem is very important for beam physics: from beam line synthesis up to long time evolution simulation. This approach is based on a Lie algebra technique. On the first step we find a special form of decom...

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Bibliographic Details
Main Authors: Andrianov, S.N., Abramova, A.S.
Format: Conference Proceeding
Language:English
Subjects:
Algebra
Chaos
Control theory
Differential equations
Particle accelerators
Particle beams
Physics
Stability
Structural beams
Online Access:Request full text
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Summary:In this paper an approach to conservative integration methods development is discussed. This problem is very important for beam physics: from beam line synthesis up to long time evolution simulation. This approach is based on a Lie algebra technique. On the first step we find a special form of decomposition for a Lie map, describing the system under study. On the second step a researcher finds exact solutions for some classes of hamiltonians in symbolic forms. These steps allows forming an integration scheme, which have a desired symplectic property. The additional invariant and symmetry properties can be included using dynamical invariants conception.
ISSN:1944-4680
2152-9582
DOI:10.1109/PAC.2005.1590667