| Title |
Control of Calculations in the Beam Dynamics using Approximate Invariants |
| Authors |
- S.N. Andrianov
St. Petersburg State University, St. Petersburg, Russia
- D. Zyuzinpresenter
FZJ, Jülich, Germany
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| Abstract |
One of the important problems in the theory of dynamical systems is to find corresponding (invariants). In this article we are discussing some problems of computing of invariant functions (invariants) for dynamical systems. These invariants can be used for describing of particle beams systems. The suggested method is constructive and based on the matrix formalism for Lie algebraic tools. We discuss two types of invariants: kinematic and dynamic. All calculations can be realized in symbolic forms, in particular, kinematic invariants are based on the theory of representations of Lie algebras (in particular, using the Casimir’s operators). For the case of nonlinear kinematic invariants we propose a recursive scheme, which can be implemented in symbolic forms using instruments of computer algebra (for example, such packages as Maple or Mathematica). The corresponding expressions for invariants can be used to control the correctness of computational experiments, first of all for long time beam dynamics.
|
| Paper |
download THPRO071.PDF [0.240 MB / 3 pages] |
| Export |
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| Conference |
IPAC2014, Dresden, Germany |
| Series |
International Particle Accelerator Conference (5th) |
| Proceedings |
Link to full IPAC2014 Proccedings |
| Session |
Poster Session, Ronaldo Area |
| Date |
19-Jun-14 16:00–18:00 |
| Main Classification |
05 Beam Dynamics and Electromagnetic Fields |
| Sub Classification |
D02 Non-linear Dynamics - Resonances, Tracking, Higher Order |
| Keywords |
controls, quadrupole, experiment, emittance, database |
| Publisher |
JACoW Publishing, Geneva, Switzerland |
| Editors |
Christine Petit-Jean-Genaz (CERN, Geneva, Switzerland); Gianluigi Arduini (CERN, Geneva, Switzerland); Peter Michel (HZDR, Dresden, Germany); Volker RW Schaa (GSI, Darmstadt, Germany) |
| ISBN |
978-3-95450-132-8 |
| Published |
July 2014 |
| Copyright |
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