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| Title | Symbolic Presentation of Nonlinear Dynamic Systems in Terms of Lego-Objects | |||||
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| Abstract | In this paper we propose a symbolic representation of the solutions of the equations of evolution of dynamical systems in the framework of matrix formalism and Lie algebra for a number of elements of the accelerator (in particular, dipole, quadrupole and octupole) up to the 4th order. The considered solutions are Lego-objects*, which are include into the general scheme of the representation beam dynamics. It allows modeling of schemes of various accelerators and thereby to increasing performance of parametrical optimization. Let us note that the symbolic approach to solving such problems is more preferable than the numerical one, which is widely used. This leads to a reduction in the time and resources spent on solving optimization problems, as well as the ability to create universal Lego objects. The paper considers the verification of the obtained formulas from the experimental data. The corresponding Lego objects are the main components of the special software for both symbolic and numerical dynamics analysis. This software is planned to be used for modeling within the framework of the NICA accelerator project. | |||||
| Footnotes & References | *S.N. Andrianov. Dynamic Modeling of Particle Beam Control Systems. Saint Petersburg State University, 2002. |
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| Paper | download THPAK090.PDF [0.238 MB / 3 pages] | |||||
| Export | download ※ BibTeX ※ LaTeX ※ Text/Word ※ RIS ※ EndNote | |||||
| Conference | IPAC2018, Vancouver, BC, Canada | |||||
| Series | International Particle Accelerator Conference (9th) | |||||
| Proceedings | Link to full IPAC2018 Proccedings | |||||
| Session | MC5 Poster Session | |||||
| Date | 03-May-18 09:00–12:00 | |||||
| Main Classification | 05 Beam Dynamics and EM Fields | |||||
| Sub Classification | D04 Beam Coupling Impedance - Theory, Simulations, Measurements, Code Developments | |||||
| Keywords | quadrupole, octupole, database, controls, dipole | |||||
| Publisher | JACoW Publishing, Geneva, Switzerland | |||||
| Editors | Shane Koscielniak (TRIUMF, Vancouver, BC, Canada); Todd Satogata (JLab, Newport News, VA, USA); Volker RW Schaa (GSI, Darmstadt, Germany); Jana Thomson (TRIUMF, Vancouver, BC, Canada) | |||||
| ISBN | 978-3-95450-184-7 | |||||
| Published | June 2018 | |||||
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