IPAC2018 - List of Authors (Choi, J.)

Paper	Title	Page
THPAK134	Dynamic Equations: The Matrix Representation of Beam Dynamic Equations Instead of Tensor Description	3554
	S.N. Andrianov, A.N. Ivanov, N.V. Kulabukhova St. Petersburg State University, St. Petersburg, Russia Chang, S. Chang KAIST, Daejeon, Republic of Korea J. Choi CAPP/IBS, Daejeon, Republic of Korea E. Krushinevskii, E. Sboeva Saint Petersburg State University, Saint Petersburg, Russia
	In this paper we consider mathematical and computer modeling of nonlinear dynamics of particle beams in cyclic accelerators in terms of the matrix representation of the corresponding nonlinear differential equations. The proposed approach is different from the usual presentations of non-linear equations in the form of Taylor series. In the paper, we use the coefficients representation in the form of two-dimensional matrices. The similar approach allows us not only to significantly reduce the time spent on modeling beam dynamics but use symbolic mathematics to calculate the necessary two-dimensional matrices. This method demonstrates the effectiveness when solving problems of dynamics problems and optimization of control systems, and for evaluating the influence of various effects on the dynamics of the beam (including taking into account the spin). Using the tools of symbolic computations not only significantly increases the computational efficiency of the method, but also allows you to create databases of "ready-made" transformations (Lego-objects), which greatly simplify the process of modeling particle dynamics. Examples of solving practical problems are given.
DOI •	reference for this paper ※ https://doi.org/10.18429/JACoW-IPAC2018-THPAK134
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Paper

Title

Page

Dynamic Equations: The Matrix Representation of Beam Dynamic Equations Instead of Tensor Description

3554

S.N. Andrianov, A.N. Ivanov, N.V. Kulabukhova
St. Petersburg State University, St. Petersburg, Russia
Chang, S. Chang
KAIST, Daejeon, Republic of Korea
J. Choi
CAPP/IBS, Daejeon, Republic of Korea
E. Krushinevskii, E. Sboeva
Saint Petersburg State University, Saint Petersburg, Russia

In this paper we consider mathematical and computer modeling of nonlinear dynamics of particle beams in cyclic accelerators in terms of the matrix representation of the corresponding nonlinear differential equations. The proposed approach is different from the usual presentations of non-linear equations in the form of Taylor series. In the paper, we use the coefficients representation in the form of two-dimensional matrices. The similar approach allows us not only to significantly reduce the time spent on modeling beam dynamics but use symbolic mathematics to calculate the necessary two-dimensional matrices. This method demonstrates the effectiveness when solving problems of dynamics problems and optimization of control systems, and for evaluating the influence of various effects on the dynamics of the beam (including taking into account the spin). Using the tools of symbolic computations not only significantly increases the computational efficiency of the method, but also allows you to create databases of "ready-made" transformations (Lego-objects), which greatly simplify the process of modeling particle dynamics. Examples of solving practical problems are given.

DOI •

reference for this paper ※ https://doi.org/10.18429/JACoW-IPAC2018-THPAK134

Export •

reference for this paper using ※ BibTeX, ※ LaTeX, ※ Text/Word, ※ RIS, ※ EndNote (xml)