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 nonlinear equations in the form of Taylor series. In the paper, we use the coefficients representation in the form of twodimensional 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 twodimensional 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 "readymade" transformations (Legoobjects), which greatly simplify the process of modeling particle dynamics. Examples of solving practical problems are given.


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※ https://doi.org/10.18429/JACoWIPAC2018THPAK134


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