Результаты исследований: Публикации в книгах, отчётах, сборниках, трудах конференций › статья в сборнике материалов конференции › научная › Рецензирование
Dynamic Equations: The Matrix Representation of Beam Dynamic Equations Instead of Tensor Description. / Andrianov, S.; Ivanov, A.; Kulabukhova, N.; Krushinevskii, E.; Sboeva, E.
Proceedings of the 9th International Particle Accelerator Conference. ред. / Shane Koscielniak; Todd Satogata; Volker RW Schaa; Jana Thomson. Geneva, Switzerland : JACoW, 2018. стр. 3554-3556.Результаты исследований: Публикации в книгах, отчётах, сборниках, трудах конференций › статья в сборнике материалов конференции › научная › Рецензирование
}
TY - GEN
T1 - Dynamic Equations: The Matrix Representation of Beam Dynamic Equations Instead of Tensor Description
AU - Andrianov, S.
AU - Ivanov, A.
AU - Kulabukhova, N.
AU - Krushinevskii, E.
AU - Sboeva, E.
PY - 2018/6
Y1 - 2018/6
N2 - 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.
AB - 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.
KW - controls
KW - sextupole
KW - operation
KW - software
KW - octupole
U2 - 10.18429/JACoW-IPAC2018-THPAK134
DO - 10.18429/JACoW-IPAC2018-THPAK134
M3 - Conference contribution
SN - 978-3-95450-184-7
SP - 3554
EP - 3556
BT - Proceedings of the 9th International Particle Accelerator Conference
A2 - Koscielniak, Shane
A2 - Satogata, Todd
A2 - Schaa, Volker RW
A2 - Thomson, Jana
PB - JACoW
CY - Geneva, Switzerland
T2 - 9th International Particle Accelerator Conference
Y2 - 29 April 2018 through 4 May 2018
ER -
ID: 47569245