The Joint Accelerator Conferences Website (JACoW) is an international collaboration that publishes the proceedings of accelerator conferences held around the world.
TY - CONF AU - Andrianov, S.N. AU - Chang, Chang, S. AU - Choi, J. AU - Ivanov, A.N. AU - Krushinevskii, E. AU - Kulabukhova, N.V. AU - Sboeva, E. ED - Koscielniak, Shane ED - Satogata, Todd ED - Schaa, Volker RW ED - Thomson, Jana TI - Dynamic Equations: The Matrix Representation of Beam Dynamic Equations Instead of Tensor Description J2 - Proc. of IPAC2018, Vancouver, BC, Canada, April 29-May 4, 2018 C1 - Vancouver, BC, Canada T2 - International Particle Accelerator Conference T3 - 9 LA - english 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. PB - JACoW Publishing CP - Geneva, Switzerland SP - 3554 EP - 3556 KW - controls KW - sextupole KW - operation KW - software KW - octupole DA - 2018/06 PY - 2018 SN - 978-3-95450-184-7 DO - 10.18429/JACoW-IPAC2018-THPAK134 UR - http://jacow.org/ipac2018/papers/thpak134.pdf ER -