### Abstract

Original language | English |
---|---|

Title of host publication | Proceedings of the 9th International Particle Accelerator Conference |

Editors | Shane Koscielniak, Todd Satogata, Volker RW Schaa, Jana Thomson |

Place of Publication | Geneva, Switzerland |

Publisher | JACoW |

Pages | 3554-3556 |

Number of pages | 3 |

ISBN (Print) | 978-3-95450-184-7 |

DOIs | |

Publication status | Published - Jun 2018 |

### Fingerprint

### Cite this

*Proceedings of the 9th International Particle Accelerator Conference*(pp. 3554-3556). Geneva, Switzerland: JACoW. https://doi.org/10.18429/JACoW-IPAC2018-THPAK134

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*Proceedings of the 9th International Particle Accelerator Conference.*JACoW, Geneva, Switzerland, pp. 3554-3556. https://doi.org/10.18429/JACoW-IPAC2018-THPAK134

**Dynamic Equations: The Matrix Representation of Beam Dynamic Equations Instead of Tensor Description.** / Andrianov, S.; Ivanov, A.; Kulabukhova, N.; Krushinevskii, E.; Sboeva, E.

Research output

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

ER -