| Paper | Title | Page |
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| THPAK087 | Software-Computing System for Numerical Modelling of Beam Dynamics in Accelerators | 3435 |
| SUSPF088 | use link to see paper's listing under its alternate paper code | |
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| The spectrum of software packages for the physics of charged particles beams is extremely wide. From most popular and effective systems can be allocated such programs as COSY Infinity, MAD X, MARYLIE, TRANSPORT. Heterogeneous individual formats of input and output data, the lack of a common and user-friendly interface and the narrow specialization of these programs poses a number of challenges for the modern researchers. It significantly reduces the effectiveness and quality of corresponding computational experiments. In this article we present a universal tool for automation and acceleration of computing experiments. The authors consider a method for developing the concept and prototype of a corresponding software package that would combine the advantages of existing (non-commercial) systems. This software will be able to unify the input and output data format for certain programs, visualize the information in various ways, provide reference and training information for "beginners". The results obtained within the developed framework will be a significant contribution both to the development of numerical and symbolical methods for solving evolution nonlinear equations. | ||
| DOI • | reference for this paper ※ https://doi.org/10.18429/JACoW-IPAC2018-THPAK087 | |
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| THPAK088 | Matrix Representation of Lie Transform in TensorFlow | 3438 |
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| In the article, we propose an implementation of the matrix representation of Lie transform using TensorFlow as a computational engine. TensorFlow allows easy description of deep neural networks and provides automatic code execution on both single CPU/GPU and cluster architectures. In this research, we demonstrate the connection of the matrix Lie transform with polynomial neural networks. The architecture of the neural network is described and realized in code. In terms of beam dynamics, the proposed technique provides a tool for both simulation and analysis of experimental results using modern machine learning techniques. As a simulation technique one operates with a nonlinear map up to the necessary order of nonlinearity. On the other hand, one can utilize TensorFlow engine to run map optimization and system identification problems. | ||
| DOI • | reference for this paper ※ https://doi.org/10.18429/JACoW-IPAC2018-THPAK088 | |
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| THPAK090 | Symbolic Presentation of Nonlinear Dynamic Systems in Terms of Lego-Objects | 3441 |
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In this paper we propose a symbolic representation of the solutions of the equations of evolution of dynamical systems in the framework of matrix formalism and Lie algebra for a number of elements of the accelerator (in particular, dipole, quadrupole and octupole) up to the 4th order. The considered solutions are Lego-objects*, which are include into the general scheme of the representation beam dynamics. It allows modeling of schemes of various accelerators and thereby to increasing performance of parametrical optimization. Let us note that the symbolic approach to solving such problems is more preferable than the numerical one, which is widely used. This leads to a reduction in the time and resources spent on solving optimization problems, as well as the ability to create universal Lego objects. The paper considers the verification of the obtained formulas from the experimental data. The corresponding Lego objects are the main components of the special software for both symbolic and numerical dynamics analysis. This software is planned to be used for modeling within the framework of the NICA accelerator project.
*S.N. Andrianov. Dynamic Modeling of Particle Beam Control Systems. Saint Petersburg State University, 2002. |
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| DOI • | reference for this paper ※ https://doi.org/10.18429/JACoW-IPAC2018-THPAK090 | |
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| THPAK134 | Dynamic Equations: The Matrix Representation of Beam Dynamic Equations Instead of Tensor Description | 3554 |
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| 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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