Abstract
The method for construction of analytical expressions for electric and magnetic fields for some set of the distributions of the charge density is described. These expressions are used for symbolic computation of the corresponding electric and magnetic fields generated by the beam during the evolution in accelerators. Here we focus on the use of the matrix form for Lie algebraic methods for calculating the beam dynamics in the presence of self-field of the beam. In particular, the corresponding calculations are based on the predictor-corrector method. The suggested approach allows not only to carry out numerical experiments, but also to provide accurate analytical analysis of the impact of different effects with the use of ready-made modules in accordance with the concept of Virtual Accelerator Laboratory. To simulate the large number of particle distributed resources for computations are used. Pros and cons of using described approach on hybrid systems are discussed. In particular, the investigation of overall performance of the predictor-corrector method is made.
The work is supported by SPbSU 0.37.155.2014 and RFBR 16-07-01113A.
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Acknowledgments
The authors would like to express gratitude to Vladimir Korkhov for valuable help. Scientific research were performed using the equipment of the Research Park of St.Petersburg State University. The work was sponsored by the Russian Foundation for Basic Research under the projects: 16-07-01113 “Virtual supercomputer as a tool for solving complex problems” and by the Saint-Petersburg State University under the project 0.37.155.2014 “Research in the field of designing and implementing effective computational simulation for hydrophisical and hydro-meteorological processes of Baltic Sea (and the open Ocean and offshores of Russia)”.
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Kulabukhova, N., Andrianov, S.N., Bogdanov, A., Degtyarev, A. (2016). Simulation of Space Charge Dynamics in High Intensive Beams on Hybrid Systems. In: Gervasi, O., et al. Computational Science and Its Applications – ICCSA 2016. ICCSA 2016. Lecture Notes in Computer Science(), vol 9786. Springer, Cham. https://doi.org/10.1007/978-3-319-42085-1_22
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