intense beams

approximation function

quasi-structured grid

least square method

In problems of modeling intense charged particles beams moving in domains with a complex configuration of boundaries, the accuracy of trajectory calculations significantly depends on the accuracy of calculation of electric fields. In this work, algorithms for calculating the strength of electric fields at the calculated points of trajectories on adaptive quasi-structured grids are developed. Special attention is given to calculations near curvilinear boundaries in order to avoid fatal errors that lead to the beam settling on the walls of the simulated device. For this purpose, special approximating functions are proposed, which are constructed at the boundary and near-boundary grid nodes based on the least squares method. Frequent cases are considered when constant values of the potential or its normal derivative are set on boundary segments, for which the developed approach, as shown by the results of numerical experiments, significantly increases the accuracy of calculations.

2024-02-06

Methods and algorithms of computational mathematics and their applications

- V. A. Syrovoy,
*Introduction to the Theory of Intense Beams of Charged Particles*(Energoatomizdat, Moscow, 2004) [in Russian]. - E. Munro, “Numerical Simulation Methods for Electron and Ion Optics, вЂ™вЂ™ Nucl. Instrum. Methods Phys. Res. Section A.
**645**(1), 266-272 (2011).

doi 10.1016/j.nima.2010.11.181 - V. M. Sveshnikov,
*Numerical Modeling of Intense Charged Particle Beams*, Doctoral Thesis in Physics and Mathematics (Inst. Comput. Math. Math. Geophys., Novosibirsk, 2006) [in Russian]. - V. P. Ilyin,
*Numerical Methods for Solving Problems in Electrophysics*(Nauka, Moscow, 1985) [in Russian]. - Comsol.

https://www.comsol.com . Cited January 27, 2024. - ANSYS.

https://www.ansys.com . Cited January 27, 2024. - Opera.

https://www.3ds.com/ru/produkty-i-uslugi/simulia/produkty/opera . Cited January 27, 2024. - V. T. Astrelin, M. S. Vorobyov, A. N. Kozyrev, and V. M. Sveshnikov, “Numerical Simulation of the Operation of a Wide-Aperture Electron Gun with a Grid Plasma Emitter and Beam Output into the Atmosphere,” Zh. Prikl. Mekh. Tekh. Fiz.
**60**(5), 3-12 (2019) [J. Appl. Mech. Tech. Phys.**60**(5), 785-792 (2019)].

doi 10.1134/S0021894419050018 - A. N. Kozyrev and V. M. Sveshnikov, “Mathematical Modeling of Intense Charged Particles Beams in Extended Electron-Optical Systems,” Mat. Model.
**34**(3), 71-84 (2022).

doi 10.20948/mm-2022-03-04 - A. N. Kozyrev and V. M. Sveshnikov, “On the Construction of Two-Dimensional Local-Modified Quasistructured Grids and Solving on Them Two-Dimensional Boundary Value Problem in the Domains with Curvilinear Boundary,” Vestn. Yuzhn. Ural. Gos. Univ. Ser. Vychisl. Mat. Inf.
**6**(2), 5-21 (2017).

doi 10.14529/cmse170201 - R. W. Hamming,
*Numerical Methods for Scientists and Engineers*(McGraw-Hill, New York, 1962; Nauka, Moscow, 1972). - G. I. Marchuk,
*Selected Works*, Vols. 1-3(Ross. Akad. Nauk, Moscow, 2018) [in Russian]. - S. I. Molokovsky and A. D. Sushkov,
*Intensive Electron and Ion Beams*(Energoatomizdat, Moscow, 1991) [in Russian]. - I. V. Aliamovskii,
*Electron Beams and Electron Guns*(Sovetskoe Radio, Moscow, 1966) [in Russian]. - V. M. Sveshnikov, “Calculation of the Intensive Charged Particle Beams with Increased Accuracy,” Proc. SPIE.
**5398**, 34-50 (2004). - D. O. Belyaev, A. N. Kozyrev, and V. M. Sveshnikov, “Program Package ERA-DD for Solving Two-Dimensional Boundary Value Problems on Quasi-Structured Grids,” Vestn. Novosib. Gos. Univ., Ser. Inform. Tekhnol.
**8**(1), 3-11 (2010). - A. N. Kozyrev and V. M. Sveshnikov,
*Software Package for Calculating Intense Beams of Charged Particles on Quasi-Structured Grids*, Certificate of RF Computer Program Registration No. 2 014 618 881. Date of Registration: September 1, 2014.

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