Geodesic
Monte Carlo methods in beam dynamics optimization problem
Vestnik Sankt-Peterburgskogo universiteta. Prikladnaâ matematika, informatika, processy upravleniâ, no. 1 (2014), pp. 31-39 Cet article a éte moissonné depuis la source Math-Net.Ru

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In this paper, the problems of charged beams dynamics optimization are considered, when formulated to be trajectory ensemble control problems for specific dynamical systems; quality criteria are presented to be the functionals defined on beam trajectories. The problem under investigation is numerical calculation of special formed integral criteria values by Monte Carlo method. Simple computational algorithm is developed and the formula for integral criterion approximation is obtained. The problem of optimization of longitudinal beam dynamics in waveguide linear accelerator is discussed as an example. Integral quality criteria are suggested, multicriteria optimization is carried out. In the course of optimization criteria values calculation is carried out on the basis of Monte Carlo method. The results presented demonstrate beam quality increment. Bibliogr. 13. Il. 1.
Keywords: charged particle beam, beam dynamics optimization, integral functionals, Monte Carlo method, linear accelerator, multicriteria optimization. 
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L. V. Vladimirova. Monte Carlo methods in beam dynamics optimization problem. Vestnik Sankt-Peterburgskogo universiteta. Prikladnaâ matematika, informatika, processy upravleniâ, no. 1 (2014), pp. 31-39. http://geodesic.mathdoc.fr/item/VSPUI_2014_1_a3/

[1] Ovsyannikov D. A., Mathematical methods of beams control, Izd-vo Leningradskogo Universiteta, L., 1980, 276 pp. | MR

[2] Ovsyannikov D. A., Modeling and optimization of charged particle beam dynamics, Izd-vo Leningradskogo Universiteta, L., 1990, 311 pp. | MR

[3] Ermakov S. M., Monte Carlo Methods and Related Problems, Science, M., 1975, 472 pp. | MR | Zbl

[4] Feller W., An introduction to probability theory and its applications, in 2 vol. Per. s angl. R. L. Dobrushina, v. 1, ed. B. B. Dinkin, Mir, M, 1984, 528 pp. | MR

[5] Vladimirova L. V., Ovsyannikov D. A., Rubtsova I. D. e. a., “Optimization of particle dynamics in accelerating device with due account of resonators excitation by the beam”, Voprosy atomnoy nauki i tekhniki. Ser. Physical Experiment Technology, 1987, no. 4(35), 64–67

[6] Vladimirova L. V., “Optimization of Interacting Particle Beam Dynamics in Linear Accelerator”, Izv. RAN. Teoriya i sisitemy upravleniya, 1995, no. 6, 178–183

[7] Olemskoy I. V., Rubtsova I. D., “Modeling and Optimization of Beam Dynamics in Resonance Bunching and Decelerating Systems”, Proc. of the First Intern. Workshop: Beam Dynamics Optimization (St. Peterburg, 1995), 143–153

[8] Ovsyannikov D. A., Ovsyannikov A. D., Vorogushin M. F., Svistunov Yu. A., Durkin A. P., “Beam Dynamics Optimization: Models, Methods and Applications”, Nuclear Instruments and Methods in Physics Research. Section A: Accelerators, Spectrometers, Detectors and Associated Equipment, 558:1 (2006), 11–19 | DOI

[9] Sobol I. M., Statnikov R. B., Optimal Parameters Choice in Multicriteria Problems, Nauka, M., 1981, 112 pp. | MR

[10] Podinovskiy V. V., Nogin V. D., Pareto-Optimal Decisions of Multicriteria Problems, Nauka, M., 1982, 256 pp. | MR

[11] Gubanov V. A., Zakharov V. V., Kovalenko A. N., Introduction to System Analysis, Izd-vo Leningr. un-ta, L., 1988, 227 pp. | MR

[12] Vladimirova L. V., “On Application of Multicriterial Optimization in Partical Beam Control Problem”, Proc. of the 11th Intern. IFAC Workshop: Control Applications of Optimization (July 3–6, 2000, St. Petersburg, Russia), v. 1, ed. V. Zakharov, Pergamon Press, Oxford, UK, 2001, 363–367

[13] Vladimirova L. V., Multicriteria optimization in applied problems, Educational manual (for students and post-graduates of physical and mathematical specialities), Izd-vo S.-Peterb. un-ta, St. Petersburg, 2002, 24 pp.