On quasiperiodic beam of interacting particles dynamics modeling

I. D. Rubtsova

Vestnik Sankt-Peterburgskogo universiteta. Prikladnaâ matematika, informatika, processy upravleniâ, no. 1 (2014), pp. 104-119

Résumé

In this paper, the problems of modeling of intense charged particle beam dynamics in accelerating and focusing systems are considered. Longitudinal dynamics of quasiperiodic beam is described on a basis of integrodifferential model, suggested by D. A. Ovsyannikov. Smoothed particle interaction model is used under the assumption of beam spatial periodicity. Integral representation of Coulomb field is obtained. The system of integrodifferential equations describing beam evolution satisfies the conditions of solution existence and uniqueness. The assumptions are fulfilled to formulate trajectory ensemble optimal control problem. The simple method is proposed for testing of particle interaction simulation code. The method is based on Coulomb field approximation by trigonometric polynomial. The results obtained may be effectively used in solving problems of modeling and optimization of charged beam dynamics. Bibliogr. 20.

Détail

Keywords: mathematical modeling, intense charged particle beams, integrodifferential equations, quasiperiodic beam, trigonometric polynomial, code testing.

Bibliographie

[1] Ovsyannikov D. A., Modeling and optimization of charged particle beam dynamics, Izd-vo Leningr. un-ta, Leningrad, 1990, 312 pp. | MR

[2] Ovsyannikov D. A., Egorov N. V., Mathematical modeling of electron and ion beams forming systems, Izd-vo S.-Peterb. un-ta, St. Petersburg, 1998, 276 pp.

[3] Ovsyannikov D. A., Drivotin O. I., Modeling of intense charged particle beams, Izd-vo S.-Peterb. un-ta, St. Petersburg, 2003, 176 pp.

[4] Drivotin O. I., Ovsyannikov D. A., “On self-consistent distributions for charged particle beam in longitudinal magnetic field”, Dokl. RAN, 33:3 (1994), 284–287 | MR

[5] Drivotin O. I., Ovsyannikov D. A., “On new classes of stationary solutions of Vlasov equation for axial-symmetric charged particle beam with constant density”, Jurn. vychisl. matematiki i matematicheskoj phyziki, 29:8 (1989), 1245–1250 | MR

[6] Drivotin O. I., Ovsyannikov D. A., “Self-consistent distributions of charged particles in magnetic field, I”, Vestnik S.-Peterb. un-ta, ser. 10: Prikladnaya matematika, informatika, processy upravleniya, 2004, no. 1–2, 3–15

[7] Drivotin O. I., Ovsyannikov D. A., “Self-consistent distributions of charged particles in magnetic field, II”, Vestnik S.-Peterb. un-ta, ser. 10: Prikladnaya matematika, informatika, processy upravleniya, 2004, no. 1–2, 70–81

[8] Rubtsova I. D., “Modeling of longitudinal dynamics of charged particle beam in a buncher with due account of beam loading of resonators”, Matematicheskije metody modelirovanija i analiza upravliaemyh protsessov, Voprosy mekhaniki i protsessov upravlenija, 12, Izd-vo Leningr. un-ta, Leningrad, 1989, 69–77

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

[10] Ovsyannikov D. A., Edamenko N. S., “Modeling of charged particle beam dynamics”, Vestnik S.-Peterb. un-ta, ser. 10: Prikladnaya matematika, informatika, processy upravleniya, 2013, no. 2, 61–66

[11] 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

[12] Ovsyannikov D. A., Ovsyannikov A. D., Antropov I. V., Kozynchenko V. A., “BDO-RFQ Code and Optimization Models”, Proc. of Intern. Conference on Physics and Control (St. Petersburg, 2005), 282–288

[13] Bondarev B., Durkin A., Ivanov Y., Shumakov I., Vinogradov S., Ovsyannikov A., Ovsyannikov D., “The LIDOS.RFQ.DESIGNER development”, Proc. of the IEEE Particle Accelerator Conference 2001 (Chicago, IL, 2001), 2947–2949

[14] Vladimirova L. V., Ovsyannikov D. A., Rubtsova I. D., Durkin A. P., Shlygin O. Yu., Svistunov Yu. A., “Optimization of particle dynamics in accelerating device with due account of resonators excitation by the beam”, Voprosy atomnoj nauki i tekhniki, ser. Tekhnika fizich. eksperimenta, 1987, no. 4(35), 64–67

[15] Vladimirova L. V., “Optimization of Interacting Particle Beam Dynamics in Linear Accelerator”, Izvestija RAN. Teorija i sistemy upravlenija, 1995, no. 6, 178–183

[16] Zhuk V. V., Minaev S. V., Ovsyannikov D. A., Rubtsova I. D., Skopina M. A., On modeling of Coulomb field of axial-symmetric charged particle beam, Dep. v VINITY 27.01.87, No 638-B87, Izd-vo Leningr. un-ta, Leningrad, 1987

[17] Roshal' A. S., Charged beams modeling, Atomizdat, M., 1979, 224 pp.

[18] Berezin Yu. A., Vshivkov V. A., Method of particles in sparse plasma dynamics, Nauka, Syb. otd., Novosybirsk, 1980, 96 pp. | MR

[19] Potter D., Computational Physics, Translated from English by G. V. Pereverzev, ed. Yu. N. Dnestrovsky, Mir, M., 1975, 392 pp.

[20] Rubtsova I. D., Suddenko E. N., “Investigation of Program and Perturbed Motions of Particles in Linear Accelerator”, Proc. of RUPAC 2012 (St. Petersburg, Russia, 2012), 367–369