Geodesic
Investigation of numerical methods for solving the Vlasov equation by its exact solutions
Vestnik Sankt-Peterburgskogo universiteta. Prikladnaâ matematika, informatika, processy upravleniâ, no. 4 (2015), pp. 4-12 Cet article a éte moissonné depuis la source Math-Net.Ru

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Numerical methods for solving the Vlasov equation for a charged particle beam based on the method of macroparticles are considered. For solving of the boundary problem for the self field of a beam, an adaptive grid method is applied. This method gives a possibility to increase accuracy of computations. To estimate the accuracy of a numerical solution, known solutions of the Vlasov equation are used. Such approach enables us to determine optimal relations between numerical method parameters to achieve the most efficiency of the algorithm. Refs 15. Figs 3. Tables 2.
Keywords: the Vlasov equation, charged particle beam, self-consistent distributions, the method of macroparticles, adaptive grid methods.
Mots-clés : the Vlasov–Poisson system 
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O. I. Drivotin; N. V. Ovsyannikov. Investigation of numerical methods for solving the Vlasov equation by its exact solutions. Vestnik Sankt-Peterburgskogo universiteta. Prikladnaâ matematika, informatika, processy upravleniâ, no. 4 (2015), pp. 4-12. http://geodesic.mathdoc.fr/item/VSPUI_2015_4_a0/

[1] Hockney R. C., Eastwood J. W., Computer simulation using particles, McGraw Hill, New York, 1981, 540 pp.

[2] Roshal A. C., Modeling of the bunohes, Atomizdat Publ., M., 1979, 224 pp. (In Russian)

[3] Drivotin O. I., Ovsyannikov D. A., “On determination of stationary solutions of the Vlasov equation for an axially-symmetric charged particles beam in longitudinal magnetic field”, Computational mathematics and Mathematical Physics Journal, 27:3 (1987), 416–427 (In Russian)

[4] Drivotin O. I., Ovsyannikov D. A., “On new classes of stationary solutions of the Vlasov equation for an axially-symmetric charged particles beam with uniform density”, Computational mathematics and Mathematical Physics Journal, 29:8 (1989), 1245–1250 (In Russian) | MR

[5] Drivotin O. I., Ovsyannikov D. A., “On self-consistent distributions for a charged particle beam in a longitudinal magnetic field”, Proceedings of the RAN, 33:3 (1994), 284–287 (In Russian)

[6] Ovsyannikov D. A., Drivotin O. I., Modeling of high-current charged particle beam, St. Petersburg State University Press, St. Petersburg, 2003, 176 pp. (In Russian)

[7] Drivotin O. I., Ovsyannikov D. A., “Self-consistent distributions of charged particles in longitudinal magnetic field, I”, Vestnik of St. Petersburg State University. Series 10. Applied mathematics. Computer sciences. Control processes, 2004, no. 1–2, 3–15 (In Russian) | MR

[8] Drivotin O. I., Ovsyannikov D. A., “Self-consistent distributions of charged particles in longitudinal magnetic field, II”, Vestnik of St. Petersburg State University. Series 10. Applied mathematics. Computer sciences. Control processes, 2004, no. 1–2, 70–81 (In Russian)

[9] Drivotin O. I., Ovsyannikov D. A., “Modelling of self-consistent distributions for longitudinally non-uniform beam”, Nucl. Instr. Meth. Phys. Res., 558:1 (2006), 112–118 | DOI

[10] Drivotin O. I., Ovsyannikov D. A., “Self-consistent distributions for charged particle beam in magnetic field”, Intern. Journal of Modern Phys. A, 24:5 (2009), 816–842 | DOI | Zbl

[11] Drivotin O. I., Ovsyannikov D. A., Methods of analysis of self-consistent distributions for a charged particle beam, VVM Publ., St. Petersburg, 2013, 116 pp. (In Russian)

[12] Drivotin O. I., Ovsyannikov D. A., “Solutions of the Vlasov equation for a charged particle beam in magnetic field”, Izv. of Irkutsk. State University. Series Mathematics, 6:4 (2013), 2–22 (In Russian) | MR

[13] Drivotin O. I., “Covariant formulation of the Vlasov equation”, Proc. Intern. Particle Accelerators Conf. IPAC'2011 (San-Sebastian, Spain, 2011), 2277–2279 (data obrascheniya: 15.07.2015) http://accelconf.web.cern.ch/accelconf/IPAC2011/papers/wepc114.pdf

[14] Drivotin O. I., “Degenerate Solution of the Vlasov equation”, Proc. RuPAC'2012 (St. Petersburg, 2012), 376–378 (data obrascheniya: 15.07.2015) http://accelconf.web.cern.ch/accelconf/rupac2012/papers/tuppb028.pdf

[15] Ovsyannikov N. V., “Adaptive method for solving boundary value problems for the Poisson equation with rapidly changing potential”, Vestnik of St. Petersburg State University. Series 10. Applied mathematics. Computer sciences. Control processes, 2015, no. 1, 64–75 (In Russian)