The effect of ions dynamics on the breaking of plane electron oscillations
Matematičeskoe modelirovanie, Tome 27 (2015) no. 12, pp. 3-19.

Voir la notice de l'article provenant de la source Math-Net.Ru

The effect of the dynamics of ions on the breaking of planar relativistic electron oscillations is studied by methods of numerical simulation. To simulate the finite difference method the numerical algorithm based on Eulerian variables is constructed and a preliminary analytical study carried out. A new type of breaking long-lived oscillations, different from previously known is presented. Part of the calculations was carried on the supercomputer "Chebyshev" (Lomonosov Moscow State University).
Keywords: numerical simulation, effect of breaking, finite difference method
Mots-clés : plasma oscillations, perturbation method, Eulerian variables.
@article{MM_2015_27_12_a0,
     author = {A. A. Frolov and E. V. Chizhonkov},
     title = {The effect of ions dynamics on the breaking of plane electron oscillations},
     journal = {Matemati\v{c}eskoe modelirovanie},
     pages = {3--19},
     publisher = {mathdoc},
     volume = {27},
     number = {12},
     year = {2015},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MM_2015_27_12_a0/}
}
TY  - JOUR
AU  - A. A. Frolov
AU  - E. V. Chizhonkov
TI  - The effect of ions dynamics on the breaking of plane electron oscillations
JO  - Matematičeskoe modelirovanie
PY  - 2015
SP  - 3
EP  - 19
VL  - 27
IS  - 12
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/MM_2015_27_12_a0/
LA  - ru
ID  - MM_2015_27_12_a0
ER  - 
%0 Journal Article
%A A. A. Frolov
%A E. V. Chizhonkov
%T The effect of ions dynamics on the breaking of plane electron oscillations
%J Matematičeskoe modelirovanie
%D 2015
%P 3-19
%V 27
%N 12
%I mathdoc
%U http://geodesic.mathdoc.fr/item/MM_2015_27_12_a0/
%G ru
%F MM_2015_27_12_a0
A. A. Frolov; E. V. Chizhonkov. The effect of ions dynamics on the breaking of plane electron oscillations. Matematičeskoe modelirovanie, Tome 27 (2015) no. 12, pp. 3-19. http://geodesic.mathdoc.fr/item/MM_2015_27_12_a0/

[1] E. Esarey, C. B. Schroeder, W. P. Leemans, “Physics of laser-driven plasma-based electron accelerators”, Rev. Mod. Physics, 81:3 (2009), 1229–1285 | DOI

[2] L. M. Gorbunov, A. A. Frolov, “Low-frequency transition radiation from a short laser pulse at the plasma boundary”, Sov. Phys. JETP, 102:6 (2006), 894–901 | DOI

[3] Ia. B. Zeldovich, A. D. Myshkis, Elementy matematicheskoi fiziki, Nauka, M., 1973, 352 pp. | MR

[4] L. M. Gorbunov, A. A. Frolov, E. V. Chizhonkov, N. E. Andreev, “Breaking of nonlinear cylindrical plasma oscillations”, Plasma Phys. Reports, 36:4 (2010), 345–356 | DOI | MR | MR

[5] J. M. Dawson, “Nonlinear electron oscillations in a cold plasma”, Phys. Rev., 113:2 (1959), 383–387 | DOI | MR | Zbl

[6] E. V. Chizhonkov, “To the question of large-amplitude electron oscillations in a plasma slab”, Comp. Math. Math. Phys., 51:3 (2011), 423–434 | DOI | MR | Zbl

[7] A. A. Frolov, E. V. Chizhonkov, “O reliativistskom oprokidyvanii elektronnykh kolebanii v plazmennom sloe”, Vychisl. Metody Programm., 15 (2014), 537–548

[8] B. L. Rozhdestvenskii, N. N. Ianenko, Sistemy kvazilineinykh uravnenii i ikh prilozheniia k gazhovoi dinamike, Nauka, M., 1968, 592 pp. | MR

[9] S. V. Bulanov, M. Yamagiva, T. Z. Esirkepov, et al., “Electron bunch acceleration in the wake wave breaking regime”, Plasma Phys. Reports, 32:4 (2006), 263–281 | DOI

[10] A. A. Frolov, E. V. Chizhonkov, “Breaking of wake wave exited by a narrow laser pulse in a low-density plasma”, Plasma Phys. Reports, 37:8 (2011), 663–679 | DOI

[11] E. V. Chizhonkov, “Chislennoe modelirovanie aksialnykh reshenii nekotorykh nelineinykh zadach”, Vychisl. Metody i Programm., 11 (2010), 215–227 | MR | Zbl

[12] A. F. Aleksandrov, L. S. Bogdankevich, A. A. Rukhadze, Osnovy elektrodynamiki plazmy, Vys. shkola, M., 1978, 407 pp.

[13] E. V. Chizhonkov, A. A. Frolov, L. M. Gorbunov, “Modelling of relativistic cylindrical oscillations in plasma”, Rus. J. Numer. Anal. Math. Modelling, 23:5 (2008), 455–467 | MR | Zbl

[14] L. M. Gorbunov, A. A. Frolov, E. V. Chizhonkov, “O modelirovanii nereliativistskikh cilindricheskikh kolebanii v plazme”, Vychisl. Metody Programm., 9:1 (2008), 58–65 | MR

[15] A. V. Popov, E. V. Chizhonkov, “Ob odnoi raznostnoi scheme dlia rascheta plazmennykh aksial-nosimmetrichnykh kolebanii”, Vychisl. Metody i Programm., 13:1 (2012), 5–17

[16] D. A. Anderson, J. C. Tannehill, R. H. Pletcher, Computational Fluid Mechanics and Heat Transfer, Hemisphere, New York, 1984, 599 pp. | MR | MR | Zbl

[17] R. W. Hockney, J. W. Eastwood, Computer simulation using particles, McGraw-Hill Inc., New York, 1981, 523 pp.

[18] S. K. Godunov, V. S. Riabenkii, Raznostnye skhemy. Vvedenie v teoriiu, Nauka, M., 1973, 400 pp.

[19] N. S. Bakhvalov, N. P. Zhidkov, G. M. Kobelkov, Chislennye metody, 6-e izd., BINOM. Laboratoriia znanii, M., 2008, 640 pp.

[20] S. I. Pohozaev, “The general blow-up theory for nonlinear PDE's”, Function Spaces, Differential Operators and Nonlinear Analysis, The Hans Triebel Anniversary Volume, Birkhauser, Bazel, 2003, 141–159 | DOI | MR | Zbl

[21] N. N. Bogoliubov, Iu. A. Mitropolskii, Asimptoticheskie metody v teorii nelineinykh kolebanii, Nauka, M., 1974, 504 pp. | MR

[22] H. B. Dwight, Tables of integrals and other mathematical data, 4 ed., The Macmillan Co., New York, 1961, 336 pp. | MR

[23] S. V. Milyutin, A. A. Frolov, E. V. Chizhonkov, “Prostranstvennoe modelirovanie oprokidyvaniia nelineinykh plazmennykh kolebanii”, Vychisl. Metody i Programm., 14 (2013), 295–305 | Zbl