Geodesic
Breaking of two-dimensional relativistic electron oscillations under small deviations from axial symmetry
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 57 (2017) no. 11, pp. 1844-1859 
A. A. Frolov; E. V. Chizhonkov. Breaking of two-dimensional relativistic electron oscillations under small deviations from axial symmetry. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 57 (2017) no. 11, pp. 1844-1859. http://geodesic.mathdoc.fr/item/ZVMMF_2017_57_11_a8/
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     author = {A. A. Frolov and E. V. Chizhonkov},
     title = {Breaking of two-dimensional relativistic electron oscillations under small deviations from axial symmetry},
     journal = {\v{Z}urnal vy\v{c}islitelʹnoj matematiki i matemati\v{c}eskoj fiziki},
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     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZVMMF_2017_57_11_a8/}
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Voir la notice de l'article provenant de la source Math-Net.Ru

A numerical asymptotic model for the breaking of two-dimensional plane relativistic electron oscillations under a small deviation from axial symmetry is developed. The asymptotic theory makes use of the construction of time-uniformly applicable solutions to weakly nonlinear equations. A special finite-difference algorithm on staggered grids is used for numerical simulation. The numerical solutions of axially symmetric one-dimensional relativistic problems yield two-sided estimates for the breaking time. Some of the computations were performed on the “Chebyshev” supercomputer (Moscow State University).

[1] Dawson J. M., “Nonlinear electron oscillations in a cold plasma”, Phys. Review, 113:2 (1959), 383 | DOI | MR

[2] Birdsall C. K., Langdon A. B., Plasma physics via computer simulation, McGraw-Hill Inc., New York, 1985, 150–179

[3] Dnestrovskii Yu. N., Kostomarov D. P., Matematicheskoe modelirovanie plazmy, Nauka, M., 1982, 127–221

[4] Hockney R. W., Eastwood J. W., Computer simulation using particles, McGraw-Hill Inc., New York, 1981, 222–281

[5] Zeldovich Ya. B., Myshkis A. D., Elementy matematicheskoi fiziki, Nauka, M., 1973, 86–94 | MR

[6] Gorbunov L. M., Frolov A. A., Chizhonkov E. V., Andreev N. E., “Oprokidyvanie nelineinykh tsilindricheskikh kolebanii plazmy”, Fiz. plazmy, 36:4 (2010), 375

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

[8] Gorbunov L. M., Frolov A. A., Chizhonkov E. V., “O modelirovanii nerelyativistskikh tsilindricheskikh kolebanii v plazme”, Vychisl. metody i programm, 9:1 (2008), 58

[9] Konik A. A., Chizhonkov E. V., “Ob odnoi raznostnoi skheme dlya modelirovaniya kilvaternykh voln v plazme”, Vestn. MGU. Ser. 1. Matem., mekhan., 2016, no. 1, 44

[10] Chizhonkov E. V., Frolov A. A., “Numerical simulation of the breaking effect in nonlinear axially-symmetric plasma oscillations”, Russ. J. Numer. Anal. Math. Modelling, 26:4 (2011), 379 | DOI | MR

[11] Milyutin S. V., Frolov A. A., Chizhonkov E. V., “Prostranstvennoe modelirovanie oprokidyvaniya nelineinykh plazmennykh kolebanii”, Vychisl. metody i programm., 14:2 (2013), 295

[12] Chizhonkov E. V., Frolov A. A., Milyutin S. V., “On overturn of two-dimensional nonlinear plasma oscillations”, Russ. J. Numer. Anal. Math. Modelling, 30:4 (2015), 213 | DOI | MR

[13] Aleksandrov A. F., Bogdankevich L. S., Rukhadze A. A., Osnovy elektrodinamiki plazmy, Vysshaya shkola, M., 1978, 55–60

[14] Ginsburg V. L., Rukhadze A. A., Volny v magnitoaktivnoi plazme, Nauka, M., 1975, 46–51

[15] Silin V. P., Vvedenie v kineticheskuyu teoriyu gazov, Nauka, M., 1971, 119

[16] Silin V. P., Rukhadze A. A., Elektromagnitnye svoistva plazmy i plazmopodobnykh sred, Izd. 2-e ispr., Knizhnyi dom “LIBROKOM”, M., 2012, 104–110

[17] Vatazhin A. B., Lyubimov G. A., Regirer S. A., Magnitogidrodinamicheskie techeniya v kanalakh, Nauka, M., 1970, 587–592

[18] Morozov A. I., Solovev L. S., “Statsionarnye techeniya plazmy v magnitom pole”, Voprosy teorii plazmy, Atomizdat, M., 1974, 3–87

[19] Abdullaev A. Sh., Aliev Yu. M., Frolov A. A., “Generatsiya kvazistaticheskikh magnitnykh polei silnym tsirkulyarno polyarizovannym elektromagnitnym izlucheniem v relyativistskoi magnitoaktivnoi plazme”, Fiz. plazmy, 12:7 (1986), 827

[20] Bogolyubov N. N., Mitropolskii Yu. A., Asimptoticheskie metody v teorii nelineinykh kolebanii, Nauka, M., 1974, 36–49 | MR

[21] Frolov A. A., Chizhonkov E. V., “O relyativistskom oprokidyvanii elektronnykh kolebanii v plazmennom sloe”, Vychisl. metody i programm., 15 (2014), 537

[22] Frolov A. A., Chizhonkov E. V., “Vliyanie dinamiki ionov na oprokidyvanie ploskikh elektronnykh kolebanii”, Matem. modelirovanie, 27:12 (2015), 3 | MR

[23] Polyakov P. A., “K teorii nelineinykh plazmennykh voln”, Vestn. Mosk. Un-ta. Ser. 3. Fiz. Astronomiya, 1996, no. 2, 24