Mots-clés : tokamak
@article{TMF_2018_196_1_a10,
author = {A. Yu. Anikin and S. Yu. Dobrokhotov and A. I. Klevin and B. Tirozzi},
title = {Gausian packets and beams with focal points in vector problems of plasma physics},
journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
pages = {135--160},
year = {2018},
volume = {196},
number = {1},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/TMF_2018_196_1_a10/}
}
TY - JOUR AU - A. Yu. Anikin AU - S. Yu. Dobrokhotov AU - A. I. Klevin AU - B. Tirozzi TI - Gausian packets and beams with focal points in vector problems of plasma physics JO - Teoretičeskaâ i matematičeskaâ fizika PY - 2018 SP - 135 EP - 160 VL - 196 IS - 1 UR - http://geodesic.mathdoc.fr/item/TMF_2018_196_1_a10/ LA - ru ID - TMF_2018_196_1_a10 ER -
%0 Journal Article %A A. Yu. Anikin %A S. Yu. Dobrokhotov %A A. I. Klevin %A B. Tirozzi %T Gausian packets and beams with focal points in vector problems of plasma physics %J Teoretičeskaâ i matematičeskaâ fizika %D 2018 %P 135-160 %V 196 %N 1 %U http://geodesic.mathdoc.fr/item/TMF_2018_196_1_a10/ %G ru %F TMF_2018_196_1_a10
A. Yu. Anikin; S. Yu. Dobrokhotov; A. I. Klevin; B. Tirozzi. Gausian packets and beams with focal points in vector problems of plasma physics. Teoretičeskaâ i matematičeskaâ fizika, Tome 196 (2018) no. 1, pp. 135-160. http://geodesic.mathdoc.fr/item/TMF_2018_196_1_a10/
[1] F. F. Chen, Introduction to Plasma Physics and Controlled Fusion, Springer, New York, 2015; J. A. Bittencourt, Fundamentals of Plasma Physics, Springer, New York, 2004 ; J. P. Freidberg, Plasma Physics and Fusion Energy, Cambridge Univ. Press, New York, 2007 | MR
[2] R. A. Gerwin, “Initial value solution of Maxwell's equations in cold plasma”, Amer. J. Phys., 30:10 (1962), 711–715 ; S. Nowak, A. Orefice, “Three-dimensional propagation and absorption of high frequency Gaussian beams in magnetoactive plasmas”, Phys. Plasmas, 1:5 (1994), 1242–1250 ; E. Mazzucato, “Propagation of a Gaussian beam in a nonhomogeneous plasma”, Phys. Fluid B, 1:3 (1989), 1855 ; Erratum, 2:1 (1990), 228 ; J. P. Freidberg, Ideal Magnetohydrodynamics, Cambridge Univ. Press, Cambridge, 2014; G. V. Pereverzev, “Paraxial WKB description of short wavelength eigenmodes in a tokamak”, Phys. Plasmas, 8:8 (2001), 3664–3672 ; Ya. A. Kravtsov, P. B. Erczynski, “Gaussian beams in inhomogeneous media: A review”, Stud. Geophys. Geod., 51:1 (2007), 1–36 ; R. A. Cairns, V. Fuchs, “Calculation of a wave field from ray tracing”, Nucl. Fusion, 50:9 (2010), 095001, 11 pp. | DOI | MR | DOI | DOI | DOI | DOI | DOI | DOI
[3] V. P. Maslov, M. V. Fedoryuk, Kvaziklassicheskoe priblizhenie dlya uravnenii kvantovoi mekhaniki, Nauka, M., 1976 | MR | Zbl
[4] V. M. Babich, V. S. Buldyrev, Asimptoticheskie metody v zadachakh difraktsii korotkikh voln, Nauka, M., 1972 ; В. М. Бабич, В. С. Булдырев, И. А. Молотков, Пространственно-временной лучевой метод. Линейные и нелинейные волны, Изд-во Ленингр. ун-та, Л., 1985 | MR | MR | MR
[5] V. P. Maslov, Kompleksnyi metod VKB v nelineinykh uravneniyakh, Nauka, M., 1977 | MR | MR | Zbl
[6] A. Yu. Anikin, S. Yu. Dobrokhotov, A. I. Klevin, B. Tirotstsi, “Skalyarizatsiya statsionarnykh kvaziklassicheskikh zadach dlya sistem uravnenii i prilozhenie k fizike plazmy”, TMF, 193:3 (2017), 409–433 | DOI
[7] V. M. Babich, M. M. Popov, “Rasprostranenie sosredotochennykh zvukovykh puchkov v trekhmernoi neodnorodnoi srede”, Akust. zhurnal, 27:6 (1981), 828–835 ; М. М. Попов, “Метод суммирования гауссовых пучков в изотропной теории упругости”, Изв. АН СССР. Сер. Физика Земли, 9 (1983), 39–50; J. V. Ralston, “On the construction of quasimodes associated with stable periodic orbits”, Comm. Math. Phys., 51:3 (1976), 219–242 ; Erratum, 67:1 (1979), 91 | MR | DOI | MR
[8] I. A. Malkin, V. I. Manko, Dinamicheskie simmetrii i kogerentnye sostoyaniya kvantovykh sistem, Nauka, M., 1979 | MR
[9] V. G. Bagrov, V. V. Belov, A. Yu. Trifonov, A. A. Yevseyevich, “Quantization of closed orbits in Dirac theory by Maslov's complex germ method”, J. Math. Phys. A: Math. Gen., 27:3 (1994), 1021–1043 ; “Quasi-classical spectral series of the Dirac operators corresponding to quantized two-dimensional Lagrangian tori”, 27:15 (1994), 5273–5306 ; В. Г. Багров, В. В. Белов, И. М. Тернов, “Квазиклассические траекторно-когерентные состояния нерелятивистской частицы в произвольном электромагнитном поле”, ТМФ, 50:3 (1982), 390–396 | DOI | MR | DOI | MR | DOI | MR
[10] V. V. Belov, V. M. Olive, J. L. Volkova, “The Zeeman effect for the ‘anisotropic hydrogen atom’ in the complex WKB approximation. I. Quantization of closed orbits for the Pauli operator with spin-orbit interaction”, J. Phys. A: Math. Gen., 28:20 (1995), 5799–5810 ; “II. Quantization of two-dimensional Lagrangian tori (with focal points) for the Pauli operator with spin-orbit interaction”, 5811–5829 | DOI | MR | DOI
[11] V. V. Belov, S. Yu. Dobrokhotov, “Kvaziklassicheskie asimptotiki Maslova s kompleksnymi fazami. I. Obschii podkhod”, TMF, 92:2 (1992), 215–254 ; В. В. Белов, О. С. Доброхотов, С. Ю. Доброхотов, “Изотропные торы, комплексный росток и индекс Маслова, нормальные формы и квазимоды многомерных спектральных задач”, Матем. заметки, 69:4 (2001), 483–514 ; С. Ю. Доброхотов, А. И. Шафаревич, “Квазиклассическое квантование изотропных многообразий гамильтоновых систем”, Топологические методы в теории гамильтоновых систем, Факториал, М., 1998, 41–114 | DOI | MR | DOI | DOI | MR | Zbl
[12] S. Yu. Dobrokhotov, A. Kardinali, A. I. Klevin, B. Tirotstsi, “Kompleksnyi rostok Maslova i vysokochastotnye gaussovy puchki v kholodnoi plazme v toricheskoi oblasti”, Dokl. RAN, 469:6 (2016), 666–671 | DOI | DOI
[13] V. I. Arnold, Matematicheskie metody klassicheskoi mekhaniki, Nauka, M., 1974 ; R. Abraham, J. E. Marsden, Foundations of Mechanics, Benjamin/Cummings Publ., Reading, MA, 1978 ; A. V. Tsiganov, “The Maupertuis principle and canonical transformations of the extended phase space”, J. Nonlinear Math. Phys., 8:1 (2001), 157–182 ; S. Yu. Dobrokhotov, M. Rouleux, “The semi-classical Maupertuis–Jacobi correspondence for quasi-periodic Hamiltonian flows with applications to linear water waves theory”, Asymptotic. Anal., 74:1–2 (2011), 33–73 ; С. Ю. Доброхотов, М. Руло, “Квазиклассический аналог принципа Мопертюи–Якоби и его приложение к линейной теории волн на воде”, Матем. заметки, 87:3 (2010), 458–463 ; С. Ю. Доброхотов, Д. С. Миненков, М. Руло, “Принцип Мопертюи–Якоби для гамильтонианов вида $f(x,|p|)$ в некоторых двумерных стационарных квазиклассических задачах”, Матем. заметки, 97:1 (2015), 48–57 | MR | MR | DOI | MR | MR | DOI | DOI | MR | Zbl | DOI | DOI | MR | Zbl