Geodesic
Mathematical properties of the model of vertical plasma instability in tokamak
Matematičeskoe modelirovanie, Tome 23 (2011) no. 4, pp. 69-82.

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

The model of vertical plasma instability is investigated. Fast MHD, slow resistive and hybrid instabilities are studied. For the case of slow instability the models of linear and nonlinear, passive and active feedbacks are investigated. Several theorems whose interpretations are of physical importance have been proved.
Mots-clés : tokamak
Keywords: vertical plasma instability, linear and nonlinear feedbacks, mathematical theorems, physical interpretation of theorems. 
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     title = {Mathematical properties of the model of vertical plasma instability in tokamak},
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D. Yu. Sychugov; Yu. N. Dnestrovskii; D. P. Kostomarov; V. V. Amelin; N. A. Gasilov. Mathematical properties of the model of vertical plasma instability in tokamak. Matematičeskoe modelirovanie, Tome 23 (2011) no. 4, pp. 69-82. http://geodesic.mathdoc.fr/item/MM_2011_23_4_a4/

[1] Laval G., Pellat R., Soule G., “Hydromagnetic stability of a current-carrying pinch with noncircular cross section”, The Physics of Fluids, 17:4 (1974), 835–845 | DOI

[2] Jardin S. C., Larrabee D. A., “Feedback stabilization of rigid axisymmetric modes in tokamaks”, Nuclear fusion, 22:8 (1982), 1095–1098 | DOI

[3] Andreev V. F., Dnestrovskii Yu. N., Kostomarov D. P., Popov A. M., Sychugov D. Yu., “Vertikalnaya ustoichivost v tokamake s zheleznym serdechnikom”, Voprosy atomnoi nauki i tekhniki. Ser. Termoyadernyi sintez, 1986, no. 3, 33–39

[4] Gerasimov S. N., Popov A. M., Sychugov D. Yu., “Sravnenie matematicheskogo modelirovaniya ravnovesiya i MGD-ustoichivosti plazmy s eksperimentom na ustanovke T-12”, Fizika plazmy, 9:4 (1983), 688–696

[5] Dnestrovskii Yu. N., Kostomarov D. P., Pistunovich V. I., Popov A. M., Sychugov D. Yu., “Stabilizatsiya vertikalnoi neustoichivosti v tokamake s poloidalnym divertorom”, Fizika plazmy, 10:4 (1984), 688–694

[6] Gasilov N. A., Gerasimov S. N., Zotov I. V., Sychugov D. Yu., Modelirovanie eksperimenta po issledovaniyu neustoichivosti plazmy v tokamake s divertorom, preprint IAE-4327, RNTs “Kurchatovskii institut”, M., 1986

[7] Bondarchuk E. N., Dnestrovskij Yu. N., Leonov V. M., Maksimova I. I., Sychugov D. Yu., Tsaun S. V., Voznesensky V. A., “Vertical MHD Stability Of The 15M Tokamak Plasma”, Plasma Devices and Operations, 11:4 (2003), 219–227 | DOI

[8] Sychugov D. Yu., Amelin V. V., Gasilov N. A., Tsaun S. V., “Chislennoe issledovanie vertikalnoi neustoichivosti plazmy v tokamake pri konechnoi provodimosti stabiliziruyuschikh elementov”, Vestnik MGU, ser. 15. Vychislitelnaya matematika i kibernetika, 2004, no. 4, 27–32 | MR | Zbl

[9] Kakurin A. M., Leonov V. M., Notkin G. E., Khvostenko P. P., Tsaun S. V., Bondarchuk E. N., Vasilev V. I., Mineev A. B., Maksimova I. I., Amelin V. V., Gasilov N. A., Sychugov D. Yu., “Osnovnye stsenarii razryada tokamaka T-15M”, Voprosy atomnoi nauki i tekhniki. Seriya Termoyadernyi sintez, 2005, no. 4, 53–75

[10] Mitrishkin Yu. V., Lukash V. E., Khairutdinov R. R., “Sistema robastnogo upravleniya tokom, polozheniem i formoi plazmy v ITER”, Voprosy atomnoi nauki i tekhniki. Seriya Termoyadernyi sintez, 2005, no. 1, 61–81

[11] Sychugov D. Yu., Amelin V. V., Gasilov N. A., “Modul “TOKSTAB” (Modul biblioteki programm “VIRTUALNYI TOKAMAK”)”, Voprosy atomnoi nauki i tekhniki. Seriya Termoyadernyi sintez, 2010, no. 3, 46–49

[12] Ivanov A. A., Khayrutdinov R. R., Medvedev S. Yu., Poshekhonov Yu. Yu., “New adaptive grid plasma evolution code SPIDER”, 32nd EPS Conference on Plasma Phys. (Tarragona, 27 June – 1 July 2005), ECA, 29C, 2005, 5.063

[13] Degtyarev L., Martynov A., Medvedev S., Troyon F., Villard L., Gruber R., “The KINX ideal MHD stability code for axisymmetric plasmas”, Computer Physics Communications, 103 (1997), 10–27 | DOI

[14] Lukash V. E., Khairutdinov R. R., “Modul ‘DINA-EqDsk’ ”, Voprosy atomnoi nauki i tekhniki. Seriya Termoyadernyi sintez, 2009, no. 3, 64–66

[15] Landau L. D., Lifshits E. M., Teoreticheskaya fizika, v 10 tomakh, v. 8, Elektrodinamika sploshnykh sred, Nauka, M., 1982 | MR

[16] Korn G., Korn T., Spravochnik po matematike dlya inzhenerov i nauchnykh rabotnikov, Gl. red. fiziko-matematicheskoi literatury, M., 1970

[17] Emelyanov S. V., Korovin S. K., Fomichev V. V., Fursov A. S., Zadachi i teoremy po teorii lineinoi obratnoi svyazi, Izdatelskii otdel fakulteta VMiK MGU im. M. V. Lomonosova, M., 2004

[18] Emelyanov S. V., Korovin S. K., Novye tipy obratnoi svyazi, Nauka, M., 1997 | MR