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Methods for MHD plasma equilibria mathematical modelling
Matematičeskoe modelirovanie, Tome 20 (2008) no. 5, pp. 3-34 Cet article a éte moissonné depuis la source Math-Net.Ru

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The paper gives an overview of the state of the art of the MHD plasma equilibrium modelling. The statements of the problems, its mathematical properties and numerical algorithms are considered. 
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D. P. Kostomarov; S. Yu. Medvedev; D. Yu. Sychugov. Methods for MHD plasma equilibria mathematical modelling. Matematičeskoe modelirovanie, Tome 20 (2008) no. 5, pp. 3-34. http://geodesic.mathdoc.fr/item/MM_2008_20_5_a0/

[1] V. D. Shafranov, “O ravnovesnykh magnitogidrodinamicheskikh konfiguratsiyakh”, ZhETF, 33:3 (1957), 710–722 | Zbl

[2] V. D. Shafranov, “Ravnovesie plazmy v magnitnom pole”, Voprosy teorii plazmy, 2, Gosatomizdat, M., 1963, 92–131

[3] L. E. Zakharov, V. D. Shafranov, “Ravnovesie plazmy s tokom v toroidalnykh sistemakh”, Voprosy teorii plazmy, 11, Energoizdat, M., 1982, 118 | MR

[4] Yu. N. Dnestrovskii, D. P. Kostomarov, Matematicheskoe modelirovanie plazmy, Izdatelskaya firma “Fiziko-matematicheskaya literatura”, Nauka, M., 1993, 125–147

[5] I. B. Bernstein, E. A. Frieman, M. D. Kruskal, R. M. Kulsrud, Proc. Roy. Soc. A, 244 (1958), 17 | DOI | MR | Zbl

[6] B. B. Kadomtsev, “Gidromagnitnaya ustoichivost plazmy”, Voprosy teorii plazmy, 2, Gosatomizdat, M., 1963, 132

[7] M. D. Kruskal, R. M. Kulsrud, Physics of Fluids, 1 (1958), 265 | DOI | MR | Zbl

[8] L. M. Kovrizhnykh, S. V. Schepetov, “Opisanie plazmy v stellaratore s pomoschyu usrednennykh MGD uravnenii”, Fizika plazmy, 6 (1980), 976

[9] Todoroki J., “Averaging method for stadying magnetohydrodynamic equilibrium and stability of toroidal helical systems”, Journal of Physical Society of Japan, 56 (1987), 128–138 | DOI

[10] D. Yu. Sychugov, S. V. Schepetov, “Ravnovesnye plazmennye konfiguratsii s magnitnymi ostrovami pri bolshikh $\beta$”, Fizika plazmy, 14 (1988), 663–667

[11] A. B. Kuznetsov, D. Yu. Sychugov, S. V. Schepetov, “Razrushenie vneshnikh magnitnykh poverkhnostei v stellaratorakh iz-za effektov konechnogo davleniya”, Voprosy atomnoi nauki i tekhniki, ser. Termoyadernyi sintez, 1993, no. 1–2, 65–70

[12] A. B. Kuznetsov, D. Yu. Sychugov, S. V. Shchepttov, “Finite pressure induced destruction of the plasma boundary in stellarators”, Nuclear Fusion, 35:2 (1995), 183–193 | DOI

[13] J. M. Greene, J. L. Johnson, “Determination of hydromagnetic equilibria”, Physics of Fluids, 4 (1961), 875–890 | DOI | MR | Zbl

[14] H. R. Strauss, “Stellarator equations of motion”, Plasma Physics, 22 (1980), 733–745 | DOI

[15] H. R. Strauss, D. A. Monticello, “Limiting beta of stellarator with no net current”, Physics of Fluids, 24 (1982), 1148–1155 | DOI

[16] L. M. Kovrizhnykh, S. V. Shchepetov, “MHD equilibrium and stability of a stellarator plasma”, Nuclear Fusion, 23 (1983), 859–867

[17] V. D. Pustovitov, “Plasma equilibrium equation for a stellarator for arbitrary aspect ratio”, Nuclear Fusion, 23 (1983), 1079–1088

[18] V. D. Pustovitov, V. D. Shafranov, “Ravnovesie i ustoichivost plazmy v stellaratorakh”, Voprosy teorii plazmy, 15, ed. Kadomtsev B. B., Energoatomizdat, M., 1987, 146–291

[19] L. S. Solovev, “Simmetrichnye magnitogidrodinamicheskie techeniya i vintovye volny v kruglom plazmennom tsilindre”, Voprosy teorii plazmy, 3, Gosatomizdat, M., 1963, 245

[20] L. E. Zakharov, M. L. Mikhailov, V. I. Pistunovich, PPCNFR Proc. 8th Intern. Conf. (Brussels, 1980), 1, IAEA, Vienna, 1981, 313

[21] F. S. Zaitsev, Matematicheskoe modelirovanie evolyutsii toroidalnoi plazmy, Maks-Press, M., 2005, 524 pp.

[22] A. I. Morozov, L. S. Solovev, “Statsionarnye techeniya plazmy v magnitnom pole”, Voprosy teorii plazmy, 8, Gosatomizdat, M., 1974, 3–87

[23] J. P. Goedbloed, Physics of Plasmas, 11 (2004), L81–L84 | DOI | MR

[24] E. Hameiri, Physics of Fluids, 26 (1983), 230 | DOI | MR | Zbl

[25] L. S. Solovev, ZhETF, 26 (1968), 400

[26] S. I. Pokhozhaev, “O sobstvennykh funktsiyakh uravneniya $\Delta u+\lambda f(u)=0$”, DAN SSSR, 165 (1965), 36–39 | MR | Zbl

[27] H. Keller, D. J. Cohen, “Some positone problems suggested by nonlinear heat generation”, Journal of Mathematics and Mechanics, 19:12 (1967), 1361–1376 | MR

[28] K. Georg, “On the convergence of an inverce iteration method for nonlinear elliptic eigenvalue problems”, Numer. Math., 32:1 (1979), 69–74 | DOI | MR | Zbl

[29] P. L. Lions, “On the existence of positive solutions of semilinear elliptic equations”, SIAM Reviev, 24:4 (1982), 441–467 | DOI | MR | Zbl

[30] D. A. De Feguiriedo, “Positive solutions of semilinear elliptic problems”, Differential equations, Lect. Notes in Math., 957, Springer, Berlin–New York, 1982, 34–87 | MR

[31] R. P. Sperb, “Extension of two theorems of Payne to some nonlinear Dirichlet problems”, Z. Angew. Math. and Phys., 26:6 (1975), 721–726 | DOI | MR | Zbl

[32] A. Acker, Math. Meth. Anal. Sci., 3:3 (1981), 435–443 | DOI | MR | Zbl

[33] L. M. Kovrizhnykh, D. P. Kostomarov, D. Yu. Sychugov, S. V. Schepetov, “Svoistva struktur magnitnykh poverkhnostei v toroidalnoi plazme”, Differentsialnye uravneniya, 25:6 (1989), 983–989 | MR | Zbl

[34] L. M. Kovrizhnykh, S. V. Schepetov, “Sovremennoe sostoyanie teorii MGD ravnovesiya i ustoichivosti plazmy v stellaratore”, Uspekhi fiz. nauk, 148:4 (1986), 637–670

[35] A. A. Samarskii, E. S. Nikolaev, Metody resheniya setochnykh uravnenii, Nauka, M., 1978, 592 | MR | Zbl

[36] K. Lakner, “Computation of ideal MHD equilibria”, Computer Physics Communications, 12:1 (1976), 33–44 | DOI

[37] V. A. Voznesenskii, N. A. Gasilov, Yu. N. Dnestrovskii, A. B. Kuznetsov, D. Yu. Sychugov, S. V. Tsaun, TOKAMEQ – kod dlya rascheta ravnovesiya plazmy v tokamake, preprint IAE, No 6208/7, Rossiiskii nauchnyi tsentr “Kurchatovskii institut”, M., 2001

[38] V. A. Voznesenskii, D. Yu. Sychugov, “Modernizirovannyi chislennyi metod rascheta MGD ravnovesiya plazmennogo shnura v tokamake”, Vestnik MGU, cer. 15 “Vychislitelnaya matematika i kibernetika”, 2005, no. 1, 24–29 | Zbl

[39] A. M. Kakurin, V. M. Leonov, G. E. Notkin, P. P. Khvostenko, S. V. Tsaun, E. N. Bondarchuk, V. I. Vasilev, A. B. Mineev, I. I. Maksimova, V. V. Amelin, N. A. Gasilov, D. Yu. Sychugov, “Osnovnye stsenarii razryada tokamaka T-15M”, Voprosy Atomnoi Nauki i Tekhniki. Seriya Termoyadernyi Sintez, 4, 2005, 53–75

[40] H. R. Wilson, G. M. Voss, R. J. Akers, L. Appel, J. P. Christiansen, A. Dnestrovskij, O. Keating, T. C. Hender, M. J. Hole, G. Huysmans, A. Kirk, P. J. Knight, M. Louglin, K. G. McClemens, M. R. O'Brien, D. Yu. Sychugov and M. Valovic, “The Physics Basis jf a Spherical Tokamak Components Test Facility”, 31st EPS Conference on Plasma Physics (London, 28 June–2 July), ECA, 28G, 2004, 4–196

[41] H. R. Wilson, G. M. Voss, R. J. Akers, L. Appel, I. Chapman, J. P. Christiansen, A. Dnestrovskij, O. Keating, T. C. Hender, M. J. Hole, G. T. A. Huysmans, A. Kirk, P. J. Knight, M.Loughlin, K. G. McClements, A. W. Morris, M. R. O'Brien, D. Yu. Sychugov and M. Valovic, A Steady State Spherical Tokamak for Components Testing, 20th IAEA Fusion Energy Conference, Vilamoura, Portugal, 1–6 November 2004

[42] Yu. N. Dnestrovskij, S. V. Tsaun, D. P. Kostomarov, A. M. Popov, Control. Fusion and Plasma Phys. (CFPP), Proc. 10th Europ. Conf. (Moscow, 1981), v. 1. p. B14

[43] V. F. Andreev, Yu. N. Dnestrovskii, D. P. Kostomarov, A. M. Popov, S. V. Tsaun, Fizika plazmy, 12 (1986), 387

[44] L. E. Zakharov, Metod elektrodinamicheskikh momentov dlya rascheta ravnovesiya toroidalnoi plazmy, preprint IAE-4114/6, IAE, M., 1985

[45] Yu. N. Dnestrovskii, A. M. Popov, S. V. Tsaun, Redutsirovannaya model ravnovesiya plazmy s separatrisoi v tokamake s zheleznym serdechnikom, Preprint IAE-5178/7, M., 1990

[46] V. F. Andreev, Yu. N. Dnestrovskii, D. P. Kostomarov, A. M. Popov, VANT, Ser. Termoyadernyi sintez, 1988, 36

[47] L. M. Degtyarev, V. V. Drozdov, S. Yu. Medvedev, “Chislennoe modelirovanie ravnovesiya i ustoichivosti toroidalnoi plazmy.”, Itogi nauki i tekhniki, seriya: Fizika plazmy, 6, VINITI, M., 1985, 81–134

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

[49] L. M. Degtyarev, V. V. Drozdov, “An inverse variable technique in the MHD-equilibrium problem”, Computer Physics Reports, 2 (1985), 341–387 | DOI

[50] S. P. Hirshman, W. I. Van Rij, P. Merkel, “Three-dimensional free boundary calculations using a spectral green's function method”, Computer Physics Communications, 43 (1986), 143–155 | DOI | MR

[51] D. P. Kostomarov, D. Yu. Sychugov, S. V. Schepetov, “Primenenie neodnoznachnykh potokovykh peremennykh k resheniyu zadach MGD ravnovesiya plazmy (metod bazovykh koordinat)”, Matem. modelirovanie, 4:10 (1992), 71–87 | MR

[52] A. B. Kuznetsov, D. Yu. Sychugov, S. V. Shchepetov, “Plasma equilibria with stochastic regions and magnetic islands”, Transactions of Fusion Technology, 27 (1995), 455–458

[53] D. Yu. Sychugov, S. V. Schepetov, “Modelirovanie vintovogo ravnovesiya s magnitnymi ostrovami pri pomoschi potokovykh koordinat”, Matem. modelirovanie, 8:2 (1996), 57–65 | MR | Zbl