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Simulation of MHD processes in high-temperature plasma

  • III. Mathematical Modeling
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Abstract

The paper analyzes a number of mathematical models and numerical codes developed for the study of magnetohydrodynamic (MHD) processes in high-temperature tokamak plasma. Various approaches are discussed to numerical solution of the nonlinear problems for systems of MHD equations arising in controlled thermonuclear fusion research.

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Literature Cited

  1. Yu. N. Dnestrovskii and D. P. Kostomarov, "Simulation of MHD processes," in:Mathematical Modeling of Plasma [in Russian], Nauka, Moscow (1982), pp. 127–218.

    Google Scholar 

  2. L. E. Zakharov and V. D. Shafranov, "Equilibrium of a current-carrying plasma in toroidal systems," in: M. A. Leontovich and B. B. Kadomtsev (eds.),Topics in Plasma Theory [in Russian], No. 11, Énergoizdat, Moscow (1982), pp. 118–235.

    Google Scholar 

  3. Yu. N. Dnestrovskii, D. P. Kostomarov, and A. M. Popov, "Numerical calculation of equilibria in tokamak systems,"Zh. Tekh. Fiz. 42, No. 11, 2255–2260 (1972).

    Google Scholar 

  4. J. Blum, G. Cissoko, and Dei Cas, "Development of MAKOKOT code," in:Plasma Physics and Controlled Nuclear Fusion Research, Vol. 1, IAEA, Vienna (1979), pp. 521–534.

    Google Scholar 

  5. E. N. Bondarchuk, N. I. Doinikov, and B. S. Mingalev, "Numerical modeling of equilibrium of tokamak plasma in the presence of a ferromagnet,"Zh. Tekh. Fiz. 47, 521–526 (1977).

    Google Scholar 

  6. Yu. N. Dnestrovskii, D. P. Kostomarov, A. M. Popov, and S. V. Tsaun, "Computation of plasma equilibrium in tokamak with iron core," Proc. 10th Europ. Conf. on Controlled Fusion and Plasma Physics, Vol. 1, Moscow (1981), p. B-14.

  7. J. Blum, J. Le Fall, and B. Thooris, "The self-consistent equilibrium and diffusion code SCED,"Comput. Phys. Commun. 24, 235–254 (1981).

    Google Scholar 

  8. Yu. N. Dnestrovskii, D. P. Kostomarov, and A. M. Popov, "Screw instability of a plasma with distributed current,"Zh. Tekh. Fiz. 42, No. 9, 1825–1838 (1972).

    Google Scholar 

  9. A. M. Popov and E. A. Shagirov, "MHD models for the study of stability of internal modes in tokamak," in: D. P. Kostomarov (ed.),Mathematical Modeling of Kinetic and MHD Processes in Plasma [in Russian], No. 8, Moscow State Univ. (1979), pp. 55–78.

  10. B. B. Kadomtsev and O. P. Pogutse, "Nonlinear helical perturbations of tokamak plasma,"Zh. Éksp. Teor. Fiz. 65, No. 2, 575–589 (1973).

    Google Scholar 

  11. Yu. N. Dnestrovskii, D. P. Kostomarov, A. M. Popov, and E. A. Shagirov, "Nonlinear evolution of helical modes in a low-q tokamak," in: Europ. Conf. on Controlled Fusion and Plasma Physics, Aachen, West Germany [in Russian], Vol. 1 (1983), p. 52.

  12. Yu. N. Dnestrovskii, D. P. Kostomarov, A. M. Popov, and D. Yu. Sychugov, "Stabilization of vertical instability in a tokamak with a diverter,"Fiz. Plazmy 10, No. 4, 519–521 (1984).

    Google Scholar 

  13. J. Killen (ed.),Methods in Computational Physics, Academic Press, New York (1976).

    Google Scholar 

  14. R. Gruber, F. Troyon, D. Berger, et al., "ERATO stability code,"Comput. Phys. Commun. 21, 323–371 (1981).

    Google Scholar 

  15. A. F. Danilov, Yu. N. Dnestrovskij, D. P. Kostomarov, and A. M. Popov, "Three-dimensional code for studying MHD motion of tokamak plasma," in: Proc. 8th Europ. Conf. on Controlled Fusion and Plasma Physics, Vol. 1, Prague (1977), p. 48.

  16. A. Sykes, "Developments of the Culham 3D nonlinear MHD-code,"Comput. Phys. Commun. 24, 437–439 (1981).

    Google Scholar 

  17. S. C. Jardin and J. L. Johnson, in: Proc. 8th Conf. on Numerical Simulation of Plasmas, paper DB-2, GA, LLNL Report CONF-780614 (1978).

  18. V. M. Goloviznin, A. A. Samarskii, and A. P. Favorskii, "Using the principle of least action to construct discrete mathematical models in magnetohydrodynamics,"Dokl. Akad. Nauk SSSR 246, No. 5, 1083–1086 (1979).

    Google Scholar 

  19. C. H. Finnan III and J. Killen, "Solution of the time-dependent three-dimensional resistive MHD equations,"Comput. Phys. Commun. 24, 441–463 (1981).

    Google Scholar 

  20. I. Kawakami, "Finite element method for 3D MHD simulations," in: Proc. US-Japan Theory Workshop on 3D MHD Studies for Toroidal Devices (1981), pp. 207–216.

  21. A. F. Danilov, Yu. N. Dnestrovskii, D. P. Kostomarov, and A. M. Popov, "Nonlinear helical waves in plasma allowing for finite conductivity,"Fiz. Plazmy 2, No. 1, 167–170 (1976).

    Google Scholar 

  22. M. N. Rosenbluth et al., "Numerical studies of nonlinear evolution of kink modes in tokamaks,"Phys. Fluids 19, No. 12, 1987–1996 (1976).

    Google Scholar 

  23. V. E. Lynch, B. A. Carreras, H. R. Hicks, et al., "Resistive MHD studies of high-β tokamak plasmas,"Comput. Phys. Commun. 24, 465–476 (1981).

    Google Scholar 

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Authors
  1. A. M. Popov
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Translated from Metody Matematicheskogo Modelirovaniya, Avtomatizatsiya Obrabotki Nablyudenii i Ikh Primeneniya, pp. 243–259, 1986.

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Popov, A.M. Simulation of MHD processes in high-temperature plasma. Comput Math Model 1, 234–244 (1990). https://doi.org/10.1007/BF01129066

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