Mathematical Models and Computer Simulations

, Volume 3, Issue 6, pp 671–679 | Cite as

Mathematical properties of plasma vertical instability in Tokamak

  • D. Yu. Sychugov
  • Yu. N. Dnestrovskii
  • D. P. Kostomarov
  • V. V. Amelin
  • N. A. Gasilov
Article

Abstract

The model of plasma vertical instability in tokamak has been investigated. Fast, slow and hybrid magnetohydrodynamical instabilities have been studied. The models of passive, active, linear and nonlinear feedback have been studied. Several theorems, which are interesting from the physical point of view, have been proven.

Keywords

tokamak plasma vertical instability linear and nonlinear feedback mathematical theorems physical interpretation of theorems 

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References

  1. 1.
    G. Laval, R. Pellat, and G. Soule, “Hydromagnetic Stability of a Current-Carrying Pinch with Non-circular Cross Section,” The Physics of Fluids 17(4), 835–845 (1974).CrossRefGoogle Scholar
  2. 2.
    S. C. Jardin, and D. A. Larrabee, “Feedback Stabilization of Rigid Axisymmetric Modes in Tokamaks,” Nuclear Fusion 22(8), 1095–1098 (1982).CrossRefGoogle Scholar
  3. 3.
    V. F. Andreev, Yu. N. Dnestrovskii, D. P. Kostomarov, A. M. Popov, and D. Yu. Sychugov, “Vertical Stability in Tokamak with Iron Core,” Voprosy Atomnoi Nauki i Tehniki, seriya “Termoyadernyi Sintez”, No. 3, 33–39 (1986).Google Scholar
  4. 4.
    S. N. Gerasimov, A. M. Popov, and D. Yu. Sychugov, “Comparison of Mathematical Modelling of Equilibrium and Magnetohydrodynamical Stability of Plasma with Experiment in device T12,” Phizika Plazmy, 9(4), 688–696 (1983).Google Scholar
  5. 5.
    Yu. N. Dnestrovskii, D. P. Kostomarov, V. I. Pistunovich, A. M. Popov, and D. Yu. Sychugov, “Stabilization of Vertical Instability in Tokamak with Poloidal Divertor,” Phizika Plazmy 10(4), 688–694 (1984).Google Scholar
  6. 6.
    N. A. Gasilov, S. N. Gerasimov, I. V. Zotov, and D. Yu. Sychugov, “Modelling of Experiment on Studying Plasma Instability in a Tokamak with Divertor,” Preprint IAE-4327 (National Research Centre Kurchatov Institute, Moscow, 1986).Google Scholar
  7. 7.
    E. N. Bondarchuk, Yu. N. Dnestrovskij, V. M. Leonov, I. I. Maximova, D. Yu. Sychugov, S. V. Tsaun, and V. A. Voznesensky, “Vertical MHD Stability of the 15M Tokamak Plasma,” Plasma Devices and Operations 11(4), 219–227 (2003).CrossRefGoogle Scholar
  8. 8.
    D. Yu. Sychugov, V. V. Amelin, N. A. Gasilov, and S. V. Tsaun, “Numerical Study of Plasma Vertical Instability in Tokamak with Finite Conductivity of Stabilizing Elements,” Moscow State University Bulletin “Computational Mathematics and Cybernetics” No. 4, 27–32 (2004).Google Scholar
  9. 9.
    A. M. Kakurin, V. M. Leonov, G. E. Notkin, P. P. Khvostenko, S. V. Tsaun, E. N. Bondarchuk, V. I. Vasiliev, A. B. Mineev, I. I. Maximova, V. V. Amelin, N. A. Gasilov, and D. Yu. Sychugov, “Main Discharge Scenarios for Tokamak T-15N,” Voprosy Atomnoi Nauki i Tehniki. Seriya “Termoyadernyi Sintez”, No. 4, 53–75 (2005).Google Scholar
  10. 10.
    Yu. V. Mitrishkin, V. E. Lukash, and R. R. Khayrutdinov, “Plasma Current, Position and Shape Robust Control System in ITER,” Voprosy Atomnoi Nauki i Tehniki. Seriya “Termoyadernyi Sintez”, No. 1, 61–81 (2005).Google Scholar
  11. 11.
    D. Yu. Sychugov, V. V. Amelin, and N. A. Gasilov, “The Code ‘TOKSTAB’ (Module of Program Library ‘Virtual Tokamak’),” Voprosy Atomnoi Nauki i Tehniki. Seriya “Termoyadernyi Sintez”, No. 3, 46–49 (2010).Google Scholar
  12. 12.
    A. A. Ivanov, R. R. Khayrutdinov, S. Yu. Medvedev, and Yu. Yu. Poshekhonov, “New Adaptive Grid Plasma Evolution Code SPIDER,” presented at 32nd EPS Conference on Plasma Phys., June 27–July 1 (Tarragona, 2005), ECA v.29C, p-5.063.Google Scholar
  13. 13.
    L. Degtyarev, A. Martynov, S. Medvedev, F. Troyon, L. Villard, and R. Gruber, “The KINX Ideal MHD Stability Code for Axisymmetric Plasmas,” Computer Physics Communications 103, 10–27 (1997).CrossRefGoogle Scholar
  14. 14.
    V. E. Lukash and R. R. Khayrutdinov, “’DINA-EqDsk’ Module,” Voprosy Atomnoi Nauki i Tehniki. Seriya “Termoyadernyi Sintez”, No. 3, 64–66 (2009).Google Scholar
  15. 15.
    L. D. Landau and E. M. Lifshitz, Theoretical Physics. Volume 8. Electrodynamics of Continuous Media (“Nauka”, Moscow, 1982) [in Russian].Google Scholar
  16. 16.
    G. Korn and T. Korn, Mathematical Handbook for Scientists and Engineers (Glavnaya Redaktsiya Phiziko-Matematicheskoi Literatury, Moscow, 1970) [in Russian].Google Scholar
  17. 17.
    S. V. Emel’yanov, S. K. Korovin, V. V. Fomichev, and A. S. Fursov, Problems and Theorems on Linear Feedback Theory (Moscow State University, Faculty of Computational Mathematics and Cybernetics, Moscow, 2004) [in Russian].Google Scholar
  18. 18.
    S. V. Emel’yanov and S. K. Korovin, New Types of Feedback (Nauka, Moscow, 1997) [in Russian].Google Scholar

Copyright information

© Pleiades Publishing, Ltd. 2011

Authors and Affiliations

  • D. Yu. Sychugov
    • 1
  • Yu. N. Dnestrovskii
    • 2
  • D. P. Kostomarov
    • 1
  • V. V. Amelin
    • 1
  • N. A. Gasilov
    • 3
  1. 1.Department of Computational Mathematics and CyberneticsMoscow State UniversityMoscowRussia
  2. 2.National Research Center Kurchatov InstituteMoscowRussia
  3. 3.Baskent UniversityAnkaraTurkey

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