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Plasmastatic models of galathea traps with magnetically transparent boundaries

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Abstract

Mathematical models and results of calculation of plasma equilibrium in a circular cylinder with three helical or straight imbedded current-carrying conductors (i.e., in a straightened analog of a toroidal Galathea trap) are presented. The equilibrium is described in the framework of two-dimensional boundary value problems with plane and helical analogs of the Grad-Shafranov equation for the scalar magnetic flux function. Problems with first-kind boundary conditions corresponding to a magnetically transparent boundary of the cylinder and problems with second-kind boundary conditions and a given value of the electric current flowing in plasma (in addition to those flowing in the conductors) are considered. Deformations of magnetoplasma configurations in the cylinder for different formulations of the above-specified problems are investigated numerically.

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References

  1. A. I. Morozov, Sov. J. Plasma Phys. 18, 159 (1992).

    Google Scholar 

  2. A. I. Morozov and V. V. Savel’ev, Phys. Usp. 41, 1049 (1998).

    Article  ADS  Google Scholar 

  3. A. M. Bishaev, A. I. Bugrova, M. B. Gavrikov, M. V. Kozintseva, A. S. Lipatov, V. V. Savel’ev, A. S. Sigov, P. G. Smirnov, I. A. Tarelkin, and P. P. Khramtsov, Tech. Phys. 58, 498 (2013).

    Article  Google Scholar 

  4. A. I. Morozov and A. G. Frank, Plasma Phys. Rep. 20, 879 (1994).

    ADS  Google Scholar 

  5. K. V. Brushlinskii, A. M. Zaborov, and S. I. Syrovatskii, Sov. J. Plasma Phys. 6, 165 (1980).

    ADS  Google Scholar 

  6. S. Yu. Bogdanov, V. B. Burilina, N. P. Kirii, V. S. Markov, A. I. Morozov, and A. G. Frank, Plasma Phys. Rep. 24, 427 (1998).

    ADS  Google Scholar 

  7. K. V. Brushlinskii and P. A. Ignatov, Comp. Math. Math. Phys. 50, 2071 (2010).

    Article  MathSciNet  Google Scholar 

  8. K. V. Brushlinskii, A. S. Gol’dich, and A. S. Desyatova, Math. Models Comp. Simulat. 5, 156 (2013).

    Article  MathSciNet  Google Scholar 

  9. K. V. Brushlinskii and A. S. Gol’dich, Vest. Natsional. Issled. Yad. Univ. MIFI, No. 3, 292 (2013).

    Google Scholar 

  10. K. V. Brushlinskii and K. P. Gorshenin, Mat. Model. 9(5), 28 (1997).

    MATH  Google Scholar 

  11. G. I. Dudnikova, A. I. Morozov, and M. P. Fedoruk, Plasma Phys. Rep. 23, 357 (1997).

    ADS  Google Scholar 

  12. K. V. Brushlinskii and N. A. Chmykhova, Math. Models Comp. Simulat. 3, 9 (2011).

    Article  MathSciNet  Google Scholar 

  13. A. I. Morozov and V. D. Pustovitov, Sov. J. Plasma Phys. 17, 740 (1991).

    Google Scholar 

  14. K. V. Brushlinskii, N. M. Zueva, M. S. Mikhailova, A. I. Morozov, V. D. Pustovitov, and N. B. Tuzova, Plasma Phys. Rep. 20, 257 (1994).

    ADS  Google Scholar 

  15. K. V. Brushlinskii, A. I. Morozov, and N. B. Petrovskaya, Mat. Model. 10(11), 29 (1998).

    Google Scholar 

  16. V. D. Shafranov, Sov. Phys. JETP 6, 545 (1958).

    ADS  MathSciNet  Google Scholar 

  17. H. Grad and H. Rubin, in Proceedings of the Second United Nations Conference on the Peaceful Uses of Atomic Energy, Geneva, 1958 (Columbia Univ. Press, New York, 1959), Vol 31, p. 190.

    Google Scholar 

  18. J. L. Johnson, C. R. Oberman, R. M. Kulsrud, and E. A. Frieman, Phys. Fluids 1, 281 (1958).

    Article  ADS  MATH  MathSciNet  Google Scholar 

  19. V. D. Pustovitov and V. D. Shafranov, in Reviews of Plasma Physics, Ed. by B. B. Kadomtsev (Energoatomizdat, Moscow, 1987; Consultants Bureau, New York, 1990), Vol. 15.

  20. K. V. Brushlinskii, Mathematical and Computational Problems in Magnetic Gasdynamics (BINOM, Moscow, 2009) [in Russian].

    Google Scholar 

  21. D. W. Peaceman and H. H. Rachford, J. Soc. Industr. Appl. Mat. 3(1), 28 (1955).

    Article  MATH  MathSciNet  Google Scholar 

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Authors and Affiliations

  1. Keldysh Institute of Applied Mathematics, Russian Academy of Sciences, Miusskaya pl. 4, Moscow, 125047, Russia

    K. V. Brushlinskii

  2. National Research Nuclear University Moscow Engineering Physics Institute, Kashirskoe sh. 31, Moscow, 115409, Russia

    K. V. Brushlinskii & A. S. Goldich

Authors
  1. K. V. Brushlinskii
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  2. A. S. Goldich
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Correspondence to K. V. Brushlinskii.

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Original Russian Text © K.V. Brushlinskii, A.S. Goldich, 2014, published in Fizika Plazmy, 2014, Vol. 40, No. 8, pp. 687–696.

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Brushlinskii, K.V., Goldich, A.S. Plasmastatic models of galathea traps with magnetically transparent boundaries. Plasma Phys. Rep. 40, 591–600 (2014). https://doi.org/10.1134/S1063780X14080029

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  • DOI: https://doi.org/10.1134/S1063780X14080029

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