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Zh. Vychisl. Mat. Mat. Fiz., 2010, Volume 50, Number 12, Pages 2184–2194 (Mi zvmmf4982)  

This article is cited in 11 scientific papers (total in 11 papers)

A plasmastatic model of the galathea-belt magnetic trap

K. V. Brushlinskiia, P. A. Ignatovb

a Keldysh Institute of Applied Mathematics, Russian Academy of Sciences, Miusskaya pl. 4, Moskow, 125047 Russia
b National Researh Nuclear University, Moscow Institute of Engineering Physics, Kashirskoe sh. 31, Moscow, 115409 Russia

Abstract: The mathematical apparatus of plasmastatics, which includes the MHD equilibrium equation and steady-state Maxwell equations, is reduced, in two-dimensional problems arising due to symmetry, to a single scalar second-order elliptic equation with a nonlinear right-hand side known as the Grad-Shafranov equation. In this paper, we numerically solve a series of boundary value problems for this equation that model equilibrium plasma configurations in the magnetic field of the belt-like galathea trap in a cylinder with two plasma embedded conductors. The mathematical model is outlined, the results of calculations of the magnetic field and plasma pressure in the cylinder depending on the parameters of the problem are presented, and the main integral characteristics of the trap are calculated. The existence and uniqueness of the solution is discussed; the limiting values of the maximal pressure at which there exists a solution of the equilibrium problem are found.

Key words: mathematical apparatus of plasmastatics, Grad-Shafranov equation, calculations of equilibrium plasma configurations in magnetic traps.

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English version:
Computational Mathematics and Mathematical Physics, 2010, 50:12, 2071–2081

Bibliographic databases:

UDC: 519.634
Received: 28.04.2010

Citation: K. V. Brushlinskii, P. A. Ignatov, “A plasmastatic model of the galathea-belt magnetic trap”, Zh. Vychisl. Mat. Mat. Fiz., 50:12 (2010), 2184–2194; Comput. Math. Math. Phys., 50:12 (2010), 2071–2081

Citation in format AMSBIB
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\by K.~V.~Brushlinskii, P.~A.~Ignatov
\paper A plasmastatic model of the galathea-belt magnetic trap
\jour Zh. Vychisl. Mat. Mat. Fiz.
\yr 2010
\vol 50
\issue 12
\pages 2184--2194
\mathnet{http://mi.mathnet.ru/zvmmf4982}
\adsnasa{http://adsabs.harvard.edu/cgi-bin/bib_query?2010CMMPh..50.2071B}
\transl
\jour Comput. Math. Math. Phys.
\yr 2010
\vol 50
\issue 12
\pages 2071--2081
\crossref{https://doi.org/10.1134/S0965542510120092}
\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-78650601560}


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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. K. V. Brushlinsky, A. S. Goldich, A. S. Desyatova, “Plasmastatic models of Galateya magnetic traps”, Math. Models Comput. Simul., 5:2 (2013), 156–166  mathnet  crossref  mathscinet  elib
    2. Brushlinskii K.V., Goldich A.S., “Kraevye zadachi vychislitelnoi plazmostatiki”, Vestnik Natsionalnogo issledovatelskogo yadernogo universiteta MIFI, 2:3 (2013), 292–304  elib
    3. Brushlinskii K.V., Goldich A.S., “Plasmastatic Models of Galathea Traps With Magnetically Transparent Boundaries”, Plasma Phys. Rep., 40:8 (2014), 591–600  crossref  adsnasa  isi  elib  scopus
    4. K. V. Brushlinsky, A. S. Goldich, N. A. Davydova, “Plasma configurations in galatheya traps and current sheets”, Math. Models Comput. Simul., 9:1 (2017), 60–70  mathnet  crossref  mathscinet  elib
    5. Brushlinskii K.V., Goldich A.S., “Mathematical model of the Galathea-belt toroidal magnetic trap”, Differ. Equ., 52:7 (2016), 845–854  crossref  mathscinet  zmath  isi  elib  scopus
    6. Brushlinskii K.V., Kondratyev I.A., “Numerical Simulation of Equilibrium Plasma Configurations in Toroidal Magnetic Traps and Their Cylindrical Analogues”, Vi International Conference Problems of Mathematical Physics and Mathematical Modelling, Journal of Physics Conference Series, 937, IOP Publishing Ltd, 2017, UNSP 012006  crossref  isi  scopus
    7. Brushlinskii K.V., Goldich A.S., “Plasmastatic Model of Toroidal Trap “Galatea-Belt””, V International Conference on Problems of Mathematical and Theoretical Physics and Mathematical Modelling, Journal of Physics Conference Series, 788, IOP Publishing Ltd, 2017, UNSP 012008  crossref  isi  scopus
    8. K. V. Brushlinskii, I. A. Kondratev, “Matematicheskie modeli ravnovesiya plazmy v toroidalnykh i tsilindricheskikh magnitnykh lovushkakh”, Preprinty IPM im. M. V. Keldysha, 2018, 020, 20 pp.  mathnet  crossref  elib
    9. K. V. Brushlinskii, I. A. Kondratev, “Sravnitelnyi analiz raschetov ravnovesiya plazmy v toroidalnykh i tsilindricheskikh magnitnykh lovushkakh”, Matem. modelirovanie, 30:6 (2018), 76–94  mathnet
    10. Brushlinskii K.V., “Mathematical Models of Plasma in Morozov'S Projects”, Plasma Phys. Rep., 45:1 (2019), 33–45  crossref  isi  scopus
    11. Tao B., Jin X., Li Zh., Tong W., “Equilibrium Configuration Reconstruction of Multipole Galatea Magnetic Trap Based on Magnetic Measurement”, IEEE Trans. Plasma Sci., 47:7, 2 (2019), 3114–3123  crossref  isi
  • Журнал вычислительной математики и математической физики Computational Mathematics and Mathematical Physics
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