Advertisement

Doklady Mathematics

, Volume 98, Issue 2, pp 518–521 | Cite as

Efficient Parallel Algorithm for Calculating Electric Currents in a Toroidal Plasma

  • F. S. Zaitsev
  • F. A. Anikeev
Mathematical Physics
  • 2 Downloads

Abstract

In the six-dimensional (6D) phase space, a new statement of the problem of calculating the electric current due to the pressure gradient in a toroidal plasma is considered. A semi-Lagrangian approach is applied. A new efficient parallel algorithm is developed for the numerical solution of a 6D kinetic equation with the Coulomb collision operator. By the DiFF-PK code developed by the authors, a 5D problem is solved under the conditions of ITER-scale facilities. The bootstrap current of electrons is calculated. A good agreement with the previously known limit cases is demonstrated. The method proposed can be applied to the high-precision computation of a large class of problems whose solution within existing approaches is complicated. For these purposes, the mini-supercomputer at the Research Institute for Systems Analysis, Russian Academy of Sciences, or pentaflop class supercomputers can be used. The problems include, for example, the calculation of the bootstrap current of alpha particles–a product of thermonuclear fusion, the calculation of the electric current produced by neutrals injected into a plasma, and simulation of radial electric fields and instabilities of plasma.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    F. S. Zaitsev, Mathematical Modeling of Toroidal Plasma Evolution, 2nd rus. ed. (MAKS Press, Moscow, 2011).Google Scholar
  2. 2.
    F. S. Zaitsev, Mathematical Modeling of Toroidal Plasma Evolution, English ed. (MAKS Press, Moscow, 2014).Google Scholar
  3. 3.
    A. Galeev and R. Sagdeev, “Neoclassical theory of diffusion,” in Reviews of Plasma Physics, Ed. by M. A. Leontovich (Atomizdat, Moscow, 1973), No. 7, pp. 205–245 [in Russian].Google Scholar
  4. 4.
    E. Kalnay, Atmospheric Modeling, Data Assimilation, and Predictability (Cambridge Univ. Press, Cambridge, 2002).CrossRefGoogle Scholar
  5. 5.
    J. Demmel, S. Eisenstat, J. Gilbert, X. Li, and J. Liu, SIAM J. Matrix Anal. Appl. 20, 720–755 (1999).MathSciNetCrossRefGoogle Scholar

Copyright information

© Pleiades Publishing, Ltd. 2018

Authors and Affiliations

  1. 1.Scientific Research Institute for Systems AnalysisRussian Academy of SciencesMoscowRussia
  2. 2.Moscow State UniversityMoscowRussia

Personalised recommendations