Skip to main content
Log in

Development of a free-boundary tokamak equilibrium solver for advanced study of tokamak equilibria

  • Published:
Journal of the Korean Physical Society Aims and scope Submit manuscript

Abstract

A free-boundary Tokamak equilibrium solver (TES), developed for advanced study of tokamak equilibra, is described with two distinctive features. One is a generalized method to resolve the intrinsic axisymmetric instability, which is encountered in all equilibrium calculations with a freeboundary condition. The other is an extension to deal with a new divertor geometry such as snowflake or X divertors. For validations, the uniqueness of a solution is confirmed by the independence of variations in the computational domain, the mathematical correctness and accuracy of equilibrium profiles are checked by using a direct comparison with an analytic equilibrium known as a generalized Solov’ev equilibrium, and the governing force balance relation is tested by examining the intrinsic axisymmetric instabilities. As an application of an advanced equilibrium study, a snow-flake divertor configuration that requires a second-order zero of the poloidal magnetic flux is discussed in the circumstance of the Korea superconducting tokamak advanced research (KSTAR) coil system.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. Tatsuoki Takeda and Shinji Tokuda, J. Comp. Phys. 93, 1 (1991).

    Article  MATH  MathSciNet  ADS  Google Scholar 

  2. V. D. Shafranov, ZhETF 33, 710 (1957); Sov. Phys. JETP 8, 494 (1958).

    Google Scholar 

  3. H. Grad and H. Rubin, Proceedings of 2nd International Conference on the Peaceful Uses of Atomics Energy 31, (United Nations, Geneva, 1958), p. 190.

    Google Scholar 

  4. D. D. Ryutov, Phys. Plasmas 14, 064502 (2007).

    Article  ADS  Google Scholar 

  5. M. Kotschenreuther, P. M. Valanju, S. M. Mahajan and J. C. Wiley, Phys. Plasmas 14, 072502 (2007).

    Article  ADS  Google Scholar 

  6. F. Piras et al., Plasma Phys. Control. Fusion 51, 055009 (2009).

    Article  ADS  Google Scholar 

  7. V. A. Soukhanovskiil et al., Nucl. Fusion 51, 012001 (2011).

    Article  ADS  Google Scholar 

  8. K. Lackner and H. Zohm, Fusion Sci. Tech. 63, 43 (2013).

    Article  Google Scholar 

  9. G. Lee et al., Nucl. Fusion 40, 575 (2000).

    Article  ADS  Google Scholar 

  10. J. L. Johnson et al., J. Comp. Phys. 32, 212 (1979).

    Article  MATH  ADS  Google Scholar 

  11. S. C. Jardin, N. Pomphrey and J. Delucia, J. Comp. Phys. 66, 481 (1986).

    Article  MATH  ADS  Google Scholar 

  12. F. Hofmann, Comput. Phys. Commun. 48, 207 (1988).

    Article  ADS  Google Scholar 

  13. R. Albanese and F. Villone, Nucl. Fusion 38, 012001 (1998).

    Article  Google Scholar 

  14. H. P. William, A. T. Saul, T. V. William and P. F. Brian, Numerical Recipes, 3rd Edition: The Art of Scientific Computing (Cambridge University Press, New York, 2007).

    MATH  Google Scholar 

  15. O. Buneman, Stanford University Institute for Plasma Research Rept. SUIPR-294 (1968).

    Google Scholar 

  16. E. Kreyszig, Advanced Engineering Mathematics, 8th Edition, (John Wiley & Sons, Hoboken, 1998).

    Google Scholar 

  17. K. Miyamoto, Plasma Physics for Nuclear Fusion, revised Edition (The MIT Press, Cambridge, 1989).

    Google Scholar 

  18. L. L. LoDestro and L. D. Pearlstein, Phys. Plasmas 1, 90 (1994).

    Article  ADS  Google Scholar 

  19. A. N. Tikhonov and V. Y. Arsenin, Solutions of Ill-posed Problems (Winston and Sons, Washington, 1977).

    MATH  Google Scholar 

  20. S. B. Zheng, A. J. Wootton and Emilia R. Solano, Phys. Plasmas 3, 1176 (1996).

    Article  ADS  Google Scholar 

  21. A. Fukuyama, S. Seki, H. Momota and R. Itatani, Jpn. J. Appl. Phys 14, 871 (1975).

    Article  ADS  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Young Mu Jeon.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Jeon, Y.M. Development of a free-boundary tokamak equilibrium solver for advanced study of tokamak equilibria. Journal of the Korean Physical Society 67, 843–853 (2015). https://doi.org/10.3938/jkps.67.843

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.3938/jkps.67.843

Keywords

Navigation