Plasma and Fusion Research

Volume 16, 1403097 (2021)

Regular Articles

Construction of Smooth Flux Surfaces via Multiple Field-Line Tracings
Seikichi MATSUOKA1,2)
1)
National Institute for Fusion Science, Toki 509-5292, Japan
2)
The Graduate University for Advanced Studies, SOKENDAI, Toki 509-5292, Japan
(Received 12 June 2021 / Accepted 2 September 2021 / Published 1 November 2021)

Abstract

In this study, a new numerical method for constructing flux surfaces for three-dimensional (3D) toroidal magnetic fields is proposed. In the method, multiple field lines starting from all grid points in the computational domain are simultaneously followed to obtain the field-line average. The field-line average obtained for the entire domain is used to label flux surfaces as the radial coordinate based on a reasonable assumption that the field-line average approximates the flux surface average when continuous nested surfaces exist. It is demonstrated that a severe numerical discontinuity in the constructed surfaces, which is often observed near a low-order rational surface in a conventional method based on the Poincaré map, can be avoided using the proposed method, enabling the construction of smooth flux surfaces.

Keywords

magnetic coordinate, flux surface, stellarator, heliotron, field-line tracing

DOI: 10.1585/pfr.16.1403097

Full Text

PDF format (7.4Mbytes) PDF Download

References

  • [1] A.H. Boozer, Phys. Fluids 25, 520 (1982).
  • [2] G. Kuo-Petravic et al., J. Comput. Phys. 51, 261 (1983).
  • [3] G. Kuo-Petravic and A.H. Boozer, J. Comput. Phys. 73, 107 (1987).
  • [4] A.H. Reiman and H.S. Greenside, J. Comput. Phys. 75, 423 (1988).
  • [5] V.V. Nemov, Nucl. Fusion 28, 1727 (1988).
  • [6] X. Bonnin et al., Nucl. Fusion 45, 22 (2005).
  • [7] S.A. Bozhenkov et al., Fusion Eng. Des. 88, 2997 (2013).
  • [8] I. Predebon et al., Plasma Phys. Control. Fusion 60, 045003 (2018).
  • [9] J. Todoroki, J. Plasma Fusion Res. 79, 321 (2003).
  • [10] W.D. D'haeseleer, W.N.G. Hitchon, J.D. Callen and J.L. Shohet, Flux Coordinates and Magnetic Field Structure (Springer Berlin Heidelberg, Berlin, Heidelberg, 1991).
  • [11] W. Dommaschk, Comput. Phys. Commun. 40, 203 (1986).
  • [12] P. Merkel, J. Comput. Phys. 66, 83 (1986).
  • [13] Y. Suzuki et al., Nucl. Fusion 46, L19 (2006).
  • [14] C. Zhu et al., Nucl. Fusion 58, 016008 (2018); ibid. 60, 089601 (2020).