[Table of Contents]

Plasma and Fusion Research

Volume 9, 1402046 (2014)

Regular Articles

Reconstruction of the Eddy Current Distribution on the Vacuum Vessel in a Reversed Field Pinch Device based on the External Magnetic Sensor Signals
Masafumi ITAGAKI, Akio SANPEI1), Sadao MASAMUNE1) and Kiyomasa WATANABE2)
Faculty of Engineering, Hokkaido University, Sapporo, Hokkaido 060-8628, Japan
1)
Graduate School of Science and Technology, Kyoto Institute of Technology, Kyoto 606-8585, Japan
2)
National Institute for Fusion Science, Toki, Gifu 509-5292, Japan
(Received 30 November 2013 / Accepted 17 March 2014 / Published 7 May 2014)

Abstract

For the MHD equilibrium reconstruction of a reverse field pinch device, it is a big issue to identify accurately the strong eddy current flow on the shell. In the present work, boundary integrals of the eddy current along the shell are added to the conventional Cauchy-condition surface method formulation. The eddy current profile is unknown in advance but straightforwardly identified using only the signals from magnetic sensors located outside the plasma. Two ideas are introduced to overcome the numerical difficulties encountered in the problem. One is an accurate boundary integral scheme to damp out the near singularity occurring at the sensor position very close to the shell. The other is the modified truncated singular value decomposition technique to solve an ill-conditioned matrix equation when a large number of nodal points exist on the shell. The capability of the new method is demonstrated for a test problem modeling the RELAX device.

Keywords

reversed field pinch, RELAX, eddy current, Cauchy condition surface method, singular boundary integral, modified truncated SVD method

DOI: 10.1585/pfr.9.1402046

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References

  • [1] K. Kurihara, Fusion Eng. Des. 51-52, 1049 (2000).
  • [2] M. Itagaki, S. Yamaguchi and T. Fukunaga, Nucl. Fusion 45, 153 (2005).
  • [3] M. Itagaki, T. Maeda, T. Ishimaru, G. Okubo, K. Watanabe, R. Seki and Y. Suzuki, Plasma Phys. Control. Fusion 53(10), 105007 (2011).
  • [4] M. Itagaki, G. Okubo, M. Akazawa, Y. Matsumoto, K. Watanabe, R. Seki and Y. Suzuki, Plasma Phys. Control. Fusion 54, 125003 (2012).
  • [5] M. Itagaki, K. Ishimaru, Y. Matsumoto, K. Watanabe, R. Seki and Y. Suzuki, Plasma Fusion Res. 8, 1402134 (2013).
  • [6] S. Masamune, A. Sanpei, R. Ikezono, T. Onchi, K. Oki, T. Yamashita, H. Shimazu, H. Himura and R. Paccagnella, J. Fusion Energy 28, 187 (2009).
  • [7] P. Bettini, F. Trevisan and A. Formisano, IEEE Trans. Magn. 38(2), 1089 (2002).
  • [8] C.V. Atanasiu and L.E. Zakhanov, Phys. Plasmas 20, 092506 (2013).
  • [9] V.D. Pustovitov, Plasma Phys. Control. Fusion 50, 105001 (2008).
  • [10] K. Kurihara, Y. Kawamura, M. Sueoka, H. Hosoyama, I. Yonekawa, T. Suzuki, T. Oikawa, S. Ide and JT-60 Team, Fusion Eng. Des. 74, 527 (2005).
  • [11] K. Nakamura, Y. Jiang, X.L. Liu, O. Mitarai, K. Kurihara, Y. Kawamata, M. Sueoka, M. Hasegawa, K. Tokunaga, H. Zushi, K. Hanada, A. Fujisawa, M. Sakamoto, H. Idei, S. Kawasaki, H. Nakashima, A. Higashijima and K. Arai, Fusion Eng. Des. 86, 1080 (2011).
  • [12] C.A. Brebbia and J. Dominguez, Boundary Elements An Introductory Course (Southampton, Computational Mechanics Publications, 1998).
  • [13] M. Itagaki and T. Fukunaga, Eng. Anal. Bound. Elem. 30, 747 (2006).
  • [14] M. Itagaki and H. Shimoda, Eng. Anal. Bound. Elem. 33, 845 (2009).
  • [15] P.C. Hansen, Rank-Deficient and Discrete Ill-Posed Problems - Numerical Aspects of Linear Inversion (Philadelphia, SIAM, 1998).
  • [16] H. Ma and N. Kamiya, Eng. Anal. Bound. Elem. 25, 833 (2001).
  • [17] L. Eldén, BIT 22, 487 (1982).
  • [18] Y. Nakamura, Advanced Robotics: Redundancy and Optimization (Reading, MA, Addison-Wesley, 1991).
  • [19] P.C. Hansen, T. Sekii and H. Shibahashi, SIAM J. Sci. Stat. Comput. 13, 1142 (1992).
  • [20] A. Sanpei, K. Oki, R. Ikezoe, T. Onchi, K. Murata, H. Shimazu, T. Yamashita, S. Fujita, H. Himura, S. Masamune and J.K. Anderson, J. Phys. Soc. Jpn. 78(1), 013501 (2009).
  • [21] J.K. Anderson, C.B. Forest, T.M. Biewer, J.S. Sarff and J.C. Wright, Nucl. Fusion 44, 162 (2004).

This paper may be cited as follows:

Masafumi ITAGAKI, Akio SANPEI, Sadao MASAMUNE and Kiyomasa WATANABE, Plasma Fusion Res. 9, 1402046 (2014).