Plasma and Fusion Research

Volume 8, 1402134 (2013)

Regular Articles

Improved Three-Dimensional CCS Method Analysis for the Reconstruction of the Peripheral Magnetic Field Structure in a Finite Beta Helical Plasma

Masafumi ITAGAKI, Kenzo ISHIMARU, Yutaka MATSUMOTO, Kiyomasa WATANABE¹⁾, Ryosuke SEKI¹⁾ and Yasuhiro SUZUKI¹⁾

: Graduate School of Engineering, Hokkaido University, Sapporo, Hokkaido 060-8628, Japan
1): National Institute for Fusion Science, Toki, Gifu 509-5292, Japan

(Received 25 May 2013 / Accepted 16 August 2013 / Published 15 November 2013)

Abstract

In the previous 3D Cauchy-condition surface (CCS) method analysis to reconstruct the magnetic field profile in the Large Helical Device (LHD), one assumed an impractically large number of magnetic sensors, i.e., 440 field sensors and 126 flux loops. In the singular value decomposition (SVD) process employed in the CCS method, a gap is found in the magnitude of the singular values. The most accurate field results can be obtained if all the singular values smaller than the gap threshold are eliminated, independent of the number of boundary elements on the CCS and the number of sensors as well. With the reduction in the number of boundary elements, the required numbers of field sensors and flux loops are significantly reduced to 110 and 25, respectively, without losing the solution accuracy. They can be further reduced to 58 and 13 respectively if considering the symmetry of the field profile in the LHD. This result suggests the possibility of actual application to the LHD.

Keywords

magnetic sensor, plasma boundary, last closed magnetic surface, Cauchy condition surface method, vacuum field, singular value decomposition, condition number

DOI: 10.1585/pfr.8.1402134

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References

[1] L.L. Lao, H. St. John, R.D. Stambaugh and W. Pfeiffer, Nucl. Fusion 25, 1421 (1985).
[2] D.W. Swain and G.H. Neilson, Nucl. Fusion 22, 1015 (1982).
[3] J. Svensson, A. Werner and JET-EFDA Contributors, Plasma Phys. Control. Fusion 50, 085002 (2008).
[4] W. Feneberg, K. Lackner and P. Martin, Comp. Phys. Commun. 31, 143 (1984).
[5] F. Hofmann and G. Tonetti, Nucl. Fusion 28, 519 (1988).
[6] K. Kurihara, Fusion Eng. Des. 51-52, 1049 (2000).
[7] M. Itagaki, S. Yamaguchi and T. Fukunaga, Nucl. Fusion 45, 153 (2005).
[8] M. Itagaki, T. Maeda, T. Ishimaru, G. Okubo, K. Watanabe, R. Seki and Y. Suzuki, Plasma Phys. Control. Fusion 53, 105007 (2011).
[9] M. Itagaki, G. Okubo, M. Akazawa, Y. Matsumoto, K. Watanabe, R. Seki and Y. Suzuki, Plasma Phys. Control. Fusion 54, 125003 (2012).
[10] M. Itagaki, T. Ishimaru and K. Watanabe, Proc. the 32nd International Conf. on Boundary Elements and Other Mesh Reduction Methods (Southampton, U.K., 2010), (WIT Press, Southampton, U.K., 2010) p.133.
[11] P.C. Hansen, Rank-Deficient and Discrete Ill-Posed Problems - Numerical Aspects of Linear Inversion (Philadelphia: SIAM, 1998).
[12] M.D. Buhmann, Radial Basis Function (Cambridge, Cambridge University Press, 2003).
[13] M. Itagaki and N. Sahashi, J. Nucl. Sci. Technol. 33, 7 (1996).
[14] W.H. Press, B.P. Flannery, S.A. Teukolsky and W.T. Vetterling, Numerical Recipes - The Art of Scientific Computing (Cambridge, Cambridge University Press, 1986).
[15] R. Seki, Y. Matsumoto, Y. Suzuki, K. Watanabe and M. Itagaki, Plasma Fusion Res. 3, 016 (2008).
[16] Y. Suzuki, N. Nakajima, K. Watanabe, Y. Nakamura and T. Hayashi, Nucl. Fusion 46, L19 (2006).
[17] LHD Experimental Board, LHD Experiment Technical Guide 2009 (Toki, Japan, National Institute for Fusion Science, 2009) Section 6.
[18] M. Itagaki, K. Nakata, H. Tanaka and A. Wakasa, Eng. Anal. Bound. Elem. 33, 1258 (2009).

This paper may be cited as follows:

Masafumi ITAGAKI, Kenzo ISHIMARU, Yutaka MATSUMOTO, Kiyomasa WATANABE, Ryosuke SEKI and Yasuhiro SUZUKI, Plasma Fusion Res. 8, 1402134 (2013).