[Table of Contents]

Plasma and Fusion Research

Volume 7, 2405024 (2012)

Regular Articles

Accurate and Stable Numerical Method for Analyzing Shielding Current Density in High-Temperature Superconducting Film Containing Cracks
Atsushi KAMITANI, Teruou TAKAYAMA, Ayumu SAITOH1) and Hiroaki NAKAMURA2)
Yamagata University, Yamagata 992-8510, Japan
University of Hyogo, Hyogo 671-2280, Japan
National Institute for Fusion Science, Gifu 509-5292, Japan
(Received 27 November 2011 / Accepted 23 February 2012 / Published 10 May 2012)


A numerical method is proposed for analyzing the shielding current density in a high-temperature superconducting (HTS) film containing cracks/holes. If an HTS film contains cracks or holes, an integral form of Faraday's law is also imposed as the boundary condition. Since the integral form can be completely incorporated into the weak form, it is regarded as the natural boundary condition. Thus, the weak form has only to be solved with the essential boundary conditions. However, the resulting numerical solution does not satisfy the integral form exactly. In order to resolve this problem, the following method is proposed: virtual voltages be applied along the surfaces of cracks and holes so as to have Faraday's law numerically satisfied. By using the proposed method, the influence of a crack on the permanent magnet method is investigated numerically.


critical current density, finite element method, high-temperature superconductor, integro-differential equation, Newton method

DOI: 10.1585/pfr.7.2405024


  • [1] Y. Yoshida, M. Uesaka and K. Miya, IEEE. Trans. Magn. 30, 3503 (1994).
  • [2] A. Kamitani, T. Takayama and S. Ikuno, IEEE. Trans. Magn. 44, 926 (2008).
  • [3] A. Kamitani, T. Takayama and S. Ikuno, IEEE. Trans. Magn. 47, 1138 (2011).
  • [4] S. Ohshima, K. Takeishi, A. Saito, M. Mukaida, Y. Takano, T. Nakamura, T. Suzuki and M. Yokoo, IEEE Trans. Appl. Supercond. 15, 2911 (2005).
  • [5] S. Ikuno, T. Takayama, A. Kamitani, K. Takeishi, A. Saito and S. Ohshima, IEEE Trans. Appl. Supercond. 19, 3750 (2009).
  • [6] R. Fresa, G. Rubinacci, S. Ventre, F. Villone and W. Zamboni, IEEE. Trans. Magn. 45, 988 (2009).
  • [7] G.P. Lousberg, J.F. Fagnard, M. Ausloos, P. Vanderbemden and B. Vanderheyden, IEEE Trans. Appl. Supercond. 20, 33 (2010).

This paper may be cited as follows:

Atsushi KAMITANI, Teruou TAKAYAMA, Ayumu SAITOH and Hiroaki NAKAMURA, Plasma Fusion Res. 7, 2405024 (2012).