Abstract
The central solenoid (CS) is one of the key components of the International Thermonuclear Experimental Reactor (ITER) tokamak and which is often considered as the heart of this fusion reactor. This solenoid will be built by using \(\hbox {Nb}_{3}\hbox {Sn}\) cable-in-conduit conductors (CICC), capable of generating a 13 T magnetic field. In order to assess the performance of the \(\hbox {Nb}_{3}\hbox {Sn}\) CICC in nearly the ITER condition, many short samples have been evaluated at the SULTAN test facility (the background magnetic field is of 10.85 T with the uniform length of 400 mm at 1% homogeneity) in Centre de Recherches en Physique des Plasma (CRPP). It is found that the samples with pseudo-long twist pitch (including baseline specimens) show a significant degradation in the current-sharing temperature (Tcs), while the qualification tests of all short twist pitch (STP) samples, which show no degradation versus electromagnetic cycling, even exhibits an increase of Tcs. This behavior was perfectly reproduced in the coil experiments at the central solenoid model coil (CSMC) facility last year. In this paper, the complex structure of the \(\hbox {Nb}_{3}\hbox {Sn}\) CICC would be simplified into a wire rope consisting of six petals and a cooling spiral. An analytical formula for the Tcs behavior as a function of the axial strain of the cable is presented. Based on this, the effects of twist pitch, axial and transverse stiffness, thermal mismatch, cycling number, magnetic distribution, etc., on the axial strain are discussed systematically. The calculated Tcs behavior with cycle number show consistency with the previous experimental results qualitatively and quantitatively. Lastly, we focus on the relationship between Tcs and axial strain of the cable, and we conclude that the Tcs behavior caused by electromagnetic cycles is determined by the cable axial strain. Once the cable is in a compression situation, this compression strain and its accumulation would lead to the Tcs degradation. The experimental observation of the Tcs enhancement in the CS STP samples should be considered as a contribution of the shorter length of the high field zone in SULTAN and CSMC devices, as well as the tight cable structure.
Similar content being viewed by others
References
Mitchell, N., Devred, A., Libeyre, P., et al.: The ITER magnets: design and construction status. IEEE Trans. Appl. Supercond. 22, 4200809 (2012)
Ekin, J.: Superconductor Materials Science: Metallurgy, Fabrication, and Applications. Springer, Berlin (1981)
Nijhuis, A., Pompe van Meerdervoort, R.P., Krooshoop, H.J.G., et al.: The effect of axial and transverse loading on the transport properties of ITER \(\text{ Nb }_{3}\text{ Sn }\) strands. Supercond. Sci. Technol. 26, 084004 (2013)
Nijhuis, A., Ilyin, Y., Wessel, W.A.J., et al.: Critical current and strand stiffness of three types of \(\text{ Nb }_{3}\text{ Sn }\) strand subjected to spatial periodic bending. Supercond. Sci. Technol. 19, 1136–45 (2006)
Kudoh, H., Yagai, T., Hamano, K., et al.: Theoretical and experimental analysis of \(\text{ Nb }_{3}\text{ Sn }\) strand buckling in large scale CIC conductor. Plasma Fusion Res. 9, 3405063 (2014)
Yagai, T., Kudo, H., Hamano, K., et al.: Investigation of frictional force applied to strands surrounded by other strands and tribological analysis of contact surface in CIC conductor. IEEE Trans. Appl. Supercond. 24, 1–4 (2014)
March, S.A., Bruzzone, P., Stepanov, B., et al.: Effect of thermal loading on CICC performance. IEEE Trans. Appl. Supercond. 22, 4803604 (2012)
Martovetsky, N., Michael, P., Minervini, J., et al.: Test of the ITER central solenoid model coil and CS insert. IEEE Trans. Appl. Supercond. 12, 600–5 (2002)
Mitchell, N.: Mechanical and magnetic load effects in \(\text{ Nb }_{3}\text{ Sn }\) cable-in-conduit conductors. Cryogenics 43, 255–70 (2003)
Mitchell, N.: Summary, assessment and implications of the ITER model coil test results. Fusion Eng. Des. 66–68, 971–93 (2003)
Mitchell, N.: Operating strain effects in \(\text{ Nb }_{3}\text{ Sn }\) cable-in-conduit conductors. Supercond. Sci. Technol. 18, S396–S404 (2005)
Mitchell, N.: Assessment of conductor degradation in the ITER CS insert coil and implications for the ITER conductors. Supercond. Sci. Technol. 20, 25 (2006)
Nijhuis, A., Ilyin, Y.: Transverse load optimization in \(\text{ Nb }_{3}\text{ Sn }\) CICC design; influence of cabling, void fraction and strand stiffness. Supercond. Sci. Technol. 19, 945–962 (2006)
Nijhuis, A.: A solution for transverse load degradation in ITER \(\text{ Nb }_{3}\text{ Sn }\) CICCs: verification of cabling effect on Lorentz force response. Supercond. Sci. Technol. 21, 054011 (2008)
Zhai, Y., Bird, M.D.: Florida electro-mechanical cable model of \(\text{ Nb }_{3}\text{ Sn }\) CICCs for high-field magnet design. Supercond. Sci. Technol. 21, 115010 (2008)
Zhai, Y.: Electro-mechanical modeling of \(\text{ Nb }_{3}\text{ Sn }\) CICC performance degradation due to strand bending and inter-filament current transfer. Cryogenics 50, 149–57 (2010)
Bajas, H., Durville, D., Ciazynski, D., et al.: Approach to heterogeneous strain distribution in cable-in-conduit conductors through finite element simulation. IEEE Trans. Appl. Supercond. 22, 4803104 (2012)
Bajas, H., Durville, D., Devred, A.: Finite element modelling of cable-in-conduit conductors. Supercond. Sci. Technol. 25, 054019 (2012)
Jewell, M.C., Lee, P.J., Larbalestier, D.C.: The influence of \(\text{ Nb }_{3}\text{ Sn }\) strand geometry on filament breakage under bend strain as revealed by metallography. Supercond. Sci. Technol. 16, 1005 (2003)
Nunoya, Y., Isono, T., Okuno, K.: Experimental investigation on the effect of transverse electromagnetic force on the VT curve of the CIC conductor. IEEE Trans. Appl. Supercond. 14, 1468–1472 (2004)
Sanabria, C., Lee, P.J., Starch, W., et al.: Evidence that filament fracture occurs in an ITER toroidal field conductor after cyclic Lorentz force loading in SULTAN. Supercond. Sci. Technol. 25, 075007 (2012)
Sheth, M., Lee, P., McRae, D., et al.: Study of filament cracking under uniaxial repeated loading for ITER TF strands. IEEE Trans. Appl. Supercond. 22, 4802504 (2012)
Sheth, M.K., Lee, P., McRae, D.M., et al.: Procedures for evaluating filament cracking during fatigue testing of \(\,\text{ Nb }_{3}\text{ Sn }\) strand. AIP Conf. Proc. 1435, 201–208 (2012)
Sanabria, C., Lee, P.J., Starch, W., et al.: Metallographic autopsies of full-scale ITER prototype cable-in-conduit conductors after full cyclic testing in SULTAN: II. Significant reduction of strand movement and strand damage in short twist pitch CICCs. Supercond. Sci. Technol. 28, 125003 (2015)
Sanabria, C., Lee, P.J., Starch, W., et al.: Metallographic autopsies of full-scale ITER prototype cable-in-conduit conductors after full cyclic testing in SULTAN: III. The importance of strand surface roughness in long twist pitch conductors. Supercond. Sci. Technol. 29, 074002 (2016)
Devred, A., Backbier, I., Bessette, D., et al.: Challenges and status of ITER conductor production. Supercond. Sci. Technol. 27, 044001 (2014)
Hemmi, T., Nunoya, Y., Nabara, Y., et al.: Test results and investigation of Tcs degradation in Japanese ITER CS conductor samples. IEEE Trans. Appl. Supercond. 22, 4803305 (2012)
Nabara, Y., Nunoya, Y., Isono, T., et al.: Examination of Japanese mass-produced conductors for ITER toroidal field coils. IEEE Trans. Appl. Supercond. 22, 4804804 (2012)
Hemmi, T., Harjo, S., Nunoya, Y., et al.: Neutron diffraction measurement of internal strain in the first Japanese ITER CS conductor sample. Supercond. Sci. Technol. 26, 084002 (2013)
Harjo, S., Hemmi, T., Abe, J., et al.: Residual strains in ITER conductors by neutron diffraction. Mater. Sci. Forum 777, 84–91 (2014)
Sanabria, C., Lee, P.J., Starch, W., et al.: Metallographic autopsies of full-scale ITER prototype cable-in-conduit conductors after full testing in SULTAN: 1. The mechanical role of copper strands in a CICC. Supercond. Sci. Technol. 28, 085005 (2015)
Takahashi, Y., Nabara, Y., Ozeki, H., et al.: Cabling technology of conductor for ITER central solenoid. IEEE Trans. Appl. Supercond. 24, 1–4 (2014)
Tomone, S., Yoshihiro, N., Yoshikazu, T., et al.: Influence of indentation on the critical current of \(\text{ Nb }_3\text{ Sn }\) strands. Phys Procedia 67, 908–913 (2015)
Qin, J.G., Xue, T.J., Liu, B., et al.: Cabling technology of \(\text{ Nb }_3\text{ Sn }\) conductor for CFETR central solenoid model coil. IEEE Trans. Appl. Supercond. 26, 1–5 (2016)
Tronza, V.I., Lelekhov, S.A., Stepanov, B., et al.: Test results of RF ITER TF conductors in the SULTAN test facility. IEEE Trans. Appl. Supercond. 24, 1–5 (2014)
Devred, A., Jong, C., Mitchell, N.: Strain redistribution effects on current-sharing measurements on straight samples of large \(\text{ Nb }_{3}\text{ Sn }\) cable-in-conduit conductors. Supercond. Sci. Technol. 25, 054009 (2012)
Martovetsky, N., Bessette, D., Yoshikazu, T., et al.: ITER central solenoid insert test results. IEEE Trans. Appl. Supercond. 26, 4200605 (2016)
Martovetsky, N.: Characterization of the ITER CS Conductor and Projection to the ITER CS Performance. Lawrence Livermore National Laboratory (LLNL), Livermore (2016)
Costello, G.A.: Theory of Wire Rope. Springer, Berlin (1997)
Mitchell, N., Devred, A.: ITER magnet design description document 11-7 Conductors ITER project. Internal document reference ITER D 2NBKXY v1.2 (2009)
Nijhuis, A., Ilyin, Y.: Transverse cable stiffness and mechanical losses associated with load cycles in ITER \(\text{ Nb }_{3}\text{ Sn }\) and NbTi CICCs. Supercond. Sci. Technol. 22, 055007 (2009)
March, S.A., Bruzzone, P., Stepanov, B., et al.: Results of the TFEU6 sample tested in SULTAN. IEEE Trans. Appl. Supercond. 23, 4200204 (2013)
Breschi, M., Devred, A., Casali, M., et al.: Results of the TF conductor performance qualification samples for the ITER project. Supercond. Sci. Technol. 25, 095004 (2012)
Acknowledgements
This work was supported by the National Natural Science Foundation of China (Grant 11622217), the National Key Project of Scientific Instrument and Equipment Development (Grant 11327802), National Program for Special Support of Top-Notch Young Professionals. This work was also supported by the Fundamental Research Funds for the Central Universities (Grants lzujbky-2017-ot18, lzujbky-2017-k18).
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Yue, D., Zhang, X. & Zhou, YH. Theoretical analysis for the mechanical behavior caused by an electromagnetic cycle in ITER \(\hbox {Nb}_{3}\hbox {Sn}\) cable-in-conduit conductors. Acta Mech. Sin. 34, 614–622 (2018). https://doi.org/10.1007/s10409-017-0748-6
Received:
Revised:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10409-017-0748-6