Theoretical analysis for the mechanical behavior caused by an electromagnetic cycle in ITER $$\hbox {Nb}_{3}\hbox {Sn}$$ cable-in-conduit conductors

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.