Effect of self-field and current non-uniformity on the voltage–temperature characteristic of the ITER central solenoid insert coil by numerical calculations

Abstract

For the optimisation of a magnet design with cable-in-conduit conductor (CICC) technology it is essential to comprehend the scaling of the critical current from the separate strand characteristics to the finally assembled cable performance in a coil. Several model coils have been tested in the framework of research for the International Thermonuclear Experimental Reactor (ITER). At present, the scaling of the critical current from the strand to the full cable performance and the apparent decrease of the n-index from strand to cable in the voltage–current curves is not understood. It is important to recognize the mechanisms behind this phenomenon in relation to the cost of the superconducting strand, which is significant in the manufacture of the magnets. Therefore, basic phenomena like the cable conductor self-field, the current unbalance introduced by the non-uniformity of the joints and a possible reversible or irreversible degradation of the voltage current characteristic of a strand during cable manufacture or electromagnetic loading of the magnet have to be considered. The voltage–current characteristic of the strand is extensively explored for the relevant range of magnetic field, temperature and axial strain space. Accordingly a numerical six-element network model is developed to simulate the conditions and behaviour of the last stage cable elements of a full-size ITER conductor. The experimental data, mainly in terms of voltage–current ( VI) or -temperature ( VT) characteristics, are obtained on the central solenoid insert coil (CSIC) experiment performed in Naka (Japan) in the framework of the research for ITER. The numerical model, which is briefly introduced, is used to study the cable performance by using experimentally obtained cable parameters like inter-strand (and bundle) contact resistance, strand critical current data as a function of magnetic field, temperature and applied axial strain, and external cable self-field measurements by Hall sensors for reconstruction of the current non-uniformity. The effect of a current redistribution due to the cable self-field on the voltage–temperature curve is calculated in correlation with the transverse resistance between the strands and last cabling stage bundles (petals). A realistic unbalanced current distribution is established by introducing non-uniform joints at the extremities of the CS-insert cable. It appears that the cable self-field effect hardly gives any change in the shape of the VT curve but merely a shift towards lower temperature giving a reduction of the current sharing temperature T cs (10 μV/m) of <0.1 K. For typical CICCs with Cr-coated Nb 3Sn strands, there is practically no current redistribution due to the cable self-field, because of the high inter-strand contact resistance. An unbalanced current distribution also gives an earlier voltage rise in the VT curve, mainly at low levels of the electric field. At a 10 μV/m criterion practically no reduction of the T cs (<0.1 K) is found by the numerical simulation. However, in the CSIC the experimentally obtained overall reduction in T cs from strand to cable is 0.7 K for an operating current of 40 kA at 12.5 T background field. According to the results of the numerical simulation, the cable self-field effect and the non-uniform current distribution, which is unavoidably caused by the joints, cannot explain the early voltage rise and low n-index in the VT curve of the CS-insert coil. It is very likely that electromagnetic forces play a role in causing reversible degradation in critical current or even irreversible due to strand (filament) damage. Neither can it be excluded that strand deformation during cabling has an impact on the final conductor performance as well. Therefore additional effort is required in detailed 3D modeling of the possible strand deformations inside a cable and the impact it has on the strand performance by experimental verification on strand level.