Multidisciplinary problems in computational fusion technology

After the last year’s decision about the construction site, ITER (International Thermonuclear Experimental Reactor) experimental reactor has entered its realization phase. During the last decade an extensive Research and Development (R&D) program has been performed to demonstrate the feasibility of its magnet system. The major elements of this program have been the construction and test of real scale coils (the Central Solenoid Model Coil CSMC and the Toroidal Field Model Coil TFMC) as well as solenoid prototypes (the various Insert Coils). The testing of the model coils has provided valuable information to finalize the design of the magnetic system. However the behavior of Nb3Sn based cables was not as good as expected on the basis of the characteristics evaluated for the uncabled strands. This degradation in Nb3Sn performance seems to be due to various factors, among which the strain state of the filaments. It is worth to mention that Nb3Sn critical current depends upon the strain state, in addition to the applied magnetic field and temperature. A Nb3Sn strand inside a superconducting cable behaves like a beam loaded by Lorentz forces and supported by strand-to-strand contacts. Due to the strand material heterogeneity and the complex cable layout the strain field developed is not easy to study. In this work we present a hierarchical beam model to analyse a superconducting cable level by level. The basic idea is to perform a recursive substitution of discrete models involving many beams with a single, continuous beam model, which behaviour can be deduced from the preceding cabling stage. The theory of asymptotic homogenisation is here suitably extended for the analysis of the SC fibrous composite with non-linear, temperature dependent components. We account also for local material yielding at the stage of microanalysis. The transformation strains due to cool down from the reaction temperature to the cable operating conditions are computed, as well as the following distribution of strain due to energisation. To recover the strain inside each single strand and in the filaments, a suitable unsmearing technique is applied. The method is applied to the real case of the 3x3 and 3x3x5 CICC sub-size samples tested at FZK in Germany.