Mathematical model of voltage–current characteristics of Bi(2223)/Ag magnets under an external magnetic field

We have developed a mathematical model, which enables us to predict the voltage–current V(I) characteristics of a solenoidal high-temperature superconductor (HTS) magnet subjected to an external magnetic field parallel to the magnet axis. The model takes into account the anisotropy in the critical current–magnetic field (Ic(B)) characteristic and the n-value of Bi(2223)Ag multifilamentary tape at 20 K. From the power law between the electric field and the ratio of the operating and critical currents, the voltage on the magnet terminals is calculated by integrating the contributions of individual turns. The critical current of each turn, at given values of operating current and external magnetic field, is obtained by simple linear interpolation between the two suitable points of the Ic(B) characteristic, which corresponds to the angle α between the vector of the resulting magnetic flux density and the broad tape face. In fact, the model is valid for any value and orientation of external magnetic field, and is only limited by the validity of the electric field power law as a function of operating current. Electric fields of individual turns of the model magnet, which consists of 22 pancake coils, have been analysed for different values of operating current and external magnetic field. The voltage distribution on individual pancake coils and the overall voltage between the magnet terminals have also been analysed. Finally, the influence of external magnetic field on the V(I) characteristics of the magnet have been studied for different values of operating current. We report on a new and rather unexpected behaviour of the HTS magnets at different operating conditions, together with a theoretical explanation.