Analytical Formulae for Hysteresis Power Loss in Twisted Stacked HTS Cables

In many advanced applications, such as Tokamak fusion reactors, the twisted stacked tape cable (TSTC) configuration based on high-temperature-superconducting (HTS) tapes is one of the most promising one. Among the various designs proposed for the European DEMOnstration Fusion Power Plants (DEMO) magnets, several options include conductors based on the HTS-TSTC technology, especially for an Insert of the Central Solenoid (CS). An important main design criterion to be fulfilled by superconducting magnets in operation is related to the temperature margin, which should be lower than a given threshold. For a pulsed magnet as the CS, properly determining its value is only possible with a reliable knowledge of the instantaneous losses entering the superconducting cable. Previous works presented an analytical formulation for the computation of instantaneous magnetisation losses in a HTS-TSTC conductor during a generic cycle of transport current and external magnetic field in phase with each other. Further validation of these formulae is presented by comparison with a 2D numerical model. A complete analysis of a plasma scenario is impossible with this formulation, considering that transport current and external magnetic field are not jointly in phase during the plasma breakdown. This work presents an extension of the previously developed analytical formulae to the more realistic case where the magnetic field and the transport current are not in phase with each other. The new formulae are validated in a case study of technical interest, by comparison with a 1D numerical model suited for the computation of magnetisation losses in these conductors.