AC transport current loss analysis for a face-to-face stack of superconducting tapes

AC Losses for face to face stacks of four identical coated conductors (CCs) were numerically calculated using the H-formulation combined with the E-J power law and the Kim model. The motive sample was the face to face stack of four 2 mm-wide CC tapes with 2 ${\mu}m$ thick superconducting layer of which the critical current density, $J_c$, was $2.16{\times}10^6A/cm^2$ on IBAD-MgO template, which was suggested for the mitigation of ac loss as a round shaped wire by Korea Electrotechnology Research Institute. For the calculation the cross section of the stack was simply modeled as vertically aligned 4 rectangles of superconducting (SC) layers with $E=E_o(J(x,y,t)/J_c(B))^n$ in x-y plane where $E_o$ was $10^{-6}$ V/cm, $J_c$(B) was the field dependence of current density and n was 21. The field dependence of the critical current of the sample measured in four-probe method was employed for $J_c$(B) in the equation. The model was implemented in the finite element method program by commercial software. The ac loss properties for the stacks were compared with those of single 4 cm-wide SC layers with the same critical current density or the same critical current. The constraint for the simulation was imposed in two different ways that the total current of the stack obtained by integrating J(x,y,t) over the cross sections was the same as that of the applied transport current: one is that one fourth of the external current was enforced to flow through each SC. In this case, the ac loss values for the stacks were lower than those of single wide SC layer. This mitigation of the loss is attributed to the reduction of the normal component of the magnetic field near the SC layers due to the strong expulsion of the magnetic field by the enforced transport current. On the contrary, for the other case of no such enforcement, the ac loss values were greater than those of single 4cm-wide SC layer and. In this case, the phase difference of the current flowing through the inner and the outer SC layers of the stack was observed as the transport current was increased, which was a cause of the abrupt increase of ac loss for higher transport current.