# Homogenized current flow model of a pancake coil

OData: XML JSON What's this?Multilayer second generation high temperature superconducting (HTS) coils have drawn a lot of attention in recent years, considering the research tendency of applied superconductivity. Modelling the physical behaviour with finite element method has always been a challenge because it is required to study densely wound coils with tape thickness much smaller than the characteristic length in different domain sizes. Therefore a variety of simplified coil models have been developed based on certain homogenization principles. Many of those aim at modelling the high-frequency behaviour (including skin effect and proximity effect) of coils that are made of thin wire filaments. The physical problem currently being investigated differs in many respects. When a local temperature rise created in a HTS coil is high enough to turn the superconductor from superconducting state to normal state, the transport current flowing in the HTS layer redistributes to the stabilizer in which Joule heating occurs. Then the high-temperature zone starts to propagate inside the coil. Normal Zone Propagation Velocity (NZPV) is an essential value, which is very slow, thus the detection is quite difficult. The phenomena described above is the quench. These instabilities are unlikely, however the superconducting layer becomes potentially damaged in case of permanent existence. The conductivity of this material is highly nonlinear, in addition temperature-dependent, consequently we have to face with a coupled electromagnetic and heat transfer problem. But it follows from the statements above, that in electromagnetic aspect it is possible to apply stationary approach.

In this work a new homogenization method is introduced, whereby the detailed geometry of the coil is substituted by a specific homogenized medium with anisotropic conductivity \cite{sajat}. Promising results can be found in the literature. Besides the 2-D axial symmetric FE models with tape-level discretization, there exist 3-D mixed dimensional models in which the thin HTS tape is represented by interior boundary condition. Yet there are 3-D homogenized coil models based on anisotropic conductivity tensor, with the latter having diagonal form in a cylindrical frame. Common to all these solutions is that the total current is prescribed in each turn, and the coil voltage is computed by integration. It seems that no one in the literature has utilized the underlying spiral geometry in such homogenization yet. Thus we derived a specific anisotropic conductivity tensor for this purpose. Moreover the method makes voltage constraint on the coil terminals directly available.

In this work, homogenizing the geometry of the coil, and studying the accuracy of the stationary current flow model and magnetic field distribution was the main task on a less densely wound second generation HTS coil with lower number of turns, which is easier to handle. The validation was performed using both feasibility study and sensitivity analysis. Then the model was illustrated with more realistic parameters. The goal is naturally to simulate the quench phenomena considering the multilayer structure.