Computer modelling of high-temperature superconductors using an A-V formulation

Numerical methods for calculating the current and field distribution in high-temperature superconductors under non-uniform time-varying fields are being investigated. The highly non-linear behaviour of superconductors makes them difficult to analyse and computationally expensive. This non-linear behaviour is often accounted for through a non-linear E-J constitutive law. This paper proposes a fast method based on the finite element method to solve 2D and axially symmetric problems that contain superconducting materials. An E-J power law together with an A-V formulation is used to calculate the induction of currents in the superconductor due to time-varying external magnetic fields or forced transport current. Experimental data of a magnet-above-superconductor system is obtained in order to validate the model. In the experimental set-up a magnet is brought towards a superconducting puck at different speed rates and is also vibrated on top of it. The force between the magnet and the superconductor is measured and is found to vary with both time and frequency of excitation.