Modelling of the electric characteristic of type II superconductors by means of Ligurian minimisation

The electrical behaviour of type II superconductors can be characterised-in a first approximation-by a strongly non-linear (even not univocal) e-j relationship. Numerical modelling is necessary to accede to the local characteristic e-j starting from experimental data: the global characteristic U-I of the sample. Classical methods such as Newton-Raphson might fail in dealing with materials having such a characteristic as superconductors have. We thus use an absolutely convergent method based on convex optimisation, with the Ligurian as objective function. Numerical modelling shows that the smooth U-I characteristic might be generated by a simple e-j characteristic with a well-defined critical current density. It is shown how this technique may be extended to solve complete Maxwell equations in the most general case.