### Superconductor Modelling

For FEM modelling we are using two commercial software
packages, FLUX2D and FLUX3D, produced by CEDRAT.
Despite the similar name they work in quite different way. The former is used
for 2D simulations, the latter may be used both in 2D and 3D.

One of the most important application of superconductivity is the production of
long electric conductors. In order to reduce the complexity of the problem and
the computation time, it is therefore possible to assume that the physical and
geometrical properties do not vary along the length of the conductors, which may
be considered as infinitely long. The 2D simulations is therefore performed on
the transversal cross-section.

Nonetheless in some cases the 2D simplification cannot take into account either geometries or physical effect which are typically 3D.

##### Here below you can find some examples of typical FEM computations:

- Different arrangements of the filaments inside tapes and wires (FLUX2D)
- Coupling effect in external magnetic field (FLUX3D)
- Current distributions in 3D geometries (FLUX3D)

##### Different arrangements of the filaments

##### Coupling effect

The presence of a magnetic field induces current loops in the superconductor(a). If the field rate is sufficiently high the induced voltage is sufficient to overcome the resistive drop across the matrix: the loop is closed through the silver matrix and the current flows in opposite direction in each filament (b). Since the resistivity of the silver is much higher compared to superconductor's one, this gives an important contribution to the total ac losses. The coupling effect usually depends on several parameters: the field variation rate, the resistivity of the matrix material, the size of the filaments, the critical current density and the length of the superconductor.

The next picture shows the coupling current in the uncoupled (a) and coupled (b) case. In order to reduce the computation time only 1/8 of the full geometry has been considered. Conditions of symmetry have been applied on the three main planes (XY,XZ, YZ).

##### Current distributions in 3D geometries

The next two pictures show two examples of typical 3D geometries which can be simulated only by FLUX3D