Since version 2026, Flux 3D and Flux PEEC are no longer available.
Please use SimLab to create a new 3D project or to import an existing Flux 3D project.
Please use SimLab to create a new PEEC project (not possible to import an existing Flux PEEC project).
/!\ Documentation updates are in progress – some mentions of 3D may still appear.
Superconductor: standard model (power law)
Introduction
To take into account the superconducting behavior of materials, Flux offers a specific model.
Power law
Superconducting materials have a highly nonlinear current voltage characteristic. The relationship between the electric field and the current can be described under the form of a power law:
(1)
The graphical form of such a law for different values of n is presented in the figure to the right.
Starting from relationship (1), we can write the resistivity for a superconductor by the following function:
(2)
where:
- Ec is the critical electric field [V/m]
- Jc0 is the critical current density [A/mm2]
- n0 is an exponent
- ρ0 is an additional resistivity [Ω .m]
Dependence on B, dependence on T
The critical current density Jc and the exponent n are the quantities that can strongly depend on the magnetic flux density B or the temperature T.
Thus the sub-models are provided to take into account these dependencies.