A Formulation for HTS
This section presents the implementations of the A Formulation on High critical Temperature Superconductors :
-
Two Dimmensions Case : Presents the A Formulation in two dimmensions.
-
FreeFEM Cylinder 2D Magnetostatic : Presents the Test Case of Static case with FreeFEM
-
CFPDES Cylinder 2D Magnetostatic : Presents the Test Case of Static case with CFPDEs
-
Comsol Cylinder 2D Magnetostatic : Presents the Test Case of Static case with Comsol
-
GetDP Cylinder 2D Magnetostatic : Presents the Test Case of Static case with getDP
-
-
Axisymmetric Case : Presents the A Formulation in axisymmetric coordinates.
-
CFPDES Cylinder Axi : Presents the Test Case of Transient case with CFPDEs in axisymmetric coordinates
-
Test Case One Torus : Presents the Test Case of Transient case with FreeFEM in axisymmetric coordinates
-
1. Description of the problem
The section describes a problem of magnetization on a bulk cylinder made of a High critical Temperature Superconductor material :
The E-J Power Law define High critical Temperature Superconductors in the modeling. For the A Formulation, the E-J power law is defined in the electric conductivity \(\sigma\) :
With :
-
\(J\) : electric current density \((A/m^2)\)
-
\(E\) : electric filed \((V/m)\)
-
\(J_c\) : critical current density \((A/m^2)\) (the critical current is dependent of the temperature and magnetic field but here we will use it as a constant)
-
\(E_c\) : threshold electric field \((V/m)\)
-
\(n\) : material dependent exponent
If the electric current density is close to the critical density, the material starts to lose its superconducting properties :