T-A Formulation for HTS

This section presents the implementations of the T-A Formulation on High critical Temperature Superconductors :

  • General Case : Presents the T-A Formulation.

  • Axisymmetric Case : Presents the T-A Formulation in axisymmetric coordinates.

    • Comsol Pancake : Presents the Test Case of T-A formulation with Comsol in axisymmetric coordinates

    • GetDP Pancake : Presents the Test Case of T-A formulation with getDP in axisymmetric coordinates

    • Comsol Tapes Homogeneous : Presents the Test Case of T-A homogeneous formulation with Comsol in axisymmetric coordinates

    • CFPDES Tapes Homogeneous : Presents the Test Case of T-A homogeneous formulation with getDP in axisymmetric coordinates

1. Description of the problem

The section describes a problem of transport current on a Pancake made of stacked High critical Temperature Superconducting tapes :

pancake2
Figure 1. Pancake

The E-J Power Law define High critical Temperature Superconductors in the modeling. For the T-A Formulation the E-J power law is defined in the electric resistivity \(\rho\) :

E-J power law
\[E=\rho(J)J=\frac{E_c}{J_c}\left(\frac{\mid\mid J \mid\mid}{J_c}\right)^{(n)}J\]

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)

  • \(E_c\) : treshold 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 :

jc ec