T-A Formulation for HTS
This section presents the implementations of the T-A Formulation on High critical Temperature Superconductors :
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General Case : Presents the T-A Formulation.
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Axisymmetric Case : Presents the T-A Formulation in axisymmetric coordinates.
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Comsol Pancake : Presents the Test Case of T-A formulation with Comsol in axisymmetric coordinates
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GetDP Pancake : Presents the Test Case of T-A formulation with getDP in axisymmetric coordinates
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Comsol Tapes Homogeneous : Presents the Test Case of T-A homogeneous formulation with Comsol in axisymmetric coordinates
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CFPDES Tapes Homogeneous : Presents the Test Case of T-A homogeneous formulation with getDP in axisymmetric coordinates
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1. Description of the problem
The section describes a problem of transport current on a Pancake made of stacked High critical Temperature Superconducting tapes :
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 \(\rho\) :
With :
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\(J\) : electric current density \((A/m^2)\)
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\(E\) : electric filed \((V/m)\)
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\(J_c\) : 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)
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\(E_c\) : treshold electric field \((V/m)\)
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\(n\) : material dependent exponent
If the electric current density is close to the critical density, the material starts to lose its superconducting properties :