H Formulation for HTS
This section presents the implementations of the H Formulation on High critical Temperature Superconductors :
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General Case : Presents the H Formulation.
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Comsol Cylinder Axi : Presents the Test Case of Transient case with Comsol in axisymmetric coordinates
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H-ϕ Formulation : Presents the H-ϕ Formulation.
1. Description of the problem
The section describes a problem of magnetisation 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 H 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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\(E_c\) : threshold 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 :