Phyisics Model

The field of modelling the superconducting behavior is very wide, in our software now just the London-model got implemented. The vector potential $\vec{A}$, and the superconducting current density $\vec{j_s}$, are related in the superconductor according to the London equation:

\[ \vec{j_s} = - \frac{1}{\mu_0 \lambda^2} \vec{A} \]

The $\lambda$ is the penetration depth in the superconductor. With the additional Maxwell equation:

\[ \nabla \times \mu^{-1} \nabla \times \vec{A} = \vec{j_{normal}} +\vec{j_s} \]

It results to the following linear equation:

\[ \nabla \times \mu^{-1} \nabla \times \vec{A} +\frac{1}{\mu_0 \lambda^2} \vec{A}= \vec{j_{normal}} \] with the $\vec{j_{normal}}$ source term.

Examples

2D Simulations

Superconducting wire in magnetic field