# Superconducting wire

 2D and 3D models of superconducting wires.

To run the model, open helix.pro with Gmsh.

The model uses an H-formulation and the Gmsh cohomology solver [1][2]. The nonlinear resistivity $\rho=\frac{E_c}{J_c}(\frac{\|\vec{J}\|}{J_c})^{n-1}$ in the superconducting filaments is linearized as in [3]. The number and layers of superconducting filaments, the twist pitch as well as the radius of the conducting matrix are parametrizable, and the model can be solved both in 2D and in 3D.

## References

1. M. Pellikka, S. Suuriniemi, L. Kettunen and C. Geuzaine, Homology and cohomology computation in finite element modeling. SIAM Journal on Scientific Computing 35(5), pp. 1195-1214, 2013.
2. A. Stenvall, V. Lahtinen and M. Lyly. An H-formulation-based three-dimensional hysteresis loss modelling tool in a simulation including time varying applied field and transport current: the fundamental problem and its solution. Supercond. Sci. Technol. 27 (2014) 104004 (7pp)
3. A. Kameni, J. Lambrechts, J.-F. Remacle, S. Mezani, F. Bouillaut and C. Geuzaine. Discontinuous Galerkin Method for Computing Induced Fields in Superconducting Materials. IEEE Transactions on Magnetics 48(2), pp 591-594, 2012.
 Model developed by C. Geuzaine, A. Kameni and A. Stenvall.