Articles techniques et présentations

High-temperature superconductor (HTS) technology is more and more commercially exploited, mainly for nuclear fusion reactors. The demand for HTS tape is met by multiple commercial manufacturers; there is a mature production process. With this technology now available, some other industries are seeing if they can use HTS for their benefit. For example, aircraft electrification research is investigating HTS technology to enable a big step in performance in electric power distribution and electric motors. Simulation of the detailed current distribution in superconductors is useful to calculate for example force densities and losses. We have used such simulations for practical applications in fusion reactors and for superconducting actuators, for example to calculate force densities and loss densities. We will give an impression of the physics and modelling techniques using some simplified toy models.

We will shortly explain the phenomenological behavior of currents in a superconductor. Notice that a large conductivity implies a small skin depth. Going to the extreme of a perfect conductor one has a skin depth of 0. For a superconductor this means even in the DC limit currents run near the surface. This means that any change in current will be concentrated on the surface of the HTS material. These surface currents will locally reach the critical current density of the HTS material, which means that the HTS locally becomes resistive. The electrical resistance changes dramatically when near the critical current density. This strongly nonlinear physics is numerically challenging, but moreover it causes hysteresis effects requiring time domain simulation.

So-called AC losses occur in superconductors whenever there is a time dependence of the current fed through the conductor itself or due to some external field inducing currents. The heat that is produced needs to be removed from the cryogenic environment. If cooling power is insufficient, the heating can cause the material to quench, i.e. cease being superconducting, which further increases the heating to cause a thermal runaway.

The MFH interface from the AC/DC Module supports a nonlinear relation between the current and electric field, such that it can be used to simulate HTS materials, and is based on the so-called H-formulation. In the application library there is an example of this: the superconducting wire. Researchers have proposed alternative mathematical formulations of the electromagnetic field and constitutive relations, attempting to improve performance of simulating HTS materials. These formulations can be implemented in COMSOL® through custom weak forms, or by modifying and combining the standard AC/DC Module interfaces. Each of these so-called mixed formulations has its own advantages and disadvantages. For every calculation this has to be considered to choose an appropriate formulation.