The lecture will introduce the main modelling technique used in the design of superconducting electrical coils for commercial and research applications. The superconducting capability is, primarily, used to carry larger currents than possible with copper coils to produce magnetic fields necessary for the operation of the equipment.
After a review of requirements for some of the major applications of both low (LTS) and high temperature superconducting (HTS) coils at application level, the latter part of the lecture will concentrate on models where the superconducting nature of the material must be included.
In electromagnetic field modelling at application level, the superconducting properties of the material are not usually captured and superconducting coils can be treated identically to resistive coils, allowing the magnetic field from coil systems in free-space to be calculated by the Biot-Savart equation. However, in most practical magnetic systems, other materials also exist (shields, cryostats, vacuum vessels, magnetic cores, structural steel etc.) and the Biot-Savart expression alone is not sufficient to calculate the field, requiring a discrete numerical model to be used.
The most commonly used is the finite element method (FEM). Solutions of magnetic field equations using FEM will be briefly explained. A range of examples, including MRI systems, accelerator magnets, fusion devices and electrical machines will illustrate the advantage of this method, as well as some of the multiphysics design issues associated with using superconducting coils in these applications.
The second part of the lecture will cover application modelling where the superconducting properties of the coil must be included. Superconducting quench in LTS coils is an important consideration for designers and a pragmatic approach to simulating this using FEM will be explained. Modelling of a quench in an HTS wire will also be covered.