APECS: An Analytical Equations Toolkit for Magnet Design and Electromagnetic Analysis

There is a myriad of variables that must be considered when designing a superconducting magnet. Two of these are: the local magnetic field, dictating the response of the superconductor, and the mutual inductance matrix, dictating the generated voltage. These issues may be resolved with the help of finite element analysis tools, but this is not practical at the very beginning of coil design or when many concepts must be analysed quickly. Then comes the problem of robustly constructing the coil's winding pack such that it will operate as required. Analytical Python Electromagnetic Coil Simulator (APECS) offers one solution to the above. It uses accepted analytical and semi-numerical methods to calculate, at any point in space, the magnetic field generated by circular loop coils, such as a tokamak's poloidal field magnets, as well as straight-edge loop coils, such as a rectangular toroidal field magnet in a spherical tokamak. Combined with knowledge about the performance of the superconducting material and a user-specified cable design, APECS can construct a “minimum viable” winding pack for each poloidal field magnet to aid further analysis and design iteration. Despite that it cannot presently optimize the cable design or the thermo-hydraulics, superconductor/copper content, or the stress and failure, it is an invaluable tool used extensively in the design and analysis of the poloidal field (PF) magnet system on U.K.’s Spherical Tokamak for Energy Production (STEP).