An analytical approach to modeling the effect of magnetic permeable materials on the magnetic fields produced by coils

Creating precise magnetic fields is crucial for the successful operation of a magnetic confinement device. Vacuum fields from electromagnetic coils can be inexpensively modeled with high fidelity using the Biot-Savart law, but fields in the presence of magnetic permeable materials are difficult to model analytically. As future plasma plants will necessarily have such materials in the form of blankets, it is important to have fast, high fidelity methods to model these magnetic fields in order to include these corrections in the coil optimization process.

We present an analytical approach for determining the magnetic field in the presence of magnetic permeable materials in blanket geometries. Using this approach, we find solutions to the relevant Poisson’s equation in three separate topologies: the volume bounded by the innermost blanket surface, the volume of any given blanket layer, and the volume outside the outermost blanket layer. Methods for determining all the necessary coefficients are presented in a way which allows for computational implementation.