Discrepancies in Modeling Magnets Utilizing ${\rm MgB}_{2}$ Conductor With Ferro- and Non-Magnetic Matrix Configurations

The electromagnetic properties of an ${\rm MgB}_{2}$ superconductor depend on a matrix metal. Therefore, the design principles of an ${\rm MgB}_{2}$ magnet are greatly affected by the matrix metal of the conductor. A ferromagnetic matrix requires a complex non-linear modeling whereas in case of non-magnetic matrix the models developed for LTS magnets can be adopted. In this paper a design analyses of linear and non-linear ${\rm MgB}_{2}$ coils are compared. Also, feasibility of linear model in non-linear case is studied. As an example a design scheme of a $\mu$-SMES solenoid with ${\rm MgB}_{2}$-W/Fe and ${\rm MgB}_{2}$-SiC/Nb/AgMg wires is outlined.