An Actively Shielded 1.5T MgB$_2$ MRI Magnet Design*

Superconducting magnets for MRI are often constructed with NbTi wire cooled below 4.2K using liquid helium. As helium costs have more than tripled in the last decade, there is a need for a cryogen-free conduction-cooled alternative. A key reason for pursuing MgB$_2$ superconductor wire in the design of MRI magnets is its superior critical current compared to NbTi over a temperature range of 10-15K. We present a 1.5T whole body actively shielded main magnet design assuming second-generation multifilament MgB$_2$ wire using an improved functional approach. The design exhibits 4 pairs of primary bundles and 1 pair of shielding bundles with an inner (outer) diameter of 1.1 (1.89)m and a length of 1.54m. The imaging volume is 45cm with a maximum of 9ppm inhomogeneity. The wire dimension is assumed to be 1mm$^2$ and the wire current is 135A. The maximum field on a wire is found to be 4.1T well below the critical field value of approximately 6T at 10K for the second-generation wire. The 5-Gauss footprint for the new magnet is found to be 2.7 (3.7)m in the radial (axial) direction. The maximum hoop stress and axial force on a bundle, respectively, are 82.9MPa and 2680.2kN. Trade-offs for the reduction of any given parameter are analyzed.