A conduction cooled Magnesium diboride (MgB₂) based 1.5T MRI magnet system is proposed and extensive numerical studies has been performed by Baig et al.¹ Although, numerical computation has confirmed the required field homogeneity, the low failure strain of MgB₂ raises the questions of the feasibility of such system. However, the practicality of the system is promising as different compositions and configurations of composite MgB₂ wires have shown improved failure strain limit of 0.4% for tensile and -0.6% for compressive loading^2,3. The strain study of a complete 1.5T conduction cooled MgB₂ system has been studied previously where the wire material properties were approximated using simple ‘Rule of Mixture’ (ROM) formula to reduce the computational intensity.⁴ The use of ROM is a general approach to estimate the wire property values with acceptable inaccuracy that lays the groundwork for the multiscale modeling of the system from the wire length scale to the coil bundle length scale. In order to improve the accuracy of the multiscale model, numerical homogenization of the wire is important as it helps to improve the precision in the modeling of the coil bundle. This study considers three different homogenization approach— rule of mixture, transverse isotropy and orthotropy to model the composite wire at the wire length scale. Moving from the wire length scale to bundle length scale of the system, a 1.5T MgB₂ based conduction cooled system was analyzed for the variation in hoop strain development at the final stage, namely electromagnetic excitation that follows coil winding and thermal cooldown to 10K.An optimized electromagnetic design of the 1.5T MgB₂ magnet¹ has eight primary coils and two shield coils as shown in the quarter axisymmetric analysis in Figure 1. The shield coils which are larger in radius faces the maximum stress during electro-magnetic charging. Hence, investigation is restricted only to the shield coils. This coil has 28 layers of MgB₂ superconducting wire with a stainless steel mandrel 10 mm thick. The 36 filament MgB₂ wire (Figure 2) provided by Hypertech Research considered for the design is modeled and detailed in Table 1. The winding process is modeled in commercially available software package ANSYS APDL using the birth and death of elements, and subsequently cool down from 298K to 10K is modeled by applying -288K uniform temperature load. Magnetic charging is modeled by sequential coupling of Maxwell and Strain equations⁴. Figure 2 shows the total hoop strain developed at the time of electromagnetic charging. It is clear from the figure that considering simple ROM modeling of the composite wire underestimates the strain development in the wire bundle which is picked up if the transverse isotropic or orthotropic model is considered. Von Mises strain is also plotted in Figure 3 along with Hoop strain as some researchers have considered Von Mises strain as failure criteria.⁵The composite wire, if considered orthotropic, results in higher strains in the coil bundles which are maximum at the innermost layer of the bundle around -0.06%. If the Von Mises strain is considered, the strain is 0.07% at the innermost layer of the bundle. In both cases, the strain is well within the failure strain of MgB₂ wire in the range of -0.6% to 0.4%.