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Because the optimization used by Xu and others is convex, it represents a true optimal solution and we must relax other constraints in order to achieve shorter magnets. In the text that follows, we replicate Xu et al.’s analysis [102] for L_optimal as a function of DSV and magnet diameter for a D = 1.1 m magnet but also examined optimized designs with homogeneity targets between 1 ppm and 10 000 ppm. Figure 3.6 shows the result of this analysis. When a length-optimized design is chosen from the knee of the cost vs. length L-curve, the cost of an optimized design can be plotted as a function of the unitless L/DSV for a given homogeneity target. Figure 3.6 shows this result, which informs the potential improvements in magnet length achievable if imaging could be performed in less homogeneous fields. Unfortunately, substantial relaxation in homogeneity is needed to get a significant reduction in magnet length. For example, relaxing the 1 ppm specification to 1000 ppm reduces the magnet length from 2.92 to 2.15 in normalized units – a 26% reduction. Thus, superconducting solenoid magnets, as they are currently envisioned, are not likely to significantly change in geometry.

Figure 3.6 Tradeoffs in superconducting solenoid optimizations following the optimization of Xu et al.[] The wire cost is seen to rise significantly as the magnet length is shortened (here shown in units of the imaging volume diameter).The left graph shows the wire length–length tradeoff for different homogeneity constraints. Taking the points on the “knee” of these L-curves allows the plot of magnet length vs. homogeneity (right-hand graph).