青铜法Nb₃Sn导线热处理后的尺寸膨胀对高场强超导磁体, 特别是14 T及以上的超高场强磁共振成像(MRI)磁体的设计和制作提出了挑战。针对一个14 T动物MRI磁体, 为获得其中NbTi-CuNi加强型青铜法Nb₃Sn导线热处理后的尺寸变化规律, 该文根据NbTi-CuNi加强型青铜法Nb₃Sn导线在热处理升降温阶段的膨胀率差异, 计算了其热处理后的长度变化率, 并基于热处理过程中Nb₃Sn导线相变膨胀的机理, 预测了其热处理后的导线横截面积变化范围。计算了结果表明, 热处理后Nb₃Sn导线的长度变化率为0.5%, 横截面积变化范围为0~4.7%。设计并制作了测量Nb₃Sn单层螺线管线圈周长变化率的实验装置, 测量了使用NbTi-CuNi加强型青铜法Nb₃Sn导线绕制的单层螺线管线圈和直导线在热处理后的尺寸变化率。测量结果表明, 单层线圈和直导线热处理后的长度变化率分别为0.55%和0.52%, 导线的横截面积变化率分别为1.98%和2.22%。平均之后得到NbTi-CuNi加强型青铜法Nb₃Sn导线热处理后的长度和横截面积的变化率, 并据此讨论了14 T动物MRI磁体中Nb₃Sn线圈热处理后尺寸膨胀对磁体电磁性能的影响。

Objective: The dimensional expansion of bronze-processed Nb₃Sn wires during heat treatment presents difficulties in the design and fabrication of high-field superconducting magnets, especially for ultrahigh-field magnetic resonance imaging (MRI) magnets at 14 T and above. Thus, the characteristics of the dimensional changes in the bronze-processed Nb₃Sn wires during heat treatment must be determined. This study considered bronze-processed Nb₃Sn wires reinforced with NbTi-CuNi in a 14 T animal MRI magnet as an example to analyze its dimensional change during heat treatment. The dimensional change rates of the Nb₃Sn wire were used as a basis to discuss the influence of the dimensional expansion of the Nb₃Sn coil during heat treatment on the electromagnetic properties of the 14 T animal MRI magnet. Methods: The volume ratio of each component in the Nb₃Sn wire was analyzed before and after heat treatment. Based on the material properties of each component of the Nb₃Sn wire, the rate of change in length during the heating and cooling stages of heat treatment was calculated using an established finite element model. The sum represents the rate of length change during heat treatment. Based on the phase transformation mechanism of Nb₃Sn wires during heat treatment, the ratio of voids in the Nb₃Sn wire during heat treatment was calculated, and that of each component of the wire was added to determine the range of changes in the cross-sectional area of the Nb₃Sn wire during heat treatment. An originally designed experimental apparatus was built to measure the change rate of the circumference of the Nb₃Sn single-layer solenoid coil during heat treatment. The measurement results for the single-layer solenoid coil and straight wire were compared. In addition, the measurement findings were compared with the values obtained through calculation. Based on the average dimensional change rates of Nb₃Sn wires, we calculated the dimensional expansion of the Nb₃Sn coil in a 14 T animal MRI magnet during heat treatment and determined the magnetic field homogeneity and radial Lorentz force along the eccentric direction after heat treatment. Results: The calculation results indicate that the wire had a length change rate of 0.5% during heat treatment and a cross-sectional area change ranging between 0%-4.7%. According to the measurement results, the length change rates of the single-layer coil and straight wire during heat treatment were 0.55% and 0.52%, respectively, whereas the cross-sectional area change rates of the wires were 1.98% and 2.22%, respectively. The expansion of the inner diameter, outer diameter, and axial length of the Nb₃Sn coil in the 14 T animal MRI magnet during heat treatment reached 1.19, 2.04, and 7.44 mm, respectively. The magnetic field homogeneity of the magnet changed from 1.1×10^-6@6 cm DSV to 31×10^-6@6 cm DSV and 45×10^-6@6 cm DSV in the cases of zero radial eccentricity and a radial eccentricity of 0.595 mm in the Nb₃Sn coil. In addition, the radial eccentricity of the Nb₃Sn coil will produce a 1.9×10⁴ N Lorentz force along the eccentricity direction. Conclusions: As the dimensional change rates of the single-layer coil and straight wire during heat treatment were the same, the effect of coil winding on the dimensional change of the Nb₃Sn wires during heat treatment was negligible. Moreover, the measured change rate of the wire length was similar to the calculation result, and the measurement finding of the change rate of the wire cross-sectional area fell within the calculation range.