Analysis and measurement of dimensional changes in the bronze-processed Nb₃Sn conductor during heat treatment

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.

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.

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.

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.