The trend towards increasingly narrow apertures in multipole magnets poses a challenge to many conventional measurement methods. Consequently, these methods' applicability in small aperture multipole magnets is limited. However, the single stretched wire measurement technique has emerged as a promising alternative due to its minimal space requirements within the measurement domain. Therefore, this technique is well-suited for accurately measuring magnetic fields in small aperture magnets.

This study aims to introduce a novel approach for analyzing the gradient integral and multipole errors of the quadrupole magnet, to address the limitations associated with the current single stretched wire method (SSWM).

Firstly, a magnetic measurement system based on the single stretched wire method was constructed with two boasted key advantages: minimal space occupation within the measurement domain, and flexible motion modes. Then, leveraging these features, measurements of the four poles of a quadrupole magnet by employing a hyperbolic trajectory was acquired, and a new technique for analyzing both the gradient integral and multipole errors associated with the quadrupole magnet was developed. Finally, the feasibility of this SSWM was verified by comparing the results obtained from our system to those derived from the rotating coil method.

Measurement results of a quadrupole magnet with the inscribed radius of 11 mm and gradient of 100 T?m^-1 by SSWM show that the repeatability of three measurements is better than ±1.5×10^-4 which is less than one-third of the maximum value of multipole error of 5×10^-4, so it can meet the measurement requirements.

The methodology outlined in this study for constructing the measurement system and analyzing the resultant data offers a practical and effective solution for the future magnetic field measurements of small aperture magnets.