Design methods of the spherical quadrupole magnets and sextupole magnets

In high-energy physics, medical treatments, and space detections, quadrupole field distributions and sextupole field distributions are often required over a large spherical volume. Traditionally, these fields can be generated with cylindrical magnets. In comparison with cylindrical magnets, the spherical magnets have the advantages of smaller values of inductances, lower energy storage, and less magnetic flux leakage. To satisfy these special fields requirements, this paper describes the design methods of spherical magnets. The basic method derives from the target field approach that has been used to solve many of the inverse electromagnetic problems. Applying this approach, this paper has accomplished the design of spherical quadrupole magnets and sextupole magnets. In engineering and manufacture, the above calculation results are hard to utilize directly because of the complex magnet structures and, thus, high fabrication costs. After redesign and optimization on the above calculation results, this paper has also completed the construction of a modified spherical quadrupole magnet that has constant current distributions. This novel type of quadrupole magnet can generate nearly linear gradient fields and is easy to fabricate in engineering. Simulation and test results of this magnet are also presented