Abstract-It can be shown that, by superposing two solenoid-like thin windings that are oppositely skewed (tilted) with respect to the bore axis, the combined current density on the surface is "costheta" like and the resulting magnetic field in the bore is a pure dipole. As a proof of principle, such a magnet was designed, built and tested as part of a summer undergraduate intern project. The measured field in the 25mm bore, 4 single strand layers using NbTi superconductor, exceeded 1 T. The simplicity of this high field quality design, void of typical wedges end-spacers and coil assembly, is especially suitable for insert-coils using High Temperature Superconducting wire as well as for low cost superconducting accelerator magnets for High Energy Physics. Details of the design, construction and test are reported.Index Terms-Superconducting magnet, pure dipole, insert magnet, tilted solenoid.
I. INTRODUCTIONn a published paper by D.I. Meyer and R. Flasck in 1970 [1] the authors discussed the magnetic field resulting from the superposition of two oppositely skewed (tilted) solenoids with respect to the bore axis (Fig. 1) presently building a similar quadrupole magnet. Advantages of this concept are as follows: 1) high field quality in an extended dynamic range, 2) no field optimization required, 3) small number of components -wedges and spacers not needed, 4) coil assembly not needed (all poles are wound together around a single bore), 5) small bore sizes not limiting "cos-theta" windings, 6) continuous windings and ease of magnet "grading". There are also other open issues such as magnet protection and pre-stress that will need to be addressed in the future. The concept can work well for "stand alone" accelerator magnet as well as insert coils to existing magnets. The technology is particularly suitable for Nb 3 Sn conductor as well as high temperature superconducting wires. In section II we give a short mathematical proof addressing the perfect dipole quality followed, in section III, with details on the magnet design and construction. In section IV we report test results and draw final conclusions.
A. Mathematical ModelA simplified mathematical proof is used to show that skewed windings on the surface of a cylindrical correspond to an axial current-density distribution that is ϑ cos like, and therefore produce a "pure" dipole field. The current density flow lines that are distributed on the surface of the cylinder are elliptical (inclination angle α with respect to the cylinder axis) with flow lines coordinates expressed as (see Fig. 1-2 Since the current density is divergence free,