Electron-ion colliders (EIC) have been identified as an ideal tool to study the next frontier of nuclear physics the gluon force that holds the building blocks of matter together, and which is a fundamental component of the theory of Quantum Chromodynamics (QCD). Future electron-ion colliders under consideration can be based on the Energy Recovery Linac (ERL) architecture. The beam lines for this architecture could be built of the newly developed Non-Scaling Fixed Field Alternating Gradient (NS FFAG) structure, so that they can transfer multiple energies within the same aperture. This structure allows for the use of compact, economical quadupole permanent magnets. In this SBIR, we propose to design and to manufacture prototype quadrupole permanent magnets of focusing/defocusing combined function for use in this beam line. Wang NMR propose to design and build the focusing/defocusing quadrupole with a gradient strength of 50 T/m and with a beam gap of 16mm. The proposed permanent magnet material is SmCo because of its higher radiation resistance as compared to NdBFe2. The use of permanent magnets will reduce the overall cost. In Phase I, we shall take the recent design by Dr. Dejan Trbojevic, and then rerun Tosca code on the design to optimize the iron yoke with respect to the thickness of SmCo. In Phase I, we shall fabricate one prototype focusing/defocusing combined function quadruple. Wang NMR shall measure field quality dG/Go. In Phase II, based on Wang NMRs Phase I prototype experience, Wang NMR shall improve the design and fabricate a production quadruple, and design and incorporate coils for skew dipoles and normal quadrupole correctors, etc. In addition, we shall fabricate enough quadrupoles for one cell. The development of quadrupole permanent magnets is of fundamental importance for there application in the future electron-ion colliders. This accelerator structure will also advance the development of muon accelerators and allow for the development of compact, simplified, less expensive proton accelerators which will promote their use in areas such as proton cancer therapy, and for high-power proton drivers for tritium and neutron production, waste transmutation, driving a sub-critical nuclear reactor to produce energy, cargo contain inspection, and radioisotope production.