Study on Ampere-Turns of superconducting dipole and quadrupole magnets based on sector coils

General expressions of Ampere-Turns for superconducting dipole and quadrupole magnets based on sector coils are proposed. According to the magnetic field generated by simplified coil layouts using the line current theory, the required excitation current to achieve the desired field strength in the aperture is calculated. The contribution of magnetic field by an iron yoke is taken into account by using the image current method. The validity of derived equations is confirmed by applications to main superconducting magnets which have been built in several high energy accelerators. The proposed analytical expressions provide a simple relationship among the bore field, main dimensions of the magnet, and the total excitation current. These expressions are complementary to the existing method in the electromagnetic design, and are shown to be quite similar to those of conventional magnets. Finally, the comparison of Ampere-Turns between superconducting magnets and conventional magnets is presented.