Analytic Estimates of Magnetic Energy in Superconducting Quadrupoles

In this paper, we propose analytical formulae to determine the magnetic energy stored in superconducting quadrupoles made of sector coils. The study is based on the Fourier transformation of the current density flowing within the coils. The case of real magnets (i.e., magnets which are not made of pure sector coils) is treated and a heuristic corrective coefficient allowing taking into account the energy enhancement due to current grading is derived from a numerical study. We also introduce the effect of an unsaturated iron yoke on the stored energy and we discuss the issue of the yoke saturation.