Overview of the Electromagnetic Optimization Literature of Superconducting Solenoidal Magnets and Coils

This article is a narrative and systematic review on the electromagnetic optimization literature of superconducting solenoidal magnets and coils. Superconducting solenoids are the basis of magnetic resonance imaging machines and superconducting energy storage systems. As the literature has evolved and many optimization techniques have been used, in this article, we review the evolution of techniques used to achieve a defined field homogeneity to reduce conductor's length, achieve a defined field intensity, increase stored energy, and optimize secondary aspects. We present chronologically, discuss, and compare the referenced literature, which is also categorized in tables based on the optimization target. The tables present the optimization type, the used technique, the contribution of this article, and the material. We discuss the existing literature gaps and the optimization techniques applied for designing the two most common machines, i.e., magnetic resonance imaging and superconducting magnetic energy storage devices, and we conclude that modern techniques are not used frequently compared with the techniques that predate the year 2000.