High-field Nb ₃ Sn dipoles generating more than 15 T are strongly required, whether it is for the future circular collider studies (CERN 16 T Development Program, CEA-CERN demonstrator) or for test stations (FRESCA2, HEPDipo). The use of magnets graded with different cables now becomes unavoidable to allow for more compact and cost-effective designs. This article presents a 2-D parametric study, which explores possible options for an optimal grading. The study uses analytical formulas for current sources to allow for fast and accurate parametric studies. Block coils are considered, using different cable sizes, and therefore, different current densities. Various parameters are also explored, such as cable combinations, current density ratios, conductor performance, and position of the blocks. The article shows in particular what are the optimal grading factors and amount of conductor required to reach a given bore field, considering margins on the load line, and limitations in current density for quench protection.

中文翻译：

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分级在Nb ₃ Sn高场区线圈偶极子中的应用

高场铌 ₃ 无论是用于未来的圆形对撞机研究（CERN 16 T开发计划，CEA-CERN演示器）还是用于测试站（FRESCA2，HEPDipo），都强烈要求产生超过15 T的锡偶极子。现在已经不可避免地要使用分级电缆不同的磁体，以实现更紧凑和更具成本效益的设计。本文介绍了二维参数研究，该研究探讨了最佳分级的可能选项。该研究使用电流源的分析公式来进行快速准确的参数研究。考虑使用不同的电缆尺寸以及因此不同的电流密度的块状线圈。还探索了各种参数，例如电缆组合，电流密度比，导体性能和块的位置。