An Analytical Methodology to Dimension Self-Supporting Structures in Cos-Theta Superconducting Accelerator Magnets

Analytical approaches for dimensioning self-supporting structures in cos-theta superconducting magnets are notably scarce in the literature, despite their interest. The dimensions of these structures influence both material costs and the spacing between the coils and the iron yoke, a parameter that can significantly impact the efficiency of the superconductor depending on the design. Therefore, an analytical methodology is proposed here to dimension the self-supporting structures of cos-theta magnets, usually collar-based, by limiting the radial deformation caused by their electromagnetic forces. This approach could enable a more efficient conceptual design phase, as well as the assessment of existing simulation models. The main goal of this article is to present the core concepts of this methodology and apply them to some examples to evaluate its potential. First, the dimensioning of a standalone dipole serves as a case guide, and then the methodology is tested on the well-known design of the Tevatron. Finally, it is applied to the particularly difficult case that sparked its development: the MCBXF orbit correctors required for the high luminosity large hadron collider (HL-LHC) upgrade. In these magnets, the nested configuration implies a challenging coupling between magnetic and mechanical designs, and the simulation results provide a valuable basis for comparison with the analytical calculations.