Methodology for the structural design of single spoke accelerating cavities at Fermilab

Fermilab is planning to upgrade its accelerator complex to deliver a more powerful and intense proton-beam for neutrino experiments. In the framework of the so-called Proton Improvement Plan-II (PIP-II), we are designing and developing a cryomodule containing superconducting accelerating cavities, the Single Spoke Resonators of type 1 (SSR1). In this paper, we present the sequence of analysis and calculations performed for the structural design of these cavities, using the rules of the American Society of Mechanical Engineers (ASME) Boiler and Pressure Vessel Code (BPVC). The lack of an accepted procedure for addressing the design, fabrication, and inspection of such unique pressure vessels makes the task demanding and challenging every time. Several factors such as exotic materials, unqualified brazing procedures, limited nondestructive examination, and the general R&D nature of these early generations of cavity design, conspire to make it impractical to obtain full compliance with all ASME BPVC requirements. However, the presented approach allowed us to validate the design of this new generation of single spoke cavities with values of maximum allowable working pressure that exceeds the safety requirements. This set of rules could be used as a starting point for the structural design and development of similar objects.