Patil, M.S. Compton, C. Kim, S.H. Miller, S.J. Xu, T. JACoW Publishing Geneva, Switzerland 2673-5504 978-3-95450-234-9 10.18429/JACoW-SRF2023-TUPTB040 English 501-506 cavity SRF gun niobium vacuum Contribution to a conference proceedings 2023 2023-09 https://doi.org/10.18429/JACoW-SRF2023-TUPTB040 https://jacow.org/srf2023/papers/tuptb040.pdf A prototype SRF gun is currently being designed at FRIB, MSU for the Low Emittance Injector of the Linac Coherent Light Source high energy upgrade at SLAC. This employs a 185.7 MHz superconducting quarter-wave resonator (QWR). The mechanical design of this cavity has been optimized for performance and to comply with ASME Section VIII, Div 2, Design by analysis requirements. This paper presents the various design by analysis procedures and how they have been adopted for the SRF gun cavity design.