Uncertainty and worst-case expectation analysis for multiphysics QPR simulations

Quadrupole resonators (QPRs) serve to characterize superconducting samples. Like any cavity, during operation, they will deviate from the design geometry for various reasons. Those deviations can be static, stemming from manufacturing variations reflected in the manufacturing tolerances, or dynamic, such as electromagnetic radiation pressure (Lorentz detuning) or microphonics. As a result, a QPR's measurement accuracy and general operation can be severely limited. In particular, during operation, it became evident that the third operating mode of typical QPRs is mainly affected. In this work, by solving the underlying multiphysics problem with random input parameters, we predict the predominant sources of significant measurement bias in surface resistance. On the one hand, we employ the stochastic collocation method compound with the polynomial chaos expansion (PC-SCM) to quantify uncertainties in the physical model governed by a coupled electro-stress-heat problem. On the other hand, we explore the perturbation analysis to calculate the mean-worst-scenario bound of the merit functions due to the first-order truncation of the Taylor expansion around mean parameter values. The developed method allows us to study the effect of a small nonlinear deformation on the performance of the QPR. Finally, we discuss the simulation results and their implication for the operational conditions of the QPRs.