Numerical quality factor statistics for SRF cavities with spatially inhomogeneous multilayer coatings modeled by Gaussian random fields

TL;DR

This study models the impact of spatially inhomogeneous multilayer coatings, represented by Gaussian random fields, on the quality factors of SRF cavities, revealing that inhomogeneity can cause measurable variations.

Contribution

It introduces a stochastic modeling approach for coating inhomogeneities in SRF cavities and analyzes their effect on quality factors across different length scales.

Findings

Quality factors follow a normal distribution.

Standard deviation increases with inhomogeneity length scale.

Quality factor variations can reach 2-6% depending on inhomogeneity.

Abstract

Bulk niobium has long been the material of choice for superconducting radio-frequency applications. An alternative approach is the superconductor-insulator-superconductor multilayer structure, which enables the use of brittle high-$T_c$ materials such as NbTiN. At present, SIS coatings are limited to flat samples, with the single-cell TESLA cavity representing a key milestone. Extending coating processes to non-flat geometries is expected to introduce macroscopic inhomogeneities in coating thickness. We model these variations using Gaussian random fields parametrized by a length scale, and generated by solving a stochastic partial differential equation. The resulting field is incorporated into the boundary condition of the cavity eigenvalue problem, from which quantities of interest -- such as resonant frequency and quality factor -- are computed. This procedure is repeated for eight length scales, with \num{2048} samples per length scale, where the resulting quality factors are recorded. Our results show that the quality factors follow a normal distribution. The standard deviation increases with the length scale and can be statistically distinguished. In contrast, the mean values remain largely unchanged, with only a few significant differences. In extreme cases, depending on the length scale, the quality factor may differ from the uniform case by \SIrange{2}{6}{\percent}.