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

Aaron Gobeyn*, Wolfgang Ackermann, and Herbert De Gersem

  • *Contact author: aaron.gobeyn@tu-darmstadt.de
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Phys. Rev. Accel. Beams 29, 103802 – Published 30 October, 2026

DOI: https://doi.org/10.1103/hjqj-v5yc

Abstract

Bulk niobium has long been the material of choice for superconducting radio-frequency applications. An alternative approach is the superconductor-insulator-superconductor (SIS) multilayer structure, which enables the use of brittle high-Tc 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 nonflat geometries is expected to introduce macroscopic inhomogeneities in coating thickness. We model these variations using Gaussian random fields parameterized by a spatial correlation length 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 the quality factor—are computed. This procedure is repeated for eight correlation lengths, with 2048 samples per correlation length, where the resulting quality factors are recorded. Our results show that the quality factors follow a normal distribution. The standard deviation increases with the correlation length 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 correlation length, the quality factor may differ from the uniform case by 2%–6%.

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Phys. Rev. Accel. Beams 29, 103802– Published 30 October, 2026
  • Received 11 May 2026
  • Accepted 16 September 2026
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Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI.

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