Multilayer model for coatings with arbitrary layers for superconducting radio-frequency applications

TL;DR

This paper generalizes the multilayer model for superconducting structures to arbitrary layer sequences, accounting for all losses, and analyzes optimal configurations and modeling of transition regions for RF applications.

Contribution

It extends the multilayer model to arbitrary layer types and sequences, including losses, and introduces virtual layers for transition regions in superconducting structures.

Findings

Optimal configuration is the single-layer case with minimal performance penalty for thin coatings.

Thicker transition layers degrade maximum applicable field and increase effective penetration depth.

The model incorporates surface impedance and loss contributions, suitable for finite element simulations.

Abstract

We extend the multilayer model of \etal{Kubo} for superconductor-insulator-superconductor (SIS) structures in two ways: first, by generalizing it to arbitrary sequences of layers of arbitrary type, i.e. superconducting, normal conducting, and insulating; and second, by accounting for all contributions, including ohmic losses and dielectric effects. We examine the maximum applicable field for $(\text{SI})^n\text{S}$ structures. We find that the optimum configuration corresponds to the $n=1$ case. However, the thickness of the superconducting coating layers can be reduced to below their penetration depth with minor performance penalty. We discuss the ability to model transitions in SS bilayers by introducing a set of virtual layers that represent the transition region through interpolated parameters. We find degradation of the maximum applicable field with thicker transition layers, and a larger effective penetration depth of the electromagnetic fields. Furthermore, the surface impedance of the multilayer structure is calculated using the Leontovich boundary condition, yielding a formulation suitable for integration into finite element simulations. Additionally, the Poynting theorem is used to determine the loss contributions of individual layers.