Theoretical estimates of maximum fields in superconducting resonant radio frequency cavities: Stability theory, disorder, and laminates

TL;DR

This paper provides theoretical estimates for the maximum magnetic fields superconducting RF cavities can withstand before flux penetration, considering material properties, disorder, and layered structures, with implications for advanced superconducting materials.

Contribution

It introduces simplified estimates for the superheating field, discusses effects of anisotropy and disorder, and analyzes the potential of layered superconducting laminates to improve cavity performance.

Findings

Superheating field estimates align with experimental data.

Disorder and anisotropy significantly affect vortex entry.

Layered laminates may enhance cavity performance by controlling vortex dynamics.

Abstract

Theoretical limits to the performance of superconductors in high magnetic fields parallel to their surfaces are of key relevance to current and future accelerating cavities, especially those made of new higher-Tc materials such as Nb$_3$Sn, NbN, and MgB$_2$. Indeed, beyond the so-called superheating field $H_{\mathcal{sh}}$, flux will spontaneously penetrate even a perfect superconducting surface and ruin the performance. We present intuitive arguments and simple estimates for $H_{\mathcal{sh}}$, and combine them with our previous rigorous calculations, which we summarize. We briefly discuss experimental measurements of the superheating field, comparing to our estimates. We explore the effects of materials anisotropy and the danger of disorder in nucleating vortex entry. Will we need to control surface orientation in the layered compound MgB$_2$? Can we estimate theoretically whether dirt and defects make these new materials fundamentally more challenging to optimize than niobium? Finally, we discuss and analyze recent proposals to use thin superconducting layers or laminates to enhance the performance of superconducting cavities. Flux entering a laminate can lead to so-called pancake vortices; we consider the physics of the dislocation motion and potential re-annihilation or stabilization of these vortices after their entry.