# Depth profile of London length induced by nonuniform scattering rate maximizing breakdown magnetic field in type II superconductors

## TL;DR

This paper investigates how nonuniform depth profiles of the scattering rate in type II superconductors can optimize the London penetration depth to enhance the breakdown magnetic field, crucial for superconducting RF cavity performance.

## Contribution

It introduces an optimal depth profile of the London penetration depth that maximizes the breakdown magnetic field by ensuring the screening current reaches the depairing limit uniformly.

## Key findings

- Optimal profile involves a near-linear decrease of the London penetration depth.
- Significant enhancement of the breakdown field requires large increases in the London length.
- Thermodynamic field remains unaffected by the nonuniform scattering rate profile.

## Abstract

The breakdown magnetic field is the key parameter which determines the performance of superconducting radio-frequency cavities. This is the maximum field up to which the Meissner state remains stable and in uniform material, it is approximately given by the thermodynamic field. There are several recent suggestions to use nonuniform structures to enhance the breakdown field. One of possible realizations of such structure is depth profile of the scattering rate which, in the first approximation, modifies the London penetration depth but does not change the thermodynamic field. In this paper, we evaluate the optimal profile of the London penetration depth for which the screening current density reaches the local depairing value \emph{simultaneously at every point within finite-size region}. Such profile is realized for close-to-linear decrease of the London penetration depth within the length scale proportional to its value at the surface. Achieving noticeable enhancement of the breakdown field, however, requires strong enhancement of the London length within large region without affecting the thermodynamic field.