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The breakdown magnetic field is the key parameter which determines theperformance of superconducting radio-frequency cavities. This is the maximumfield up to which the Meissner state remains stable and in uniform material, itis approximately given by the thermodynamic field. There are several recentsuggestions to use nonuniform structures to enhance the breakdown field. One ofpossible realizations of such structure is depth profile of the scattering ratewhich, in the first approximation, modifies the London penetration depth butdoes not change the thermodynamic field. In this paper, we evaluate the optimalprofile of the London penetration depth for which the screening current densityreaches the local depairing value \emph{simultaneously at every point withinfinite-size region}. Such profile is realized for close-to-linear decrease ofthe London penetration depth within the length scale proportional to its valueat the surface. Achieving noticeable enhancement of the breakdown field,however, requires strong enhancement of the London length within large regionwithout affecting the thermodynamic field.

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