  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.
