Magnetic field enhancement at a pit on the surface of a superconducting accelerating cavity

The thermal magnetic breakdown due to the magnetic field enhancement at a pit is the major obstacle to achieving a high accelerating field using a superconducting radio-frequency cavity. The well-type pit model has attracted attention as a model of the magnetic field enhancement at a pit, whose enhancement factor depends only on an edge radius normalized by the pit width. However, many of the pits found on cavity surfaces are not well type but have gentle slopes, and the impacts of the slope angle on the enhancement factor have not yet been well understood. In the present study, we introduce a model that can describe a pit with an arbitrary slope angle and evaluate its enhancement factor. A two-dimensional model is enough to describe the magnetic field enhancement at the pit. To evaluate the enhancement factor, an analytical method based on the conformal mapping was developed. The results are compared with those obtained by a simulation method, developed in this paper, that utilizes two-dimensional electrostatics. A general formula to evaluate the enhancement factor was derived, which agreed well with the simulation results. We found that not only the normalized edge radius but also the slope angle had a substantial impact on the enhancement factor. A pit with a gentle slope angle yields a much smaller enhancement factor than a well-type pit. The results can be applied to the calculation of the enhancement factors of real pits with arbitrary slope angles.