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The field limit of superconducting radio-frequency cavity made of type IIsuperconductor with a large Ginzburg-Landau parameter is studied with takingeffects of nano-scale surface topography into account. If the surface isideally flat, the field limit is imposed by the superheating field. On thesurface of cavity, however, nano-defects almost continuously distribute andsuppress the superheating field everywhere. The field limit is imposed by aneffective superheating field given by the product of the superheating field forideal flat surface and a suppression factor that contains effects ofnano-defects. A nano-defect is modeled by a triangular groove with a depthsmaller than the penetration depth. An analytical formula for the suppressionfactor of bulk and multilayer superconductors are derived in the framework ofthe London theory. As an immediate application, the suppression factor of thedirty Nb processed by the electropolishing is evaluated by using results ofsurface topographic study. The estimated field limit is consistent with thepresent record field of nitrogen-doped Nb cavities. Suppression factors ofsurfaces of other bulk and multilayer superconductors, and those after varioussurface processing technologies can also be evaluated by using the formula.

Field limit and nano-scale surface topography of superconducting radio-frequency cavity made of extreme type II superconductor