Field-dependent surface resistance for superconducting niobium accelerating cavities

Superconducting cavities made from niobium allow accelerating gradients of about 50 MV/m close to the theoretical limit. Quite often, however, the rf losses increase with the gradient faster than quadratic. This observation is equivalent with a decrease of the quality factor Q with the gradient, called ``Q slope'' for intermediate gradients, and ``Q drop'' for larger ones. The paper provides an explanation by an elementary model based on the two-fluid theory of rf superconductivity and applies it to experimental data for a large variety of cavity tests.