Calculating the field dependent surface resistance from quality factor data

The quality factor of an RF cavity and the surface resistance are typically related with a constant geometry factor. The implicit assumption made is that the surface resistance is field independent, which is however not observed experimentally in superconducting cavities. The approximation error due to this assumption becomes larger the less homogeneous the magnetic field distribution along the cavity walls is. In this paper we calculate the surface resistance error for different cavity types. Correction factors as well as a numerical method to correct for this error are presente