Geometrical corrections for accurate fitting of the field dependent surface resistance for superconducting accelerating cavities

The different processes at the origin of the dependence of the surface resistance with the RF magnetic field are still not fully understood. Several models have emerged since many years to explain the drop of the quality factor Q0 (commonly called Q-drop) of a superconducting cavity versus the accelerating gradient. Experimental data are commonly fitted by applying a coarse approximation to convert the Q0 (a global property) into a surface resistance (local property). Extracting accurately the surface resistance from experimental data requires to take into account the RF field distribution over the accelerating structure contrary to what is commonly done in the community. Assuming a field dependent surface resistance does not allow anymore to use the well-known formula Q0=G∕Rs. This paper gives a procedure to perform an accurate conversion of the quality factor measured during a cavity test into a surface resistance to avoid any error in the evaluation of fitting parameters due to the geometry.