  A simplified numerical model has been developed to simulate non-linear
superconducting radiofrequency (SRF) losses on Nb surfaces. This study focuses
exclusively on excessive surface resistance (Rs) losses due to the microscopic
topographical magnetic field enhancements. When the enhanced local surface
magnetic field exceeds the superconducting critical transition magnetic field
Hc, small volumes of surface material may become normal conducting and increase
the effective surface resistance without inducing a quench. Using topographic
data from typical Buffered Chemical Polish (BCP) and Electropolish (EP) treated
fine grain niobium , we have estimated the resulting field-dependent losses and
extrapolated this model to the implications for cavity performance. The model
predictions correspond well to the characteristic BCP versus EP high field Q0
performance differences for fine grain niobium. We describe the algorithm of
the model, its limitations, and the effects of this non-linear loss
contribution on SRF cavity performance.
