  Controlling trapped magnetic flux in superconducting radiofrequency (RF)
cavities is of crucial importance in modern accelerator projects. In order to
study flux trapping efficiency and sensitiv- ity of surface resistance,
dedicated experiments have been carried out on different types of low-\b{eta}
superconducting accelerating cavities. Even under almost full trapping
conditions, we found that the measured magnetic sensitivities of these cavity
geometries were significantly lower than the theoretical values predicted by
commonly-used models based on local material properties. This must be resolved
by taking account of geometrical effects of flux trapping and flux oscillation
under RF surface current in such cavity shape. In this paper, we propose a new
approach to convolute the influence of geometries. We point out a puzzling
contradiction between sample measurements and recent cavity experiments, which
leads to two different hypotheses to simulate oscillating flux trapped in the
cavity surface. A critical reconsideration of flux oscillation by the RF
Lorentz force, compared with temperature mapping studies in elliptical
cavities, favoured the results of previous sample measurements, which suggested
preferential flux trapping of normal component to the cavity inner surface.
Based on this observation, we builded a new model to our experimental results
and the discrepancy between old theory and data were resolved.
