The current FCC-hh beam screen proposal includes pumping holes of considerable area hidden behind a shield. Although each hole's contribution to the ring impedance is negligible, the effect of a large number of pumping holes in a very large ring (constructive interference) has to be considered.
On one hand, due to evanescent coupling and the shield, space-discretisizing eigenmode and wakefield computations produce significant numerical noise considering those effects. On the other hand, the hole dimensions are too large in comparison to the chamber dimensions to be treated using substitute elementary dipoles.
After reviewing numerical limits of Floquet-periodic FEM eigenmode computation, we approach the problem by adapting existing Field Matching techniques to a simplified FCC-hh beam screen geometry. Due to the possibility of discretising the fields only in the hole areas, computation time and accuracy may be sufficient to yield qualitative results.