Effect of Plane Ground Waves on the Closed Orbit in Circular Colliders

The effect of plane ground waves on the closed orbit in circular storage rings is studied by computer simulation. Selected elements are displaced vertically. The displacements are computed for plane ground motion waves with given wavelength and phase. The closed orbit is computed with MAD. Results for the amplification factors are presented and discussed for simple lattices consisting only of FODO cells, for LEP and LHC. The expectation values of the orbit offsets for realistic spectra of ground motion are calculated. For all machines studied, they are orders of magnitude smaller than the beam radii. Differences in the response to ground motion waves at harmonic numbers much smaller than the tunes between simple FODO lattices, machines with symmetrical low-b insertions like LEP, and anti-symmetrical low-b insertions like LHC are also discussed