Influence of ground motion on the time evolution of beams in linear colliders

This paper resumes a series of investigations devoted to the influence of ground motion on linear colliders in the TeV energy range. We attempt to model a variety of measured ground motion data and then to calculate the behavior of beams in the linear collider affected by this motion. An adequate description of ground motion is found in the form of a two-dimensional power spectrum P(ω,k) that carries information both about the time and space dependences of displacements. We then discuss the use of this spectrum to calculate the time evolution of beam position and beam size at the interaction point. A few approximations of this spectrum for typical seismic conditions are proposed for a wide range of ω and k based on the results of absolute and relative seismic measurements. Examples of calculations of the time evolution of the beam size and position in the final focus system of a linear collider are presented. Estimations of the influence of feedback are made. © 1996 The American Physical Society.