Emittance growth in a storage ring due to ground motion

It is pointed out that, for a synchrotron light source designed for a small natural emittance, ground motion could lead to a nonnegligible growth in emittance. When the ground motion is of the plane-wave type, this dynamical process can be studied analytically by employing a method that combines the previously developed transfer function technique with a normal mode analysis that takes into account the magnification of the motion due to magnet supports. The explicit relationship between the amplitudes of the ground vibration and the emittance growth as a function of the vibration frequency is presented. Numerical examples are included. It is shown that the effects of low-frequency vibrations (below 20 Hz) can be alleviated with feedback systems using steering magnets. Higher-frequency vibrations that result in unacceptable emittance growth cannot be corrected in this manner and must be eliminated at their source or otherwise controlled