Analytic estimates of coupling in damping rings

Analytic formulas for estimating the vertical emittance in weakly coupled electron-positron storage rings are presented. Contributions from both the vertical dispersion and linear coupling of the betatron motions are considered. In addition to simple expressions for random misalignments and rotations of the magnets, formulas for calculating the vertical emittance blowup due to orbit distortions are presented. The orbit distortions are assumed to be caused by random misalignments, but because the closed orbit is correlated from point to point, the effects must be treated differently. Only corrected orbits are considered. The analytic expressions are compared with computer simulations of storage rings with random misalignments.<>