Analytic estimates of coupling in damping rings

In this paper we present analytic formulas to estimate the vertical emittance in weakly coupled electron/positron storage rings. We consider contributions from both the vertical dispersion and linear coupling of the betatron motions. In addition to simple expressions for random misalignments and rotations of the magnets, formulas are presented to calculate the vertical emittance blowup due to orbit distortions. 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. We consider only corrected orbits. Finally, the analytic expressions are compared with computer simulations of storage rings with random misalignments. 6 refs., 3 figs