The stability of ions in a storage ring in the presence of small gap insertion devices

We investigate the question of ion stability in the NSLS X-ray ring with a 0.32 m long variable gap (4-18mm) undulator and 0.95 m long, 27 mm gap undulator in it. We concentrate our attention on CO ions(A=28) since they are the most bothersome in the ring. We will show the effect of a gap in the bunch train, the effect of nonlinearity in the beam kicks and the effect of a restricted longitudinal mobility of ions. The methods used and the calculations performed are general enough to be applied to any other storage ring or accelerator