STUDY OF FAST ION INSTABILITY AT KEKB ELECTRON RING

We have studied fast ion instability (FII) in the electron ring (HER) at KEKB. We introduce an application of Singular Value Decomposition (SVD) to study multi-bunch beam oscillations. The SVD analysis[1] has been performed for a matrix consists of vertical bunch positions in a turn-byturn and bunch-by-bunch to extract wave lengths which characterized the behavior of multi-bunch beam instabilities. Multi-bunch beam instabilities were also observed by changing the beam size with adjusting the dispersion function. We found that the multi-bunch beam instabilities were stronger as the beam size decreased. We compared the wave length and growth time with the linear approximate calculation of the FII. Observed multi-bunch beam instability is consistent with the FII.