Suppression of beam-ion instability in electron rings with multibunch train beam fillings

The ion-caused beam instability in the future light sources and electron damping rings can be serious due to the high beam current and ultrasmall emittance of picometer level. One simple and effective mitigation of the instability is a multibunch train beam filling pattern which can significantly reduce the ion density near the beam, and therefore reduce the instability growth rate up to 2 orders of magnitude. The suppression is more effective for high intensity beams with low emittance. The distribution and the electric field of trapped ions are benchmarked to validate the model used in the paper. The wakefield of ion cloud and the beam-ion instability is investigated both analytically and numerically. We derived a simple formula for the buildup of ion cloud and instability growth rate with the multibunch train filling pattern. The simulation in NSLSII, PEPX, SuperKEKB, and the observation in SPEAR3 are used to compare with our analyses. The analyses agree well with simulations and observations