In a small electron storage ring, such as the Hefei Light Source (HLS) ring
, the newly generated ions, which can not escape from the beam potential an
d then are trapped from turn to turn, will lead to the beam instability. Th
e ions created by the leading bunches can perturb the trailing bunches and
also themselves during their subsequent passage, which will make the amplit
ude of beam oscillation be damped and anti-damped periodically. A computer
simulation based on the strong-weak model shows a good agreement with our a
nalytical model using the linear theory.