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The electron cloud generates not only the transverse wake field but also the longitudinal wake field. The mechanism of the bunch lengthening due to longitudinal wake produced by the electron cloud in the positron storage ring is analyzed. The longitudinal field, which depends on the density of the electron cloud in the storage ring, arises from the accumulation of the electrons near to the center of the bunch during the bunch passage. Based on the longitudinal wake field, tracking method is used to simulate variation of the bunch longitudinal profile in different electron cloud density. According to simulation, the longitudinal action on the bunch from electron cloud is the similar as the potential-well distortion to shift the bunch distribution and give a rise to the bunch deformation. The result has been used to the simulation for BEPCII.
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