Theory and Simulation of the Electron Cloud Instability

A quasi-stationary electron cloud can drive single-bunch instabilities on a circulating beam through a head-tail coupling mechanism. The oscillation frequency of the electrons in the transverse field of the bunch, and how it can be expressed as a function of the bunch properties, is essential for the understanding of this instability. The process of the instability has been investigated via computer simulation. The model that we have applied makes use of two sets of macro-particles for the bunch particles and for the electrons, too, which interact at one or more locations along the beam orbit (kick approximation). The code has been employed to simulate possible instability mechanisms in the SPS as well as in the the LER of the KEK-B factory. The dependence of the induced emittance growth rates on chromaticity, bunch intensity and length, and electron cloud density has been studied and interpreted for both cases.