Electron-cloud instabilities

Photons emitted by a stored beam hit a vacuum chamber surface and produce electrons. These photoelectrons interacts with the beam and can be responsible for the beam transverse instability. The photoelectron instability was suggested by Ohmi to describe phenomena observed at KEK PF (photon factories). Similar effects were seen at BEPC and CESR (storage rings). At certain conditions, the electrons can be accelerated by the beam to such a degree that an average secondary emission yield per one primary electron becomes higher than one. This phenomenon was paid attention and analytical estimations were suggested, primarily for PEP-II Storage Ring. In fact, the avalanche of secondary electrons is not sensitive to an origin or quantity of initial electrons: the electron density growth rate depends on the secondary emission yield per one absorbed electron. This is independent on the density itself until the space-charge limit, being only determined by the beam current, the bunch separation and the vacuum chamber. Simulations for PEP-II Storage Ring showed that the avalanche instability is prevented by TiN coating of that vacuum chamber. The growth rate of the dipole oscillations due to the interaction with primary electrons was numerically found. According to numerical results of, the avalanche instability should take place for the CERN LHC, resulting in the space-charge dominated electron cloud. The paper presented is structured in the following way. First, an analytical model of an electron response on beam transverse oscillations is presented. The transverse impedance and the instability growth rate are found, mainly for a case of factories with rather small bunch separations, s ≅ 1 m. Then, the problem of secondary electron density growth (decay) rate is treated analytically and numerically. Finally, estimations for the specific case of the CERN LHC are suggested. (author)