Photoelectrons and Multipacting in the LHC: Electron Cloud Build-up

A simple quasi-analytic model is developed for the dynamics of electron cloud generated by synchrotron radiation of the beam in the LHC beam pipe. The model allows to obtain a multipacting condition for the LHC parameters, takes into account the space charge effect and predicts an equilibrium density of the electrons. Based on this model, we find the electron lifetime and estimate the energy deposition of the electron cloud to the wall. We also estimate the emittance growth of the beam due to random fluctuations of the electric field of the cloud and find the growth rate of the beam instability caused by the electrons.