Electron Cloud: an Analytic View

Electron cloud activity has been observed in some positron storage rings but not in others. It is a major concern for the LHC. In this paper the electron cloud problematics is treated purely analytica lly. The equilibrium electron cloud density is derived from the standard photon production rate, taking into account the photo-electric yield and the process of secondary emission. A fundamental ingre dient in the derivation is the Kollath{2] energy spectrum of the secondary emission. The phenomenon of space charge is discussed as well. The transverse acceleration of the electrons by the bunches is used to introduce the concept of closely and sparsely bunched beams. There is a fundamental difference between them, especially from the point of view of power deposition. Expressions for an equivalen t transverse impedance and imaginary tune shift are derived. Finally the analysis is confronted with electron cloud observations in existing positron machines (DAPHINE, PF, BEPC) before it is applied to the LHC. It comes out rather clearly that the nominal 25ns bunch spacing in the LHC does not offer enough safety margin in terms of power deposition in the beam screen and that the alternative of 5 0 ns deserves serious consideration.