  The Electron Cloud, an undesirable physical phenomena in the accelerators,
develops quickly as photons striking the vacuum chamberwall knock out electrons
that are then accelerated by the beam, gain energy, and strike the chamber
again, producing more electrons. The interaction between the electron cloud and
a beam leads to the electron cloud effects such as single- and multi-bunch
instability, tune shift, increase of pressure and particularly can limit the
ability of recently build or planned accelerators to reach their design
parameters. We report a principal results about the analytical study to
understanding a such dynamics of electrons.
