• T. Demma
  INFN/LNF, Frascati (Roma)
• S. Petracca, A. Stabile
  U. Sannio, Benevento

The bunch-to-bunch evo­lu­tion of the elec­tron cloud den­si­ty can be mod­eled using a cubic map. The map ap­proach has been proved re­li­able for RHIC* and LHC**. The co­ef­fi­cients that pa­ram­e­ter­ize the map may be ob­tained by fit­ting from time con­sum­ing nu­mer­i­cal sim­u­la­tions. In this com­mu­ni­ca­tion we de­rive a sim­ple ap­prox­i­mate for­mu­la for the quadrat­ic co­ef­fi­cient, which de­ter­mines the sat­u­ra­tion of the cloud due to space charge, in the elec­tron cloud den­si­ty map, under the as­sump­tions of round cham­bers and free-field mo­tion of the elctrons in the cloud. Re­sults are com­pared with sim­u­la­tions for a wide range of pa­ram­e­ters gov­ern­ing the evo­lu­tion of the elctron cloud.

* U.Iriso, S.Peggs, Phys. Rev.STAB 8, 024403, 2005.
** T.Demma, S.Petracca, G.Rumolo, F.Ruggiero, F.Zimmermann, Phys. Rev.STAB 10, 114401, 2007.