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

The electron cloud effects are usually studied using numerically intensive and time consuming simulation codes. A semi analytical approach reducing considerably the computational budget has been suggested to study the electron cloud dynamics in RHIC *, and subsequently extended to LHC **. This approach is based on a quadratic map which reproduces the evolution of the electron density from bunch to bunch. The map coefficients were originally obtained by fit. We computed analytically the linear ** and quadratic *** coefficients of the mapping for the case of free electron cloud evolution using a simple physical model, obtaining a good agreement with numerical simulations, for a wide range of bunch populations.

* U. Iriso ans S. Peggs, Phys. Rev. ST-AB 8, 024403 (2005).
** T. Demma et al., Phys. Rev. ST-AB 10, 114401 (2007).
*** T. Demma et al., Proc. IPAC 2010, in print.