A Map Approach for Electron Cloud Density in a Strong LHC Dipole

The luminosity is limited by the electron cloud effects in presently running and proposed future storage rings. The evolution of the electron density during the electron cloud formation can be reproduced using a bunch-to-bunch iterative map formalism. By performing simulation codes this approach has been used to obtain a numerical prediction of the coefficients in the map, while in the presence of a magnetic field an analytic formula has been obtained for the linear coefficient. The next goal is finding a theoretical prescription of the quadratic coefficient at least in the presence of magnetic dipole. Then it will be possible to reproduce, by using the map formalism, the dynamics of electron cloud without performing the simulations.