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Electron cloud effects have recognized as as one of the most seriousbottleneck for reaching design performances in presently running and proposedfuture storage rings. The analysis of these effects is usually performed withvery time consuming simulation codes. An alternative analytic approach, basedon a cubic map model for the bunch-to-bunch evolution of the electron clouddensity, could be useful to determine regions in parameters space compatiblewith safe machine operations. In this communication we derive a simpleapproximate formula relating the linear coefficient in the electron clouddensity map to the parameters relevant for the electron cloud evolution withparticular reference to the LHC dipoles.

A Formula of the Electron Cloud Linear Map Coefficient in a Strong Dipole