  Electron cloud effects have recognized as as one of the most serious
bottleneck for reaching design performances in presently running and proposed
future storage rings. The analysis of these effects is usually performed with
very time consuming simulation codes. An alternative analytic approach, based
on a cubic map model for the bunch-to-bunch evolution of the electron cloud
density, could be useful to determine regions in parameters space compatible
with safe machine operations. In this communication we derive a simple
approximate formula relating the linear coefficient in the electron cloud
density map to the parameters relevant for the electron cloud evolution with
particular reference to the LHC dipoles.
