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 [1] and LHC [2]. 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 linear coefficient in the electron cloud density map, along the lines laid in [3], in the presence of a dipole magnetic field, and compare the result to numerical simulations, for the LHC.
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