Maps for electron cloud density in Large Hadron Collider dipoles

The generation of a quasi stationary electron cloud inside the beam pipe through beam-induced multipacting processes has become an area of intensive study. The analyses performed so far have been based on heavy computer simulations taking into account photoelectron production, secondary emission, electron dynamics, and space charge effects, providing a detailed description of the electron-cloud evolution. Iriso and Peggs [ U. Iriso and S. Peggs Phys. Rev. ST Accel. Beams 8 024403 (2005)] have shown that, for the typical parameters of RHIC, the bunch-to-bunch evolution of the average electron-cloud density at a point can be represented by a cubic map. Simulations based on this map formalism are orders of magnitude faster compared to those based on standard particle tracking codes. In this communication we show that the map formalism is also applicable to the case of the Large Hadron Collider (LHC), and that, in particular, it reproduces the average electron-cloud densities computed using a reference code to within ∼15% for general LHC bunch filling patterns. We also illustrate the dependence of the polynomial map coefficients on the physical parameters affecting the electron cloud (secondary emission yield, bunch charge, bunch spacing, etc.).