Slow beam degradation due to electron clouds at the LHC: observations and modelling
In the Large Hadron Collider, electron clouds have been consistently observed to cause slow beam degradation in the form of beam lifetime reduction and slow emittance growth. This effect is attributed to the non-linear forces induced by the electrons in the clouds that affect the single-particle dynamics. In this talk, we will present observations of how the electron cloud forming in the Inner Triplet magnets degrades the beam quality during collisions in the Large Hadron Collider, leading to a measurable loss of performance. Moreover, a method is presented for the simulation of such slow effects with arbitrarily complex electron clouds and in the presence of other non-linearities in the lattice of the accelerator. In particular, the application of the electron cloud forces, as obtained from a particle-in-cell simulation of the electron cloud dynamics, is kept symplectic by using an appropriate tricubic interpolation scheme. The properties of such an interpolation scheme are studied in detail and numerical artifacts that can be introduced by the scheme are identified and corrected through a suitable refinement procedure. The method is tested for the case of the Large Hadron Collider for protons at injection energy, using it to compute Dynamic Aperture, to perform Frequency Map Analysis, and to simulate beam losses and emittance growth by tracking particle distributions on long time scales.