In 1994 we started to develop the 2D simulation code POSINST to analyze the electron-cloud build-up in the context of the PEP-II B factory, then under construction at SLAC. This effort led to the understanding of the strong effect of the secondary emission yield (SEY) of the vacuum chamber, which, in turn, led to the decision to coat the aluminum arc chambers with TiN, a low-emission coating. Over the years we have significantly augmented POSINST, allowing the simulation of the electron-cloud build-up, specifically its distribution, growth and decay rates, and energy and time scales. The code takes as input a description of the beam and certain geometrical and electronic properties of the vacuum chamber, chiefly the SEY. We have applied this code to assess the electron-cloud at various storage rings, such as the LHC and its injectors, their proposed upgrades, the FNAL Main Injector, the ILC Damping Rings and others. Although POSINST has been validated against measurements at the APS and the PSR, reliable quantitative extrapolations to other machines are not straightforward owing to the sensitivity of the results to input parameters that are sometimes not well known. Therefore, further validation exercises are still highly desirable.
To assess the effects of the electron cloud on the beam we use the 3D code WARP, initially developed at LBNL to study the transport of intense ion beams. We have added new capabilities to WARP, incorporating effects from an electron cloud on the beam. We have successfully benchmarked this code against the CERN code HEADTAIL in the context of the LHC and the SPS, and validated its predictions against measurements at the HCX heavy-ion facility. A benchmark against the UCLA/USC code QUICKPIC is in progress. For the electron cloud buildup phase it has also been benchmarked against POSINST for the case of an ideal dipole field. A newly invented algorithm, based on a Lorentz boost to an appropriate frame of reference, holds the promise of making future fully self-consistent simulations for relativistic beams several orders of magnitude faster than traditional methods currently in use.