Simulations of the electron cloud buildup and its influence on the microwave transmission measurement

An electron cloud density in an accelerator can be measured using the Microwave Transmission (MWT) method. The aim of our study is to evaluate the influence of a realistic, nonuniform electron cloud on the MWT. We conduct electron cloud buildup simulations for beam pipe geometries and bunch parameters resembling roughly the conditions in the CERN SPS. For different microwave waveguide modes the phase shift induced by a known electron cloud density is obtained from three different approaches: 3D Particle-In-Cell (PIC) simulation of the electron response, a 2D eigenvalue solver for waveguide modes assuming a dielectric response function for cold electrons, a perturbative method assuming a sufficiently smooth density profile. While several electron cloud parameters, such as temperature, result in minor errors in the determined density, the transversely inhomogeneous density can introduce a large error in the measured electron density. We show that the perturbative approach is sufficient to describe the phase shift under realistic electron cloud conditions. Depending on the geometry of the beam pipe, the external magnetic field configuration and the used waveguide mode, the electron cloud density can be concentrated at the beam pipe or near the beam pipe center, leading to a severe over- or underestimation of the electron density.