Numerical simulation of microwave transmission in the presence of an electron cloud

Electron cloud effects on the transmission of microwaves through beam pipes in the CERN SPS experiment and the PEP-II Low Energy Ring (LER) at SLAC have been recently observed. Electrons within the vacuum chamber generated primarily via secondary electron emission have been observed to cause a phase shift in microwaves injected into the vacuum chamber. Understanding this effect may provide a useful diagnostic tool for measuring electron cloud densities in accelerators. We present numerical simulation results generated by the electromagnetic Particle-In-Cell (PIC) code VORPAL, which predicts this phase shift. We also measure the effects of non-uniform electron cloud density and externally applied magnetic fields on the transmission properties, and compare our predictions to recent experiments at the PEP-II LER.