Numerical Analysis of the Measurement of Near-Beam Electron Cloud Density in Field-Free Region at KEK B-Factory Low-Energy Ring

A large number of electrons in the so-called electron cloud are accumulated in beam chambers in positron storage rings. These electrons interact with the beam and can make the beam unstable. The density information of the electron cloud near the beam is therefore fundamental for studying beam instability and mitigation techniques related to the electron cloud. Recently, a method to measure the density of the electron cloud near the beam has been proposed by Kanazawa et al. The method enables the measurement of high-energy electrons selectively using a retarding field analyzer located on a chamber wall, noting that the electrons near the beam receive a strong kick by the beam. They calculated the density of the electron cloud simply assuming that the electrons that receive a kick are stationary. We examined the measurement technique in detail using a new computer code developed by us. The analysis showed that the volume near the beam occupied by the detected electrons, i.e., the observed volume, was strongly deformed owing to the horizontal velocity of the electrons; nevertheless this volume calculated assuming that the stationary electrons can still be used for calculating the density of the electron cloud in their measurement conditions.