Tracking Simulation of the Ions Trapped in the Nonlinear Field of Electron Beams in Storage Rings

Abstract

Tracking simulation was performed on the ions trapped in linear and nonlinear fields of an electron beam in storage rings. The stability of the ions was investigated with regard to the homogeneous partial-fill mode and the equidistant-bunch and -burst modes of the electron beam. It was found that the oscillation amplitude of the ions trapped in the beam grows very rapidly to 100–1000 times larger than the electron beam size, even in the nonlinear field, under some ion-beam conditions. The results are expressed as a stability diagram of the ions, and the diagrams for the linear and nonlinear fields are basically similar to each other, both representing a periodic structure of the parametric resonance. The critical mass in the equidistant bunched beam is the same for the linear and nonlinear fields. The present results are consistent with the experimental results in the storage rings of European Synchrotron Radiation Facility (ESRF) and Photon Factory of National Laboratory for High Energy Physics (KEK-PF).