Analysis of RF modes in an in-vacuum undulator

Electron storage rings commonly use in-vacuum undulators (IVUs) consisting of magnet arrays positioned closely above and below the electron beam to create a bright, tunable and broad spectral range with narrow peaks. These devices present several challenges to the electron beam dynamics since the magnets come within a few millimetres of the beam and a vacuum chamber around the magnets results in discontinuities in the otherwise smooth chamber. This paper analyzes the radio frequency (RF) eigenmodes that exist in the IVU chamber which have been observed at other facilities and may excite beam instabilities. An equivalent RF circuit for the IVU confirms the TEM-nature of the eigenmodes. To eliminate the problematic modes induced in IVU device that may lead to beam instabilities, a conceptual solution is proposed and initial simulations are presented.