In-vacuum undulators (IVU) and other devices used for beam manipulation, can exhibit beam instabilities when their natural modes of vibration (“trapped” resonances) are excited by the RF spectrum of the electron beam. Like many other structures, IVUs have electromagnetic (EM) properties – in addition to their intended properties used for beam manipulation (permanent magnet arrays with an adjustable gap). 3D EM simulation (CST) can be used to identify and visualise the natural modes, allowing to avoid their excitation or to suppress them by suitable means.
Two types of simulation are typically used:
- Eigenmode simulation
- Wakefield simulation
Eigenmode simulation yields the properties of the structure in terms of its natural modes of vibration. The modes extend from a mode with a lowest frequency (fundamental mode) to – in principle – infinity. Besides the mode frequencies, Eigenmode simulation also yields the EM field distributions and by post-processing, the quality factor is calculated for each mode for a given set of materials used in the structure.
Wakefield simulation injects a defined electron beam into the structure and yields the resulting Wakefields and its parameters. Typically, the Wakefield impedance magnitude is used to determine how strong a given Eigenmode is excited by the beam.