Analytical and Numerical Investigation of the Phase Shift and Magnetization Rotation in the PPM Undulator

This paper describes two modifications in the pure permanent magnet (PPM) undulators: 1) phase shift and 2) magnetization rotation, and studies their effects on the radiation harmonics properties. An analytical description for these modifications has been presented and two numerical codes, RADIA and B2E, have been used to model the PPM undulator in the presence of the aforementioned modifications and to calculate their effects on the synchrotron radiation properties. A short description of these codes has been presented. The two most important properties of the harmonics are their energy and intensity. This paper uses a simple theoretical approach to show that the phase shift mechanism can affect the K-value of the undulator and then change the harmonics energy and their intensity, while the rotation mechanism does not change harmonics properties notably. Recently, a new combined method called phase combined undulator (PCU) has been supposed. The PCU structure has been fabricated using the phase shift mechanism and applying a specific magnets arrangement to eliminate the magnetic force between upper and lower arrays. The radiation harmonic generation of this structure has been studied.