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The APPLE-Knot undulator has been proposed to reduce the large on-axis heat load of the APPLE-II at very low photon energy. However, the current designs have an inherent non-zero second field integral due to the Knot sections, resulting in a transverse deflection of the electron beam throughout the undulator. For a long device, such a deviation can degrade the brightness and power distribution of the outgoing beam. Here, a new end-Knot section is presented to compensate for the electron trajectory, and the undulator is symmetrized to balance the output power distribution. The performance of the APPLE-Knot with symmetric power distribution is investigated. The partial power, flux, and polarization are compared with the APPLE-II. In the linear mode, APPLE-Knot shows a pronounced reduction of the partial power, with a similar flux to the APPLE-II. The symmetric power density distribution reduces the hotspot by 41%, with a flux loss of less than 5%. In the circular mode and at low photon energies, the flux is limited by the phase error of the symmetric design.

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This paper describes two modifications in the pure permanent magnet, PPM, undulators: phase shift and magnetization rotation, and will study 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 study uses a simple theoretical approach to showing 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 has been supposed called phase combined undulator or PCU. The PCU structure has been fabricated by using 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.