Improved electron trajectory and power distribution in APPLE-knot undulator

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.