Some conceptual designs are made for variably polarizing Leaf undulator. Similar to the Figure-8 undulator, the Leaf undulator is a device that generates linearly polarized light with low on-axis power density. In this paper, we present some conceptual magnet designs of variably polarizing Leaf undulator that generates not only linearly polarized radiation but also circularly polarized radiation by introducing a half period phase change of magnetic field distribution along the beam axis in every two-period in an undulator. These phase changes may be achieved by moving sets of magnet array along the undulator axis in permanent magnet devices or electromagnetic devices without mechanical motion.

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