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This document discusses strong sextupole focusing in planar undulators. It examines the equations of motion for an electron in an undulator field with a strong sextupole component. It shows that the mean electron longitudinal velocity can be kept constant through each focusing and defocusing section, but differs between sections. Examples using proposed future free electron lasers are also provided to explore the effects of this stepwise velocity modulation and beam size variation computationally and theore

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