Fundamental and harmonic induction fields in PPM undulator

The standard pure permanent magnet (PPM) undulator has been analyzed by 3-dimensional electromagnetic computation software, the Modeller in Opera3D. The amplitude and phase angle of fundamental and harmonic induction fields in it are given for different air gaps. They show that all harmonic induction fields in standard PPM undulator are two orders lower than their fundamental induction field. This conclusion is verified by the related magnetic measurements to one standard PPM undulator in optical klystron with 0.5mm×1mm Hall probe. The paper also presents comparisons between theoretic results with analysis equation as well as 3D Finite Element computations and magnetic measurement with hall probe. In furthermore, inserted very small airgaps along beam direction in PPM undulator, leaving s