A magnetic field model for wigglers and undulators

Recent interest in applications of wiggler magnets in storage rings has motivated efforts to incorporate their effects in calculations of beam dynamics. This paper presents an analytic model of wiggler fields that can be used with symplectic integration to evaluate such effects. Coefficients needed by the model are generated by fitting to the results of a finite-element field calculation. The model has been used successfully in the CESR-c project, which imposes tolerances of a few parts in 10⁴ on the modeling of 2-Tesla superconducting wigglers. In contrast to models based on Fourier transforms, the model presented here uses a relatively small number of terms, leading to correspondingly fast integration times. Fringe fields are included and no assumption about the periodicity of the field is made.