Modeling the effects of a flat wiggler on a storage ring beam

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Abstract
The purpose of the present note is to show how the various effects of the wiggler may be modeled in a simple way suitable for use in machine control. It will be seen that in general a total of about 17 functions are involved. However, in typical designs many of these functions vanish identically because of symmetries, and others are neglibly small. Furthermore, each of the functions may be modeled quite accurately by a single power law in (B/sub o//E)/sup n/ where B is a measure of the field excitation. E is the beam energy, and n is an integer which takes on values of either 0, 2, 3, 4, for 5 for the different functions. Magnet saturation may cause the field distribution to vary with excitation so that the series coefficients would vary slowly with B/sub o/. A computer program has been used to obtain numerical results for typical wiggler designs. In practice, the required functions could be determined either by computer analysis of the measured field data, or by experimental calibration using the stored beam in the ring. 9 refs., 3 figs., 11 tabs.

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