Effects of the CHESS wigglers on a beam with an angular offset

The magnetic field due to a single pole of a wiggler is, by normal accelerator magnet standards, both very strong and very nonuniform. Because the poles alternate sign and are made to have the same strength the effects of the nonuniform fields on the beam largely cancel from one pole to another. In an ideal case where there are no mechanical or magnetic errors, the net integrated dipole field along a path parallel to the wiggler axis and on the midplane would be exactly zero. We estimate the integrated field along a path not parallel to the axis but still in the midplane. Such a path is typical of the closed orbit during electron injection or luminosity optics. When the path of integration is at an angle to the wiggler axis, the horizontal or vertical position in one pole is not precisely the same as the horizontal or vertical position in any other pole. Because of the relatively strong variation of field strength with position the integration over one pole does not cancel with the integration over another pole. Based on approximate expressions for the field in the wiggler, we show that the size of this effect is substantially smaller than the actual integrated dipole field measured parallel to the axis. This work has relevance to the CESR ring