Allowable field errors in undulators used as synchrotron radiation sources

High brightness synchrotron sources based on undulator radiation require both low emittance electrom beams and high precision undulators. Under many circumstances, loss of brightness due to wiggler field errors is dominated by e-beam steering from dipole errors. A simple method to calculate the allowed dipole errors is presented. The error tolerance differs depending on whether or not the emittance is large enough to preclude full spatial coherence. In the large emittance, spatially incoherent limit the storage ring betatron function can be adjusted to optimize either the spectral coherence or spatial coherence, but not both simultaneously. The calculated tolerances are compared to measured field errors of the Spectra Technology THUNDER undulator