The effect of magnetic field errors on the radiation spectrum of ELETTRA undulators

The effect of magnetic field errors on the brightness of the radiation produced by undulators in the ELETTRA low-emittance storage ring has been investigated by direct numerical calculation. The model has allowed the statistical variation in the intensity and position of spectral peaks, as well as the effect of segmenting the undulator into a number of individually compensated sections, to be studied. A comparison with an existing analytic theory is also made. It is shown that introducing additional steering elements in an undulator to reduce trajectory deviations can improve the spectral brightness, reducing the effective field errors by about a factor of 1/√n, where n is the number of sections. For the ELETTRA undulator studied, assuming separation into three sections, an RMS field error of 0.5% can be specified which, on average, gives a brightness reduction of 25% for the third harmonic and 50% for the fifth harmonic