THE EFFECTS OF FIELD ERRORS ON LOW-GAIN FREE-ELECTRON LASERS

The effects of random wiggler magnetic field errors on low-gain free-electron lasers are examined analytically and numerically through the use of ensemble averaging techniques. Wiggler field errors perturb the electron beam as it propagates and lead to a random walk of the beam centroid delta-x, variations in the axial beam energy delta-gamma-z and deviations in the relative phase of the electrons in the ponderomotive wave delta-psi. In principle, the random walk may be kept as small as desired through the use of transverse focusing and beam steering. Transverse focusing of the electron beam is shown to be ineffective in reducing the phase deviation. Furthermore, it is shown that beam steering at the wiggler entrance reduces the average phase deviation at the end of the wiggler by 1/3. The effect of the field errors (via the phase deviation) on the gain in the low-gain regime is calculated. To avoid significant reduction in gain it is necessary for the phase deviation to be small compared to 2-pi. The detrimental effects of wiggler errors on low-gain free-electron lasers may be reduced by arranging the magnet poles in an optimal ordering such that the magnitude of the phase deviation is minimized.