Reduction of FEL gain due to wiggler errors

For an FEL operating in the exponential regime before saturation, we consider the effect on the gain of longitudinal velocity variations arising from wiggler field errors. The average gain reduction and the width of the output power distribution are expressed in terms of the mean square average of the ponderomotive phase shift per gain length. A scheme for correcting the electron trajectory using position monitors and dipole correctors is analyzed. Analytic results are compared with numerical simulations. Our work is directly applicable to the design of FEL amplifiers and the results are encouraging for the feasibility of such devices.