  Various methods have been proposed to condition an electron beam in order to
reduce its emittance effect and to improve the short-wavelength free electron
laser (FEL) performance. In this paper, we show that beam conditioning does not
result in a complete elimination of the emittance effect in an
alternating-gradient focusing FEL undulator. Using a one-dimensional model and
a three-dimensional simulation code, we derive a criteria for the emittance
limitation of a perfectly conditioned beam that depends on the focusing
structure.
