Generating
a uniformly populated ellipsoidal electron distribution in a photoinjector
has been shown to produce very low transverse emittance. It reduces
the need for delicately balanced emittance correction schemes that align
different time-slices of the beam in transverse phase space. The linear
space charge forces, equal across all time slices, also produce a very
bright beam in the longitudinal phase space plane with nearly constant
slice energy spread, a parabolic time profile, and the ability to produce
high peak current directly in the photoinjector. These qualities are
ideal for preparing the beam for magnetic bunch compression and for
the needs of a seeded FEL. We investigate this improved longitudinal
phase space, using the FERMI@Elettra FEL as an example to study its
performance implications for seeded short-wavelength FELs.