  We discuss the generation of parametric X-rays in the new photoinjector at
the FAST (Fermilab Accelerator Science and Technology) facility in Fermilab.
These experiments will be conducted in addition to channeling X-ray radiation
experiments. The low emittance electron beam makes this facility a promising
source for creating brilliant X-rays. We discuss the theoretical model and
present detailed calculations of the intensity spectrum, energy and angular
widths and spectral brilliance under different conditions. We also report on
expected results with parametric X-rays generated while under channeling
conditions.
