  The energy distribution of an ultracold rubidium ion beam, which is intended
to be used as the source for a focused ion beam instrument, is measured with a
retarding field analyzer. The ions are created from a laser-cooled and
compressed atomic beam by two-step photoionization in which the ionization
laser power is enhanced in a build-up cavity. Particle tracing simulations are
performed to ensure the analyzer is able to resolve the distribution. The
lowest achieved full width 50% energy spread is $\left(0.205\pm0.006\right)$
eV. The energy spread originates from the variation in the ionization position
of the ions which are created inside an extraction electric field. This
extraction field is essential to limit disorder-induced heating which can
decrease the ion beam brightness. The ionization position distribution is
limited by a tightly focused excitation laser beam. Energy distributions are
measured for various ionization and excitation laser intensities and compared
with calculations based on numerical solutions of the optical Bloch equations
including ionization. A good agreement is found between measurements and
calculations.
