  A two-step photoionization strategy of an ultracold rubidium beam for
application in a focused ion beam instrument is analyzed and implemented. In
this strategy the atomic beam is partly selected with an aperture after which
the transmitted atoms are ionized in the overlap of a tightly cylindrically
focused excitation laser beam and an ionization laser beam whose power is
enhanced in a build-up cavity. The advantage of this strategy, as compared to
without the use of a build-up cavity, is that higher ionization degrees can be
reached at higher currents. Optical Bloch equations including the
photoionization process are used to calculate what ionization degree and
ionization position distribution can be reached. Furthermore, the ionization
strategy is tested on an ultracold beam of $^{85}$Rb atoms. The beam current is
measured as a function of the excitation and ionization laser beam intensity
and the selection aperture size. Although details are different, the global
trends of the measurements agree well with the calculation. With a selection
aperture diameter of 52 $\mu$m, a current of $\left(170\pm4\right)$ pA is
measured, which according to calculations is 63% of the current equivalent of
the transmitted atomic flux. Taking into account the ionization degree the ion
beam peak reduced brightness is estimated at $1\times10^7$ A/(m$^2\,$sr$\,$eV).
