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Focused ion beams are indispensable tools in the semiconductor industry because of their ability to image and modify structures at the nanometer length scale. Here, we report on performance predictions of a new type of focused ion beam based on photo-ionization of a laser cooled and compressed atomic beam. Particle tracing simulations are performed to investigate the effects of disorder-induced heating after ionization in a large electric field. They lead to a constraint on this electric field strength which is used as input for an analytical model which predicts the minimum attainable spot size as a function of, amongst others, the flux density of the atomic beam, the temperature of this beam, and the total current. At low currents (I<10 pA), the spot size will be limited by a combination of spherical aberration and brightness, while at higher currents, this is a combination of chromatic aberration and brightness. It is expected that a nanometer size spot is possible at a current of 1 pA. The analytical model was verified with particle tracing simulations of a complete focused ion beam setup. A genetic algorithm was used to find the optimum acceleration electric field as a function of the current. At low currents, the result agrees well with the analytical model, while at higher currents, the spot sizes found are even lower due to effects that are not taken into account in the analytical model. [ABSTRACT FROM AUTHOR]