An atomic rubidium beam formed in a 70-mm-long two-dimensional magneto-optical trap (2D MOT), directly loaded from a collimated Knudsen source, is analyzed using laser-induced fluorescence. The longitudinal velocity distribution, the transverse temperature, and the flux of the atomic beam are reported. The equivalent transverse reduced brightness of an ion beam with properties similar to the atomic beam is calculated because the beam is developed to be photoionized and applied in a focused ion beam. In a single two-dimensional magneto-optical trapping step, an equivalent transverse reduced brightness of (1.0+0.8−0.4)×106 A/(m2 sr eV) is achieved with a beam flux equivalent to (0.6+0.3−0.2) nA. The temperature of the beam is further reduced with an optical molasses after the 2D MOT. This optical molasses increases the equivalent brightness to (6+5−2)×106 A/(m2 sr eV). For currents below 10 pA, for which disorder-induced heating can be suppressed, this number is also a good estimate of the ion-beam brightness that can be expected. Such an ion-beam brightness would be a 6× improvement over the liquid-metal ion source and could improve the resolution in focused ion-beam nanofabrication.