Atom number in magneto-optic traps with millimeter scale laser beams

We measure the number of atoms N trapped in a conventional vapor-cell magneto-optic trap (MOT) using beams that have a diameter d in the range 1-5 mm. We show that the N is proportional to d(3.6) scaling law observed for larger MOTs is a robust approximation for optimized MOTs with beam diameters as small as 3 mm. For smaller beams, the description of the scaling depends on how d is defined. The most consistent picture of the scaling is obtained when d is defined as the diameter where the intensity profile of the trapping beams decreases to the saturation intensity. Using this definition, N scales as d(6) for d<2.3 mm but, at larger d, N still scales as d(3.6).