We present a rate equation model to account for the trapping mechanism
in the sodium type-II magneto-optical trap (MOT). A key feature of th
e model is that excitation from the ground F=1 state to both excited s
tates F'=1 and F'=0-possible in sodium because of the small excited st
ate separation-is confirmed to be crucial in avoiding the optical pump
ing that otherwise inhibits steady-state trapping. Furthermore, we cal
culate that the mixed polarization typically present in a three-dimens
ional trapping arrangement gives substantially better one-dimensional
trapping performance than pure circular polarization, and that the act
ive role of repumping in the trapping process is important. The model
is also applied to the type-I (F=2 to F'=3) MOT and comparisons are ma
de with experiment in both cases; The possibility of blue-detuned Sisy
phus cooling in the F=1 to F'=1 and 0 transition scheme is considered.