  The results of simulations of cooling based on Sawtooth-Wave Adiabatic
Passage (SWAP) are presented including the possibility of population leaking to
states outside of the cycling transition. The amount of population leaking can
be substantially suppressed compared to Doppler cooling, which could be useful
for systems that are difficult to repump back to the cycling transition. The
suppression of the leaked population was more effective when simulating the
slowing of a beam than in cooling a thermal distribution. As expected,
calculations of the leaked population versus branching ratio of spontaneous
emission show that the suppression is more effective for narrow linewidth
transitions. In this limit, using SWAP to slow a beam may be worth pursuing
even when the branching ratio out of the cycling transition is greater than
10%.
