Ballistic expansion of trapped thermal atoms

We study the time evolution of the distribution function for an ensemble of classical particles in a harmonic trap when the oscillation frequencies are varied with time. We compare our results with the near circular density distributions observed for the thermal part of the expanded cloud in a recent experiment demonstrating the Bose-Einstein condensation of an alkali-metal vapor. The shape and extent of this noncondensed component characterize the temperature of the original cloud.