In a major extension of our previous model [Phys. Rev. Lett. 79, 1793] of condensate growth, we take account of the evolution of the occupations of lower trap levels, and of the full Bose-Einstein formula for the occupations of higher trap levels. We find good agreement with experiment, especially at higher temperatures. We also confirm the picture of the "kinetic" region of evolution, introduced by Kagan et al., for the time up to the initiation of the condensate. The behavior after initiation essentially follows our original growth equation, but with a substantially increased rate coefficient W 1 .[ S0031-9007(98) Although the first Bose condensed atomic vapor was produced in a magnetic trap only in 1995 [1][2][3], the kinetics of condensate formation has long been a subject of theoretical study [4,5]. There is now intense theoretical work on Bose-Einstein condensation, which is excellently summarized in [6]. Most theoretical studies of condensate growth either have not treated trapping or have considered only traps which are so broad that the behavior of the vapor is not essentially different from the untrapped situation. Furthermore, they have given only qualitative estimates of condensate growth. Our previous paper [7] introduced a simplified formula for the growth of a Bose-Einstein condensate, in which growth resulted from stimulated collisions of atoms in a thermal reservoir, where one of the atoms enters the lowest trap eigenstate, whose occupation thus grows to form a condensate. We thus included the trap eigenfunctions as an essential part of our description, and gave the first quantitative formula for the growth of a condensate. The growth rate was of the order of magnitude of that estimated from experiments current at that time.This direct stimulated effect must be very important once a significant amount of condensate has formed, but in the initial stages there will also be a significant number of transitions to other low lying trap levels whose populations will then also grow. As well as this, there will be interactions between the condensate, the atoms in these low lying levels, and the atomic vapor from which the condensate forms. This paper will extend the description of the condensate growth to include these factors, and will compare the results with experimental data on condensate growth obtained at MIT [8].As in our previous work, we divide the states in the potential into the condensate band, R C , which consists of the energy levels significantly affected by the presence of a condensate in the ground state, and the noncondensate band, R NC , which contains all the remaining energy levels above the condensate band. The division between the two bands is taken to be at the value, e max . The situation is illustrated in Fig. 1. The picture we shall use assumes that R NC consists of a large "bath" of atomic vapor, in thermal equilibrium, whose distribution function is given by a time-independent equilibrium Bose-Einstein distribution ͕exp͓͑E 2 m͒͞k B T ͔ 2 1͖ 21 with positive chemical potential...

A detailed analysis of the growth of a Bose-Einstein condensate is given, based on quantum kinetic theory, in which we take account of the evolution of the occupations of lower trap levels, and of the full Bose-Einstein formula for the occupations of higher trap levels, as well as the Bose-stimulated direct transfer of atoms to the condensate level introduced by Gardiner et al. ͓Phys. Rev. Lett. 79, 1793 ͑1997͒; 81, 5266 ͑1998͔͒. We find good agreement with experiment at higher temperatures, but at lower temperatures the experimentally observed growth rate is somewhat more rapid. We also confirm the picture of the ''kinetic'' region of evolution, introduced by Kagan, Svistunov, and Shlyapnikov "Zh. Eksp. Teor. Fiz. 101, 528 ͑1992͒ ͓Sov. Phys. JETP 75, 387 ͑1992͔͒…, for the time up to the initiation of the condensate. The behavior after initiation essentially follows our original growth equation, but with a substantially increased rate coefficient. Our modeling of growth implicitly gives a model of the spatial shape of the density profile of the condensate-vapor system as the condensate grows, and thus provides an alternative to the present phenomenological fitting procedure, based on the sum of a zero-chemical potential vapor and a Thomas-Fermi-shaped condensate. Our method gives substantially different results for condensate numbers and temperatures obtained from phenomenological fits, but fits the published column density data very well.