Kinetic theory of the evaporative cooling of a trapped gas

We apply kinetic theory to the problem of evaporative cooling of a dilute collisional gas in a trap. Assuming ''sufficient ergodicity'' (phase-space distribution only a function of energy) and s-wave collisions with an energy-independent cross section, an equation for the evolution of the energy distribution of trapped atoms is derived for arbitrary trap shapes. Numerical integration of this kinetic equation demonstrates that during evaporation the gas is accurately characterized by a Boltzmann distribution of atom energies, truncated at the trap depth. Adopting the assumption of a truncated Boltzmann distribution, closed expressions are obtained for the thermodynamic properties of the gas as well as for the particle and energy loss rates due to evaporation. We give analytical expressions both for power-law traps and for a realistic trapping potential (Ioffe quadrupole trap). As an application, we discuss the evaporative cooling of trapped atomic hydrogen gas.