KINETIC-THEORY OF THE EVAPORATIVE COOLING OF A TRAPPED GAS

We apply kinetic theory to the problem of evaporative cooling of a dil ute collisional gas in a trap. Assuming ''sufficient ergodicity'' (pha se-space distribution only a function of energy) and s-wave collisions with an energy-independent cross section, an equation for the evoluti on of the energy distribution of trapped atoms is derived for arbitrar y trap shapes. Numerical integration of this kinetic equation demonstr ates 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 a s well as for the particle and energy loss rates due to evaporation. W e give analytical expressions both for power-law traps and for a reali stic trapping potential (Ioffe quadrupole trap). As an application, we discuss the evaporative cooling of trapped atomic hydrogen gas.