Kinetic theory of the evaporative cooling of a trapped gas.

Van der Waals - Zeeman Institute, University of Amsterdam, Valckenierstraat 65-67, 1018 XE Amsterdam, The Netherlands~Received 14 April 1995; revised manuscript received 22 September 1995!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 anenergy-independent cross section, an equation for the evolution of the energy distribution of trapped atoms isderived for arbitrary trap shapes. Numerical integration of this kinetic equation demonstrates that duringevaporation the gas is accurately characterized by a Boltzmann distribution of atom energies, truncated at thetrap depth. Adopting the assumption of a truncated Boltzmann distribution, closed expressions are obtained forthe thermodynamic properties of the gas as well as for the particle and energy loss rates due to evaporation. Wegive analytical expressions both for power-law traps and for a realistic trapping potential~Ioffe quadrupoletrap!. As an application, we discuss the evaporative cooling of trapped atomic hydrogen gas.PACS number~s!: 32.80.Pj, 51.10.1y, 67.65.1zI. INTRODUCTION