We present an investigation of the cesium magneto-optical trap, with p
articular regard to the best combination of atomic density and tempera
ture that can be produced. Conditions in the trap depend on four indep
endent parameters: the detuning and intensity of the Light, the gradie
nt of the magnetic field, and the number of atoms trapped. We have var
ied all these parameters and measured the temperature and density dist
ribution of the trapped cloud. Both the nonlinear variation with posit
ion of the restoring force and the reabsorption of photons scattered i
n the cloud limit the maximum density, and we present an empirical mod
el that takes this into account. This in turn limits the density in ph
ase space rho (defined as the number of atoms in a box with sides of o
ne thermal de Broglie wavelength). We have observed a maximum rho = (1
.5 +/- 0.5) x 10(-5), with a spatial density of about 2 x 10(11) atoms
/cm(3).