The cloud of cold atoms produced by a Magneto-Optical Trap is known to exhibit instabilities. We examine in this paper in which limits it could be possible to realize an experimental trap similar to the configurations studied theoretically, i.e. mainly traps where one direction is privileged. We study the static behavior of an anisotropic trap, where anisotropy results essentially from the use of two different laser frequencies for the arms of the trap. Such a trap has very surprising behaviors, in particular the cloud disappears for some laser frequencies, while it exists for smaller and larger frequencies. A model is build to explain these behaviors. We show in particular that, to reproduce the experimental observations, the model has to take into account the cross saturation effects. Moreover, the couplings between the different directions cannot be neglected.
