Driven collective instabilities in magneto-optical traps: a fluid-dynamical approach

We present a theoretical model to describe an instability mechanism in ultra-cold gases, where long-range interactions are taken into account. Focusing on the nonlinear coupling between the collective (plasma-like) and the center-of-mass modes, we show that the resulting dynamics is governed by a parametric equation of the generalized Mathieu type and compute the corresponding stability chart. We apply our model to typical ranges of magneto-optical traps (MOT) parameters and find a good agreement with previous experimental observations.