  Large clouds of atoms in a magneto-optical trap (MOT) are known to exhibit
spatiotemporal instabilities when the frequency of the trapping lasers comes
close to the atomic resonance. Such instabilities possess similarities with
stars and confined plasmas, where corresponding nonlinearities may give rise to
spontaneous oscillations. In this paper, we describe the kinetic model that has
recently been employed in three-dimensional (3D) simulations of spatiotemporal
instabilities in a MOT, yielding qualitative agreements with experimentally
observed instability thresholds and regimes. Details surrounding its
implementation are included, and the impact of its physical effects on the
instabilities is investigated to improve the understanding of the complex
mechanism at work.
