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n exhaustive kinetic model for the atoms in a 1D magneto-optical trap is derived, without any approximations. It is shown that the atomic density is described by a Vlasov-Fokker-Planck equation, coupled with two simple differential equations describing the trap beam propagation. The analogy of such a system with plasmas is discussed. This set of equations is then simplified through some approximations, and it is shown that corrective terms have to be added to the models usually used in this context. [ABSTRACT FROM AUTHOR]

The cloud of cold atoms obtained from a magneto-optical trap is known to exhibit two types of instabilities in the regime of high atomic densities: stochastic instabilities and deterministic instabilities. In the present paper, the experimentally observed deterministic dynamics is described extensively. Three different behaviors are distinguished. All are cyclic, but not necessarily periodic. Indeed, some instabilities exhibit a cyclic behavior with an erratic return time. A one-dimensional stochastic model taking into account the shadow effect is shown to be able to reproduce the experimental behavior, linking the instabilities to a several bifurcations. Erraticity of some of the regimes is shown to be induced by noise. [ABSTRACT FROM AUTHOR]

The cloud of cold atoms obtained from a magneto-optical trap is known to exhibit two types of instabilities in the regime of high atomic densities: stochastic instabilities and deterministic instabilities. In the present paper, the experimentally observed stochastic dynamics is described extensively. It is shown that it exists a variety of dynamical behaviors, which differ by the frequency components appearing in the dynamics. Indeed, some instabilities exhibit only low frequency components, while in other cases, a second time scale, corresponding to a higher frequency, appears in the motion of the center of mass of the cloud. A one-dimensional stochastic model taking into account the shadow effect is shown to be able to reproduce the experimental behavior, linking the existence of instabilities to folded stationary solutions where noise response is enhanced. The different types of regimes are explained by the existence of a relaxation frequency, which in some conditions is excited by noise. [ABSTRACT FROM AUTHOR]