A comprehensive study, supported by systematic measurements and numerical computations, of the intrinsic limits of multi-GEM detectors when exposed to very high particle fluxes or operated at very large gains is presented. The observed variations of the gain, of the ion back-flow, and of the pulse height spectra are explained in terms of the effects of the spatial distribution of positive ions and their movement throughout the amplification structure. The intrinsic dynamic character of the processes involved imposes the use of a non-standard simulation tool for the interpretation of the measurements. Computations done with a Finite Element Analysis software reproduce the observed behaviour of the detector. The impact of this detailed description of the detector in extreme conditions is multiple: it clarifies some detector behaviours already observed, it helps in defining intrinsic limits of the GEM technology, and it suggests ways to extend them.
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