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Emittance is important for analysis of particle beams. As long as the beam is only subjected to conservative forces, Liouville's theorem shows that emittance is a conserved quantity. If the distribution over phase space is represented as a cloud in a plot (see figure), emittance is the area of the cloud. A variety of more exact definitions account for the imprecise borders of the cloud and the case of a cloud that does not have an elliptical

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