Transverse phase space in the presence of dispersion

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Abstract
A generalized formalism is used to determine the beam ellipse parameters at some location in a transversely uncoupled transport line from a sufficient number of beam size measurements. We allow for contributions to the beam sizes from dispersion which can be either transported from some initial point, or generated along the transport line. We derive expressions for the pure betatron emittance in terms of the "effective" emittance (calculated from the measurements of the total transverse beam sizes) both in the presence and absence of bending magnets. We give nec- essary and sufficient conditions for determining the pure betatron emittance and show it to be the absolute min- imum of the effective emittance. Finally we show that dispersion not only directly enlarges the emittance, but also causes a &mismatch, resulting in further emittance dilution due to chromatic filamentation, and calculate the emittance blow-up due to the combined effect. 1. MEASUREMENT Let us assume a high energy linac or transport line and let 0 denote the point where we want to determine the

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