Dispersion and space charge

The presence of space charge affects the value of the dispersion function. On the other hand dispersion has a role in shaping the beam distribution and therefore in determining the resulting forces due to space charge. In this paper we present a framework where the interplay between space charge and dispersion for a continuous beam can be simultaneously treated. We revise the derivation of a new set of rms envelope-dispersion equations we have recently proposed. The new equations generalize the standard rms envelope equations currently used for matching to the case where bends and a longitudinal momentum spread are present. We report a comparison between the solutions of the rms envelope-dispersion equations and the results obtained using WARP, a Particle in Cell (PIC) code, in the modeling of the Maryland Electron Ring