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A new iterative method is developed to numerically calculate the periodic,matched beam envelope solution of the coupled Kapchinskij-Vladimirskij (KV)equations describing the transverse evolution of a beam in a periodic, linearfocusing lattice of arbitrary complexity. Implementation of the method isstraightforward. It is highly convergent and can be applied to all usualparameterizations of the matched envelope solutions. The method is applicableto all classes of linear focusing lattices without skew couplings, and alsoapplies to all physically achievable system parameters -- including where thematched beam envelope is strongly unstable. Example applications are presentedfor periodic solenoidal and quadrupole focusing lattices. Convergenceproperties are summarized over a wide range of system parameters.Comment: 20 pages, 5 figures, Mathematica source code provide

Efficient computation of matched solutions of the Kapchinskij-Vladimirskij envelope equations for periodic focusing lattices