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The WARP code is a robust electrostatic particle-in-cell simulation package used to model charged particle beams with strong space-charge forces. A fundamental operation associated with seeding detailed simulations of a beam transport channel is to generate initial conditions where the beam distribution is matched to the structure of a periodic focusing lattice. This is done by solving for periodic, matched solutions to a coupled set of ODEs called the Kapchinskij-Vladimirskij (KV) envelopedoi:10.2172/940580 fatcat:2kzliuinbrh4rptzesk6e4of4m