Implementation of an interactive matching scheme for the Kapchinskij-Vladimirskij equations in the WARP code

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) envelope equations, which describe the evolution of low-order beam moments subject to applied lattice focusing, space-charge defocusing, and thermal defocusing forces. Recently, an iterative numerical method was developed (Lund, Chilton, and Lee, Efficient computation of matched solutions to the KV envelope equations for periodic focusing lattices, Physical Review Special Topics-Accelerators and Beams 9, 064201 2006) to generate matching conditions in a highly flexible, convergent, and fail-safe manner. This method is extended and implemented in the WARP code as a Python package to vastly ease the setup of detailed simulations. In particular, the Python package accommodates any linear applied lattice focusing functions without skew coupling, and a more general set of beam parameter specifications than its predecessor. Lattice strength iteration tools were added to facilitate the implementation of problems with specific applied focusing strengths.