Solving the quasi-static field model of the pulse-line accelerator; relationship to a circuit model

The Pulse-Line Ion Accelerator (PLIA) is a promising approach to high-gradient acceleration of an ion beam at high line charge density. A recent note by R. J. Briggs suggests that a 'sheath helix' model of such a system can be solved numerically in the quasi-static limit. Such a model captures the correct macroscopic behavior from first principles without the need to time-advance the full Maxwell equations on a grid. This note describes numerical methods that may be used to effect such a solution, and their connection to the circuit model that was described in an earlier note by the author. Fine detail of the fields in the vicinity of the helix wires is not obtained by this approach, but for purposes of beam dynamics simulation such detail is not generally needed