Modeling the pulse line ion accelerator (PLIA): an algorithm for quasi-static field solution

The pulse-line ion accelerator (PLIA) is a helical distributed transmission line. A rising pulse applied to the upstream end appears as a moving spatial voltage ramp, on which an ion pulse can be accelerated. This is a promising approach to acceleration and longitudinal compression of an ion beam at high line charge density. In most of the studies carried out to date, using both a simple code for longitudinal beam dynamics and the Warp PIC code, a circuit model for the wave behavior was employed; in Warp, the helix I and V are source terms in elliptic equations for E and B. However, it appears possible to obtain improved fidelity using a "sheath helix" model in the quasi-static limit. Here we describe an algorithmic approach that may be used to effect such a solution.