  Linear gas stoppers are widely used to convert high-energy, rare-isotope
beams and reaction products into low-energy beams with small transverse
emittance and energy spread. Stopping of the high-energy ions is achieved
through interaction with a buffer gas, typically helium, generating large
quantities of He$^+$/e$^-$ pairs. The Advanced Cryogenic Gas Stopper (ACGS) was
designed for fast, efficient stopping and extraction of high-intensity,
rare-isotope beams. As part of the design process, a comprehensive
particle-in-cell code was developed to optimize the transport and extraction of
rare isotopes from the ACGS in the presence of space charge, including
He$^+$/e$^-$ dynamics, buffer gas interactions including gas flow, RF carpets,
and ion extraction through a nozzle or orifice. Details of the simulations are
presented together with comparison to experiment when available.
