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Intense beams of heavy ions are well suited for heating matter to regimes of emerging interest. A new facility, NDCX-II, will enable studies of warm dense matter at ∼1 eV and near-solid density, and of heavy-ion inertial fusion target physics relevant to electric power production. For these applications the beam must deposit its energy rapidly, before the target can expand significantly. To form such pulses, ion beams are temporally compressed in neutralizing plasma; current amplification factors of ∼50–100 are routinely obtained on the Neutralized Drift Compression Experiment (NDCX) at the Lawrence Berkeley National Laboratory. In the NDCX-II physics design, an initial non-neutralized compression renders the pulse short enough that existing high-voltage pulsed power can be employed. This compression is first halted and then reversed by the beam’s longitudinal space-charge field. Downstream induction cells provide acceleration and impose the head-to-tail velocity gradient that leads to the final neutralized compression onto the target. This paper describes the discrete-particle simulation models (one-, two-, and three-dimensional) employed and the space-charge-dominated beam dynamics being realized. [ABSTRACT FROM AUTHOR]