This article describes computer simulations of a longitudinal instability that affects induction linear accelerators for high-power ion beams. The instability is driven by axial bunching of ions when they interact with acceleration gaps connected to input transmission lines. The process is similar to the longitudinal resistive wall instability in continuous systems. Although bunching instabilities do not appear in existing induction linear accelerators for electrons, they may be important for proposed ion accelerators for heavy ion fusion. The simulation code is a particle-in-cell model that describes a drifting beam crossing discrete acceleration gaps with a self-consistent calculation of axial space charge forces. In present studies with periodic boundaries, the model predicts values for quantities such as the stabilizing axial velocity spread that are in good agreement with analytic theories. The simulations describe the nonlinear growth of the instability and its saturation with increased axial emittance. They show that an initially cold beam is subject to a severe disruption that drives the emittance well above the stabilized saturation levels. The simulation results confirm that axial space charge forces do not reduce axial beam bunching. In fact, space charge effects increase the axial velocity spread required for stability. With simple resistive driving circuits, the model predicts velocity spreads that are too high for heavy ion fusion applications. Several processes currently under study may mitigate this result, including advanced pulsed power switching methods, enhanced gap capacitance, and an energy spread impressed between individual beams of a multibeam transport system.
