For more than ten years [J. Bisognano, I. Haber, L. Smith, IEEE Trans. Nucl. Sci.NS-30, 2501 (1983)], the longitudinal wall impedance instability was thought to be a serious threat to the success of heavy-ion driven inertial confinement fusion. This instability is a “resistive wall” instability, driven by the impedance of the induction modules used to accelerate the beam. Early estimates of the instability growth rate predicted tens ofe-folds due to the instability which would modulate the current and increase the longitudinal momentum spread and prevent focusing the ion beam on the small spot needed at the target. We have simulated this instability using anr−zparticle-in-cell code which includes a model for the module impedance. These simulations, using driver parameters, show that growth due to the instability is smaller than in previous calculations. We have seen that growth is mainly limited to one head to tail transit by a space-charge wave. In addition, the capacitive component of the module impedance, which was neglected in the early work of Lee [E. P. Lee, Proc. Linear Accelerator Conference, (UCRL-86452), Santa Fe, NM, 1981] significantly reduces the growth rate. We have also included in the simulation intermittently applied axial confining fields which are thought to be the major source of perturbations to seed the longitudinal instability. Simulations show the beam can adjust to a systematic error in the longitudinal confining fields while a random error excites the most unstable wavelength of the instability. These simulations show that the longitudinal instability must be taken into account in a driver design, but it is not the major factor it was once thought to be. ©1997 American Institute of Physics.