For more than ten years [J. Bisognano, I. Haber, L, Smith, IEEE Trans,
Nucl, Sci, NS-30, 2501 (1983)], the longitudinal wall impedance insta
bility 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 u
sed to accelerate the beam. Early estimates of the instability growth
rate predicted tells of e-folds due to the instability which would mod
ulate the current and increase the longitudinal momentum spread and pr
event focusing the ion beam on the small spot needed at the target. We
have simulated this instability using an r-z particle-in-cell code wh
ich includes a model for the module impedance. These simulations, usin
g driver parameters, show that growth due to the instability is smalle
r than in previous calculations. We have seen that growth is mainly li
mited 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 Confere
nce, (UCRL-86452), Santa Fe, NM, 1981] significantly reduces the growt
h rate. We have also included in the simulation intermittently applied
axial confining fields which are thought to be the major source of pe
rturbations to seed the longitudinal instability. Simulations show the
beam can adjust to a systematic error in the longitudinal confining f
ields while a random error er;cites the most unstable wavelength of th
e instability. These simulations show that the longitudinal instabilit
y must be taken into account in a driver design, but it is not the maj
or factor it was once thought to be, (C) 1997 American Institute of Ph
ysics.