[en] In order to focus a heavy ion beam onto an ICF target, the amount of longitudinal momentum spread in the beam must be kept small. One cause of longitudinal momentum spread is errors in the external electric fields needed to confine the beam axially (ear fields). These errors can be amplified by a longitudinal instability which is based on the same principle as ''resistive wall'' amplifiers. In a heavy ion fusion driver, the impedance which drives this instability comes from the induction acceleration modules. The authors are using the electrostatic, axisymmetric WARPrz PIC code to study the longitudinal dynamics of these beams. In WARPrz, they model the impedance of the closely-spaced modules as a continuum of resistors and capacitors in parallel. They are using this code to study perturbations due to errors in the acceleration and ear fields and the growth of these perturbations due to the instability