[en] In phase two of the Dual-Axis Radiographic Hydrodynamic Test facility (DARHT-II), four electron beam pulses of variable pulse length strike an X-ray converter target to produce time-resolved X-ray image. An important requirement for the converter target is to minimize the hydrodynamic expansion of the converter material so that there is enough material to generate the required X-ray dose for all four pulses. Minimizing the hydrodynamic expansion is also important from the standpoint of beam transport. If there is too much expansion of the converter material, the spot-size of the beam will deteriorate due to the charge neutralization of the beam by the target plasma. The beam spot size can also be deteriorated by backstreaming ions. However, this effect can be minimized by placing a barrier foil in front of the target. In this paper, we present a converter target design, based on the simulations using the radiation hydrodynamics code LASNEX and the Monte Carlo radiation transport code MCNP, that can produce the required X-ray dose for all four pulses with tolerable X-ray spot size variation. Our calculations also show that the barrier foil may block the backstreaming ions for all four pulses