The design of a radiation driven capsule suitable for use in a heavy ion beam driven inertial confinement fusion reactor system is discussed. Numerical simulations of compression, ignition and burn of the capsule are presented. These simulations have been carried out using the one-dimensional, three-temperature, Lagrangian radiation hydrodynamic computer code MEDUSA-KAT. The capsule consists of a 4 mg cryogenic spherical DT shell surrounded by an ablator shell made of a mixture of 90% Li and 10% Au atoms. Inside the fuel shell there is a low density DT gas. It has been found that an input radiation energy of 5.00 MJ is needed to implode the capsule, and the implosion yields about 660 MJ output thermonuclear energy. The capsule energy gain is thus about 130, which may be sufficient to operate a heavy ion beam driven reactor system because of the relatively high efficiency of the heavy ion driver. A study of the capsule gain as a function of the input parameters has also been carried out. It is found that the gain is not sensitive to a variation in the prepulse temperature and prepulse duration of up to 50%.