Two-beam accelerators (TBAs) have been proposed as efficient power sources for next generation high-energy linear colliders. Studies have demonstrated the possibility of building TBAs from $X$-band $\(\ensuremath{\sim}8--12\mathrm{GHz}\)$ through Ka-band $\(\ensuremath{\sim}30--35\mathrm{GHz}\)$ frequency regions. The relativistic klystron two-beam accelerator project, whose aim is to study TBAs based upon extended relativistic klystrons, is described, and a new simulation code is used to design the latter portions of the experiment. Detailed, self-consistent calculations of the beam dynamics and of the rf cavity output are presented and discussed together with a beam line design that will generate nearly 1.2 GW of power from 40 rf cavities over a 10 m distance. The simulations show that beam current losses are acceptable and that longitudinal and transverse focusing techniques are sufficiently capable of maintaining a high degree of beam quality along the entire beam line.