We present the results of theoretical and simulation studies of the design and performance of a new type of FEL oscillator. This device, known by the acronym RAFEL for Regenerative Amplifier Free-Electron Laser, will be constructed in the space presently occupied by the Advanced FEL (AFEL) at Los Alamos, and will be driven by an upgraded (to higher average power) version of the present AFEL linac. In order to achieve a long-time-averaged optical output power of similar to 1 kW using an electron beam with an average power of similar to 20 kW, a rather high extraction efficiency eta similar to 5% is required. We have designed a 2 m long undulator to attain this goal; the first meter is untapered and provides high gain while the second meter is linearly tapered in magnetic field amplitude to provide high extraction efficiency in the standard K-M-R manner. Two-plane focusing and linear polarization of the undulator are assumed. Electron-beam properties from PARMELA simulations of the AFEL accelerator were used in the design. A large saturated gain, similar to 500, requires a very small optical feedback to keep the device operating at steady state. However, the large gain leads to distorted optical modes which require two and three-dimensional simulations to adequately treat diffraction effects. This FEL will be driven by 17 MeV electrons and will operate in the 16 mu m spectral region.