In this paper, we model the performance of a device with a simple architecture for high-power mid-wave infrared beam generation at a wavelength of 3.8 microns. The device is a seeded idler efficiency-enhanced optical parametric generator (IEE-OPG) based on an aperiodically poled MgO-doped LiNbO3 (APMgLN) grating pumped by a high-repetition rate nanosecond-pulsed 1064-nm laser and seeded by a low-power 1478-nm distributed feedback diode laser. In the IEE-OPG, two optical parametric amplification (OPA) processes, OPA-1 and OPA-2, are simultaneously phase matched in a single APMgLN grating. The signal at 1478 nm is amplified and the idler at 3800 nm is generated as a result of OPA-1, the signal acts as the pump for OPA-2 and the conversion efficiency of the idler is enhanced as a result of OPA-2. Also, a difference-frequency beam at 2418 nm is generated.We characterized the device performance using a realistic model that takes the diffraction of the beams into account. We designed multiple aperiodic gratings with varying relative strengths of OPA-1 and OPA-2. For various crystal lengths, optimum relative strengths of the two processes and input pump power levels for achieving the maximum mid-wave infrared conversion efficiency and output power are determined.Efficiency-enhanced mid-wave infrared beam generating optical parametric oscillators (OPOs) based on APMgLN gratings were reported before. However, no attempt was made for the optimization of the relative strengths of the simultaneously phase-matched processes in these devices. Our model calculations show that it is possible to reach and exceed the mid-wave infrared conversion efficiencies of these OPOs by correctly choosing the design parameters of the seeded OPGs based on relatively long APMgLN gratings.