A standing‐wave free‐electron laser (SWFEL) has been proposed for use in a two‐beam accelerator (TBA). We modify the previous one‐dimensional discrete cavity model of the SWFEL by introducing drifts between cavities. We also vary the input beam energy as a function of the bunch number. In this new model, we obtain a stable equilibrium solution for a well‐bunched beam (even after inluding all nonlinear terms). We obtain analytic expressions characterizing this equilibrium in the limit of small cavity lengths. We study the dependence of fluctuations in signal phase along the device as a function of detuning, input beam energy, beam length, current errors, and initial signal field amplitude. We are able to find an optimized set of parameters for which the output energy changes by less than 3% across the cavities for a 1% detuning. The maximum change in signal phase is less than 0.12 radians.