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A coherent array of fiber lasers in a self-Fourier cavity is described and analyzed. With individual regenerative feedback added to each fiber laser, the integrated gain in each individual fiber is a function of its cold cavity phase shift (fiber length). This results in a gain-dependent phase shift due to the Kramers-Kronig relations, and has been shown to partially compensate for the random differences in fiber lengths often encountered in coherent fiber arrays. A coupled cavity analysis of the active gain elements and the passive external cavity is performed and a self-consistent fundamental supermode determined. The output phase distribution of the array is determined based on a random distribution in fiber lengths. The Strehl ratio of this phase distribution is calculated and compared to experimental data.