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In this paper, a formulation of the cavity mode structure, loss, and beam quality of a ring-cavity fiber laser beam combining apparatus is developed, which shows that the resonator is rigorously single mode. The passive phasing property is clearly understood on the basis of the theory, and conditions are specified for a cavity that permits the attainment of optimum phasing conditions. An important result is that reduction of over-all cavity loss must be achieved at the price of reduction of maximum array size, although mitigated by the property that this loss occurs in the low-power feedback leg. Application of the analysis to specific examples gives the dependence of cavity loss and Strehl ratio on fiber and cavity properties.