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A ring-shaped array of Bose-Einstein condensed atomic gases can displaycircular currents if the relative phase of neighboring condensates becomeslocked to certain values. It is shown that, irrespective of the mechanismresponsible for generating these states, only a restricted set of currents arestable, depending on the number of condensates, on the interaction andtunneling energies, and on the total number of particles. Differentinstabilities due to quasiparticle excitations are characterized and possibleexperimental setups for testing the stability prediction are also discussed.Comment: 7 pages, REVTex

Persistent currents in a circular array of Bose-Einstein condensates