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We describe a simple dynamical model for an underdamped Josephson junctionarray coupled to a resonant cavity. From numerical solutions of the model inone dimension, we find that (i) current-voltage characteristics of the arrayhave self-induced resonant steps (SIRS), (ii) at fixed disorder and couplingstrength, the array locks into a coherent, periodic state above a criticalnumber of active Josephson junctions, and (iii) when $N_a$ active junctions aresynchronized on an SIRS, the energy emitted into the resonant cavity isquadratic with $N_a$. All three features are in agreement with a recentexperiment [Barbara {\it et al}, Phys. Rev. Lett. {\bf 82}, 1963 (1999)]}.Comment: 4 pages, 3 eps figures included. Submitted to PRB Rapid Com

Resonant-cavity-induced phase locking and voltage steps in a Josephson array