  We describe a simple dynamical model for an underdamped Josephson junction
array coupled to a resonant cavity. From numerical solutions of the model in
one dimension, we find that (i) current-voltage characteristics of the array
have self-induced resonant steps (SIRS), (ii) at fixed disorder and coupling
strength, the array locks into a coherent, periodic state above a critical
number of active Josephson junctions, and (iii) when $N_a$ active junctions are
synchronized on an SIRS, the energy emitted into the resonant cavity is
quadratic with $N_a$. All three features are in agreement with a recent
experiment [Barbara {\it et al}, Phys. Rev. Lett. {\bf 82}, 1963 (1999)]}.
