  We describe a simple Hamiltonian for an underdamped Josephson array coupled
to a single photon mode in a resonant cavity. Using a Hartree-like mean-field
theory, we show that, for any given strength of coupling between the photon
field and the Josephson junctions, there is a transition from incoherence to
coherence as a function of N, the number of Josephson junctions in the array.
Above that value of N, the energy in the photon field is proportional to N^2,
indicative of coherent emission. Both of these features agree with recent
experiments by Barbara et al. The experimentally observed voltage steps may
require an explicit solution of the dynamical equations.
