  We propose a minimalistic model to account for the main properties of a
continuous superradiant laser, in which a beam of atoms crosses the mode of a
high-finesse Fabry-Perot cavity, and collectively emits light into the cavity
mode. We focus on the case of weak single atom - cavity cooperativity, and
highlight the relevant regime where decoherence due to the finite transit time
dominates over spontaneous emission. We propose an original approach where the
dynamics of atoms entering and leaving the cavity is described by a Hamiltonian
process. This allows deriving the main dynamical equations for the superradiant
laser, without the need for a stochastic approach. We derive analytical
conditions for a sustained emission and show that the ultimate linewidth is set
by the fundamental quantum fluctuations of the collective atomic dipole. We
calculate steady-state values of the two-body correlators and show that the
continuous superradiant regime is tied to the growth of atom-atom correlations,
although these correlations only have a small impact on the laser linewidth.
