  A cold dilute atomic gas in an optical resonator can be radiatively cooled by
coherent scattering processes when the driving laser frequency is tuned close
but below the cavity resonance. When sufficiently illuminated, moreover, the
atoms' steady state undergoes a phase transition from homogeneous density to
crystalline order. We characterize the dynamics of this self-ordering process
in the semi-classical regime when distinct cavity modes with commensurate
wavelengths are quasi-resonantly driven by laser fields via scattering by the
atoms. The lasers are simultaneously applied and uniformly illuminate the
atoms, their frequencies are chosen so that the atoms are cooled by the
radiative processes, their intensity is either suddenly switched or slowly
ramped across the self-ordering transition. Numerical simulations for different
ramp protocols predict that the system exhibits long-lived metastable states,
whose occurrence strongly depends on initial temperature, ramp speed, and
number of atoms.
