  We explore trapped ions as a setting to investigate non-equilibrium phases in
a generalised Dicke model of dissipative spins coupled to phonon modes. We find
a rich dynamical phase diagram including superradiant-like regimes, dynamical
phase-coexistence and phonon-lasing behaviour. A particular advantage of
trapped ions is that these phases and transitions among them can be probed in
situ through fluorescence. We demonstrate that the main physical insights are
captured by a minimal model and consider an experimental realisation with Ca+
ions trapped in a linear Paul trap.
