  Cool and dense ejections, typically H$_{\alpha}$ surges, often appear
alongside EUV or X-Ray coronal jets as a result of the emergence of magnetized
plasma from the solar interior. Idealized numerical experiments explain those
ejections as being indirectly associated with the magnetic reconnection taking
place between the emerging and preexisting systems. However, those experiments
miss basic elements that can importantly affect the surge phenomenon. In this
paper we study the cool surges using a realistic treatment of the radiation
transfer and material plasma properties. To that end, the Bifrost code is used,
which has advanced modules for the equation of state of the plasma,
photospheric and chromospheric radiation transfer, heat conduction and
optically thin radiative cooling. We carry out a 2.5D experiment of the
emergence of magnetized plasma through (meso)granular convection cells and the
low atmosphere to the corona. Through detailed Lagrange tracing, we study the
formation and evolution of the cool ejection and, in particular, the role of
the entropy sources: this allows us to discern families of evolutionary
patterns for the plasma elements. In the launch phase many elements suffer
accelerations well in excess of gravity; when nearing the apex of their
individual trajectories, instead, the plasma elements follow quasi-parabolic
trajectories with acceleration close to g$_{\odot^{}}$. We show how the
formation of the cool ejection is mediated by a wedge-like structure composed
of two shocks, one of which leads to the detachment of the surge from the
original emerged plasma dome.
