Recent achievements of laboratory astrophysics experiments with high power lasers have allowed progress in our understanding of the early stages of star formation. In particular, we have recently demonstrated the possibility of simulating in the laboratory the process of accretion of matter on young stars (Revet G. et al. Science Advances 3, e1700982 (2017)). The present paper focuses on X-ray spectroscopy methods allowing us to investigate the complex plasma hydrodynamic involved in such experiments. We demonstrate that we can henceforth infer the formation of a plasma shell, surrounding the accretion column at the location of impact with the stellar surface, and thus resolve the present discrepancies between mass accretion rates derived from x-ray and optical radiation astronomical observations originating from the same object. In our experiments, the accretion column is modelled by having a collimated narrow (1 mm diameter) plasma stream first propagate along the lines of large-scale external magnetic field and then impact onto an obstacle mimicking the high-density region of the stellar chromosphere. A combined approach using steady-state and quasi-stationary models was successfully applied to measure the parameters of the plasma all along its propagation, at the impact and in the subsequent structure surrounding the impact region. The formation of a hot plasma shell surrounding the denser and colder core formed by the incoming stream of matter is observed near the obstacle using x-ray spatially resolved spectroscopy.