Abstract
Recent three-dimensional radiation (magneto-)hydrodynamic simulations of the solar atmosphere feature the chromosphere as a highly dynamic and intermittent phenomenon. It is a product of interacting shock waves that form a mesh-like pattern of hot shock fronts and cool post-shock regions on small spatial scales. Dynamic magnetic filaments develop in the compression zone behind and along shocks, whereas the magnetic field in the chromosphere is generally much more homogeneous than in the photosphere below, resulting in a dynamic small-scale 'canopy' at the boundary of these layers. Many details concerning the nature of the solar chromosphere, i.e. the involved heating mechanisms, however, still remain open and demand for detailed comparisons of observations and numerical models. I will present an overview of recent results, including the numerical modeling of the formation of carbon monoxide and non-equilibrium hydrogen ionization as well as prospects for observations with the future Atacama Large Millimeter Array (ALMA).