As discussed in the previous sections of this review, numerical models of the hydrodynamics and magneto-hydrodynamics of the solar surface layers are becoming increasingly realistic and accurate, both because of the steady growth of computing power, and because of the incorporation of increasingly complex physical mechanisms in the models.
The hydrodynamic aspects of the near-surface regions are now largely understood, both qualitatively and quantitatively, but this cannot at all be said about even the most well-known and and well-studied aspect of solar magneto-hydrodynamics; sunspots and the solar activity cycle.
The study of the magneto-hydrodynamics of the solar surface layers, and even more so the study of the overlying chromosphere and corona, which also provides the opportunity to study phenomena that go beyond classical magneto-hydrodynamics, is now the main focus area in solar physics research.
The results and experiences that will come out of these future efforts will be extremely valuable, also for other branches of astrophysics, where the “five dimensions” that are accessible in solar physics (space, time, and wavelength) are projected down to just a few – essentially one dimension when dealing with stars, and essentially only 2D projections of temporal snapshots when dealing with extended objects such as galaxies or molecular clouds.
To continue the progress the realism of the numerical simulations still needs to be improved: radiation, resolution, diffusion, non-LTE excitation, and ionization are all issues that need more work. Especially the chromospheric and coronal heating problems are also going to benefit from advances in the raw computing power, and from improved and and more efficient approximate methods to model radiation and non-equilibrium processes.
For studies that go beyond classical hydrodynamics and magneto-hydrodynamics a range of new tools need to be developed and deployed: particle-in-cell codes that can describe the near-collisionless conditions in the corona with billions to trillions of particles, codes that use hybrid fluid and particle pictures, diagnostic modules that show what would be observed with the range of new instruments and satellites that will be deployed, etc.
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