This tutorial will focus on the basic physical processes that are likely to be involved in the acceleration and heating of the solar plasma that finds its way into the heliosphere. A brief consideration of important observational constraints on these processes will be followed by the description of a theoretical framework in the conext of which these physical processes can be usefully discussed. The goal of this talk will be to provide a sound intuitive basis that will help in considering the extensive work that has been done in this area over the past several decades, as well as the work that will be presented at this meeting.

The height at which the solar wind originates in solar coronal funnels is fixed by comparison and correlation between the magnetic field, as derived by force-free field extrapolation from the photospheric magnetograms measured by MDI, and the EUV emission as obtained by SUMER on SOHO. The height of solar wind origin is determined to be larger than 5 Mm, where in coronal funnels the C IV intensity has a maximal correlation coefficient with the magnetic field strength, but no significant Doppler shift. But the height is found to be smaller than 20 Mm, where in corona funnels NeVIII is found to have large blue shifts corresponding to outflow. Based on these correlations between the ultraviolet emissions and the extrapolated magnetic field, a new 3-D solar wind formation scenario is suggested. The solar wind starts flowing from the funnels at a height of about 5 Mm, and subsequently experiences acceleration and heating in the coronal funnels. However, the solar wind gets its plasma from the magnetic loops adjacent to the funnels, through magnetic reconnection that is driven by supergranulation. The original heating of the solar wind plasma takes place in the side loops.

We investigate the plasma flow out of a coronal funnel in the framework of a forward 2D MHD model including the calculation of the EUV emission line. The computational box stretches from the chromosphere into the corona and special attention is paid to the relation of the magnetic structure at the base of the funnel to the wind outflow at its top. We use parameterized heating functions, e.g. depending on the magnetic field strength, to keep a corona and drive the wind. When observing the funnel from straight above, the highest Doppler (blue) shifts we synthesized from our model might be found above the edges of the magnetic field concentrations for some heating functions. The same hold for the intensities of coronal emission lines. Furthermore we find that the signature of the magnetic field concentration at the base of the funnel is still to be found in the density and velocity structure at the top of the funnel, where the magnetic field is (almost) homogeneous. This shows that signatures found in the solar wind at 0.3 to 1 AU on an angular scale comparable to the super-granular network of the Sun might indeed be a signature of the chromospheric magnetic network.

Plasma acceleration is one of the best established observable consequences of reconnection. For several sites of plasma acceleration detected by SOHO in the solar atmosphere we investigated the corresponding photospheric magnetic field and derived characteristic features of the related footpoint motion. Based on this information we used our newly developed chromosphere-corona model to simulate the corresponding coronal plasma dynamics resulting from the observed magnetic fields and the derived photospheric plasma motion. In the simulated corona we diagnosed the most typical features of the evolving coronal magnetic field, its topology and of the chromospheric-coronal plasma distribution. Using a plasma-physical model for the description of dissipation processes we are able to predict the potential sites, where reconnection should occur. We related these sites to the topological features of the coronal magnetic field in order to develop a prediction algorithm for the most probable sites and the strength of solar plasma acceleration. We verified our findings by comparing the model predictions with the observed plasma acceleration processes.

We model closed coronal structures extending from the solar chromosphere, using a newly developed set of multifluid transport equations that improve the description of heat flow and thermal diffusion. The code solves for a plasma consisting of hydrogen and helium. The ionization of the species, as well as radiative loss, are properly accounted for. For a prescribed heating function we study the density and temperature structures of the species and the force balance in the system. Emphasis is on how thermal diffusion in the transition region and gravitational settling affect the helium abundance along the closed structure.

The turbulence in the solar corona, with non-linear interactions between modes over a wide range of scales (down to very small scales of perhaps 10 meters), suggests to use statistics to study the heating of the corona. These statistics can be not only distribution of events, but also spectra and structure functions. However, from the numerical point of view, a statistical approach to turbulence has the contradictory needs for computing speed and for a good description of the solutions of the MHD equations. Here we address this problem by using a set of shell-models to simplify the simulation of a coronal loop. This allows to reach a wide range of wavenumbers (10⁶, far beyond the reach of other numerical models) in cross-sections of the loop. The shell-models are also coupled by Alfvén waves propagating along the loop. We study the statistical properties of intermittent energy dissipation and of the velocity and magnetic fields produced by this model, as a function of the model parameters (loop length, aspect ratio and mean field, dissipation coefficient, velocity field at the photosphere). Then we try to compare these results to observations by forward-modelling observable quantities.