This chapter contains sections titled: Introduction Mathematical Framework The Simplest Description Solar Wind Stream Interactions Energetics of the Coronal Expansion: Transport Processes Energetics of the Coronal Expansion: Energy Addition The Magnetic Field Chemical Composition and Ionization State Non-Steady Processes Kinetic Description Concluding Remarks Acknowledgements

The three‐dimensional (3‐D) density structure of the solar corona is a fundamental boundary condition on the solar wind. Most easily applied models of the global coronal density have been restricted to date to axisymmetric 2‐D cases. We present here a 3‐D model made up of a superposition of multiple streamers, having distinct gaussian widths in longitude and latitude and both longitudinal and latitudinal dependence of the neutral lines implicit beneath the streamer cores. Nonradiality of streamers and solar B‐angle tilt are also explicitly treated. We show how this simple model can capture many of the general properties of coronal white light observations and demonstrate how such a model can assist in the interpretation of the multiple views on coronal structures such as will be provided by the upcoming STEREO mission.

We are developing a time stationary self-consistent 2D MHD model of the solar corona and solar wind that explicitly solves the energy equation, using a semi-empirical 2D MHD model of the corona to provide an empirically determined effective heat flux q(eff) (i.e., the term effective means the possible presence of wave contributions). But, as our preliminary results indicate, in order to achieve high speed winds over the poles we also need to include the empirically determined effective pressure P-eff as a constraint in the momentum equation, which means that momentum addition by waves above 2 R-S are required to produce high speed winds. At present our calculations do not include the P-eff constraint. The estimates of P-eff and q(eff) come from the semi-empirical 2D MHD model of the solar corona by Sittler and Guhathakurta (1999a,2002) which is based on Mk-III, Skylab and Ulysses observations. For future model development we plan to use SOHO LASCO, CDs, EIT, UVCS and Ulysses data as constraints for our model calculations. The model by Sittler and Guhathakurta (1999a, 2002) is not a self-consistent calculation. The calculations presented here is the first attempt at providing a self-consistent calculation based on empirical constraints.