In applications of the moment Equations (32)–(37) to the modelling of coronal expansion and wind acceleration, the exchange rates on the right sides of the set must be specified. Given model VDFs such as (38), one can evaluate the self-collision integral (13), or the wave-particle exchange terms (63), and thus obtain the rates requested for closure of the set. Examples for Coulomb collisions are given in the 16-moment fluid model with Alfvén-cyclotron wave heating by Li (1999) and Lie-Svendsen et al. (2001). With respect to wave-particle interactions, the heating and acceleration rates after (63) were, for bi-Maxwellians and power-law wave ESDs, calculated by many authors (Marsch et al., 1982a; Isenberg, 1984a; Li and Habbal, 1999; Li, 1999; Marsch and Tu, 2001a).

The standard VDF, resulting from the procedure used by Demars and Schunk (1979) and Li (1999), implies the following third-order-polynomial correction function:

What they called improved transport equations for fully ionised gases were recently proposed by Killie et al. (2004) to improve the description of Coulomb collisions, for which the transfer rates for momentum, energy, and heat flux were anew calculated within the eight-moment fluid equations. They found transport coefficients that deviate by less than 20% from the rigorous values (Spitzer and Härm, 1953) obtained from solving the Fokker–Planck equation.Presently, there is no basic kinetic model of the solar corona and solar wind. The various forms of the multi-moment multi-species fluid equations were used to study different physical process and such characteristics as the dependence of solar wind parameters on variations in the coronal heating function (Olsen et al., 1998), the acceleration of the wind when being based on the above gyrotropic transport equations (Olsen and Leer, 1999), the heating and cooling of protons by turbulence-driven ion-cyclotron waves in fast solar wind (Li et al., 1999), the effect of transition region heating on the generation of the solar wind from coronal holes (Lie-Svendsen et al., 2002), and the coronal energy budget, abundances and temperatures of solar wind minor ions (Lie-Svendsen and Esser, 2005). In their 16-moment model, Lie-Svendsen et al. (2001) also included the heat-flux moment equation explicitly, and integrated the fluid Equations (32)–(37) all the way out from the chromosphere, through the corona into the inner heliosphere.

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