A Review on Solar Wind Modeling: Kinetic and Fluid Aspects

Abstract

The paper reviews the main advantages and limitations of the kinetic exospheric and fluid models of the solar wind (SW). The general theoretical background is outlined: the Boltzmann and Fokker-Planck equations, the Liouville and Vlasov equations, the plasma transport equations derived from an ''equation of change''. The paper provides a brief history of the solar wind modeling. It discusses the hydrostatic model imagined by Chapman, the first supersonic hydrodynamic models published by Parker and the first generation subsonic kinetic model proposed by Chamberlain. It is shown that a correct estimation of the electric field, as in the second generation kinetic exospheric models developed by Lemaire and Scherer, provides a supersonic expansion of the corona, reconciling the hydrodynamic and the kinetic approach. The modern developments are also reviewed emphasizing the characteristics of several generations of kinetic exospheric and multi-fluid models. The third generation kinetic exospheric models consider kappa velocity distribution function (VDF) instead of a Maxwellian at the exobase and in addition they treat a non-monotonic variation of the electric potential with the radial distance; the fourth generation exospheric models include Coulomb collisions based on the Fokker-Planck collision term. Multi-fluid models of the solar wind provide a coarse grained description of the system and reproduce with success the spatio-temporal variation of SW macroscopic properties (density, bulk velocity). The main categories of multi-fluid SW models are reviewed: the 5-moment, or Euler, models, originally proposed by Parker to describe the supersonic SW expansion; the 8-moment and 16-moment fluid models, the gyrotropic 123Surv ) 32:1-70 DOI 10.1007 approach with improved collision terms as well as the gyrotropic models based on observed VDFs. The outstanding problem of collisions, including the long range Coulomb encounters, is also discussed, both in the kinetic and multi-fluid context. Although for decades the two approaches have been seen as opposed, in this paper we emphasize their complementarity. The review of the kinetic and fluid models of the solar wind contributes also to a better evaluation of the open questions still existent in SW modeling and suggests possible future developments.

Half a Century of Kinetic Solar Wind Models

“…This correlation happens to be similar to that observed in the quiet solar wind at 1 AU (see also Fig. 4 in Echim et al 18 ).…”

“…Since Parker's pioneering work, many more sophisticated one-fluid, two-fluid or multi-fluid SW models have been published. A description of this corpus of hydrodynamic SW models can be found in Aschwanden 22 , and in the review by Echim et al 18 . Only kinetic SW models will be briefly reviewed below.…”

“…An extensive review of kinetic and hydrodynamic SW models, and of their chronologic development will be found in Echim et al 18 . The monograph by MeyerVernet 20 gives a seminal and comprehensive overview of the solar wind in general.…”

Kinetic Models of Solar Wind Electrons, Protons and Heavy Ions

“…Different models have been developed to study the steady state electron VDF in the corona and at larger radial distances in the solar wind by solving the Fokker-Planck equation (Echim et al, 2011 for a review). Lie-Svendsen et al (1997) and Lie-Svendsen & Leer (2000) solved the Fokker-Planck equation using a finite-difference scheme.…”

Coronal Temperature Profiles Obtained from Kinetic Models and from Coronal Brightness Measurements Obtained During Solar Eclipses

“…In the present work, the physical properties of the coronal and solar wind expansion have been simulated using steady state hydrodynamical and kinetic models which have been recently reviewed by Echim et al [2010]. The development of the successive generations of kinetic models (exospheric and Fokker-Planck models) have also been outlined in chronological order by Lemaire [2010].…”