8.1 Summary

This article started out with a definition of its scope and relation with previous reviews. From what we have discussed, the importance of kinetic physics has become clearly evident. A comprehensive theoretical description of the solar corona and solar wind is required, which should rely on the theory of anisotropic and multi-species fluids, and must in many cases invoke full kinetic theory, in particular to evaluate the exchange of energy and momentum. In the weakly collisional corona, waves and particles appear to be intimately linked through plasma instabilities and wave-particle interactions. These processes involve plasma waves at frequencies (up to the MHz range), much higher than the frequencies of MHD waves, which mostly have been considered in conventional fluid models.

We briefly described the main types and solar sources of the solar wind, and then addressed key issues of a kinetic description of coronal expansion and of the associated solar wind transport theory, such as the basic energetics of coronal expansion, including kinetic parameters and plasma conditions in the corona, or the exospheric paradigm and related models. The failure to heat chromosphere or corona only by collisions was discussed. After an introduction to the basics of the Vlasov–Boltzmann theory, the kinetic concepts and various fluid theories were presented, and the transport theory in a collisional plasma was outlined. New work related to the validity of the classical electron heat flux in the transition region, and to the breakdown of classical heat conduction in the corona was discussed.

Then the in situ measured particle velocity distributions were considered, in particular for solar wind electrons, protons and alpha particles, and heavy ions. In addition to the particles, plasma waves and their microinstabilities constitute the main ingredients of space plasmas. Relevant plasma waves in the solar corona and solar wind, their dispersion relations and associated Landau and cyclotron resonances were presented. Resonant wave-particle interactions, for example with Alfvén-cyclotron waves and kinetic Alfvén waves, were identified and shown to play a central role in transport phenomena.

A whole section was devoted to wave-particle interactions, and their manifestations in the VDFs through inelastic pitch-angle diffusion of ions in resonance with waves. Evidence for wave effects on protons and the kinetic shell model were discussed. The origin and regulation of proton beams, the effects of non-linear wave couplings on linear beam instabilities, the regulations of the proton core temperature anisotropy and of the electron heat flux were analysed, and plasma heating (cooling) by wave absorption (emission) was evaluated.

Subsequently, kinetic transport in the solar corona and solar wind was described in terms of higher-order, gyrotropic multi-fluid equations. The model velocity distributions derived from such moment expansions were analysed. From their defects a dire need was stated for a consistent kinetic modelling of coronal expansion. Numerical results from such kinetic models of the solar wind and for the VDFs of coronal electrons, protons and ions were presented. A summary and conclusion section rounds the review off, together with some future research perspectives that we present now.

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